Good morning and welcome to Encompass Live. My name is Michael Sowers.  And actually I'm feeling under the weather myself, so it's been a little bit of a reorganization this morning here at the Library Commission. Encompass Live is your weekly free online webinar dealing with topics of interest to Nebraska librarians and librarians from all over the world. They are always free to attend. They are held every Wednesday morning at 10 a.m. central time. And today's topic is Are You Game? Game night at Perkins Library. We have with us today Susan Franklin from the Perkins Library. Let me turn on Susan's microphone. Susan, are you there? I am. Well, good morning. Okay, what we're going to do here is we're going to dive right in. So I'm going to go ahead and give Susan presentation rights here. And let you just take it away and we do see your slides. Excellent. Okay, good morning everyone. This presentation is sort of of the how we done it good variety. So I don't go into a lot of research. Of course, there's a lot of research out there. A lot of studies and statistics that show that gaming is linked to intellect or coordination or socialization. I'm not going to worry about any of that. I will, however, talk about why we decided to experiment with game night. What equipment, supplies, publicity, and partners we needed to make it fly the first time. How we went about planning it. How the event grew. The benefits to holding your own game nights, some of the challenges or obstacles, and what we have planned for the future. So motivation, a.k.a. everybody else is doing it. And yes, I would totally jump off the bridge if it meant a new service for the library. But motivation included the North Rock Library Commission is interested in gaming. Has held gaming events at conventions. American Library Association has held gaming events at conventions. And also it has a national gaming day, which this year happens to be November 13. So you have a little less than three weeks. That's your homework from today's session to plan your own game night. Omaha Public Library did a board silly event. But theirs was an after hours in the library, a built only pay for and cash par event. Which of course, those elements would not work in my or many other environments. And then other libraries and colleagues from across the nation have experimented with gaming. And then of course, the research on millennials, they're doing it, they're gaming. But it's not just for millennials. So all of these things added up to a desire for us to try gaming. What do you have to lose if it doesn't try, basically. So we started with, well, we have two gaming systems in the very first game night we had. I borrowed one gaming system from a Republican Valley library system. And it on that state end, I think all of the regional library systems have gaming systems alone. Don't quote me on that. And the second gaming system was mine personally that I brought from home. So in the beginning, we had Wii games, we had classic games, the golf, the bowling, the baseball, those things that come with the system. We had Dance Dance Revolution 3, which was mine personally. And Cabela's Big Game Hunter, which was mine personally. And then when we advertised, we let it be known that students could BYOD or bring your own game. And guess what, they did. We also started with board games like Shoots and Ladders, Monopoly, Candyland. Card games like Slammich, Rook, Playing Cards, which I left to play pitch. It weren't for that pesky thing called needing to get your bachelor's degree. I probably would have just not gone to classes and played pitch 24 hours a day. We also had other games. So we had Factor Crap, Apples to Apples, In the Pickle, Jenga, Connect 4x4, and Vanagrams. All right. For supplies, we had one TV, the bigger the better per Wii. You can also use LCD projectors and screens if TVs aren't feasible or a projector and a wall. We needed to have long extension cords and surge suppressors. We needed buckets of batteries double A. The remotes for the Wii controllers go through them, go through batteries quite rapidly. We needed space for spectators. Of course, we already had tables throughout the library and comfy couch areas where people wanted to play traditional or card games. And then we needed food, of course. More on that later, but we all know that food is going to bring the people. If you serve food, they will come. As far as publicity, we totally saturated the campus. So we did flyers in every building and dorm. We prominently placed flyers in the library. We included our game night announcement and HC announcements, which is a daily email that goes to faculty, staff, and students. Not sure how many people read it, but hopefully they at least stem it. We notified all of Hastings College's media entities. So it's TV, newspaper, radio, and website components, all we're aware of. And hopefully it's a publicized event for us. Word of mouth. We had a Facebook ad that listed on our Facebook library group page and created a Facebook invitation. And, of course, we got student assistance buy-in. So, of course, they spread it through word of mouth to their friends and roommates. And then finally, best year coercion. I'm the faculty sponsor of a fraternity on campus, and I sort of suggested that if they knew what was good for them, they should attend. And also, my son, his roommate, and her girlfriend. It was a non-negotiable attendance for them as well, but they did have fun. So this is our first fire. And we did it right before finals week, end of the semester, couple before finals week, end of the semester. And so this is our first one, and our draw was that Dr. Dudley, our esteemed president, who will retire at the end of this school year, agreed quite gamely, no pun intended, to come and was very, very, very gracious about trying out games and sticking around to play with the students. I hope everyone is still with me. I hope I'm not going too quickly. Two ingredients to our success. Snacks, as I mentioned before. The first time we had trail mix, which we purchased, and homemade caramel bugles. That's right, homemade. You can buy caramel bugles in a bag, but they're like $3 for five ounces or something ridiculous like that. You can make your own, and they are a perfect combination of sweet and salty. It was like sherry crack for the students. They kept coming back to caramel bugles, and then they'd go game. And then secondly, as I said, President Dudley is buying. People wanted to see what he would play and challenge him. So those were the two cards the first time.  But this is President Dudley playing Dance Dance Revolution 3 with a student. And of course, he had no idea what he was doing.  So the final scores for observations for our first game night were that freestyle gaming was successful. And by that, I mean what we did. If I remember the two Wii consoles set up at two different TVs, two different places. We just had, we had the snacks on one table area, and then we just put all of our other games and played them on the other table. And so there was no sort of organization or sign up for games or whatever. We just let students, faculty, and staff who attended groups themselves grab a game and go. And it actually turned out really, really well. Homemade snacks, of course. Trump store bought ones. And this is where I will offer to solve my caramel bugle recipe to the highest bidder. So we can talk about that at the end during the question portion. And we had approximately 50 students, faculty, and staff for that first night. They played a range of games. Some were surprising. Some were new, like nerds. I'd never heard of nerds before. But it's a multiplayer game. Each person needs a deck of cards, and it's sort of like a solitaire except you're playing solitaire yourself and also against other people. So it's kind of interesting, fast-paced game. And I'll talk a little bit more about that later. Game nights started out slow, but 30 to 60 participants how come each event. And we've had, I think, four now. And we have what we've found, which isn't surprising. We have our core group of library groupies, as I call them, and student assistants. And then you have people who are in the library sometimes. But then you have this great group of people that you've never seen before who are now in the library because a roommate or a friend or maybe they've just seen the sign and decided that game night sounds like something they would like to try out. So it really is a way to burrow into some untapped users in your community. And then volunteers and staff, by volunteers I mean the captive student assistants who are on duty, need to mingle even though they are sought after opponents. So someone has to sort of mingle, take pictures, keep the snacks flowing, make sure that people are having a good time, make sure that there aren't any technical difficulties. That sort of thing. All right, so the first game night was so successful that word of mouth buzzed from two students who attended it back to the Dean of Students the next day because they happened to serve on a committee with the Dean of Students. So that's the first part. They buzzed about it and said, oh, that was great.  They were recapping some of the things that happened like presently playing bandstand for evolution. And so then our Dean of Students came to me and said, hey, by the way, good job.  I was told how much fun it was. And I said, yes, it absolutely was. I said that the library was planning to make it a semesterly event, but ruminated out loud, not really the intention of soliciting a donation, but just said, ideally, though, we need to figure out how to purchase our own gaming systems because, you know, just more convenient than borrowing from the library system, bringing my own personal one, asking students to bring their own personal consoles. And I was elated at the fact that he said, well, hey, we have an Armstrong McDonald, McDonald's Armstrong. I can't remember which one it goes now. Grant for Enhancement for Student Life. And I have some extra money. We're to the end of the grant. And if you give me an idea of how much two consoles plus overalls you need would cost, I can see if I can pay for it. So the money tree was right there. And through this grant, Dean of Students generously purchased two gaming systems, two equipment bags, because our systems circulate when we're not having game night. Four additional Wii remotes, because as you may or may not know, there are lots of games that you can have multiple players, four, six, whatever. And then three Wii games. He bought Mario Party, which is a hit with students regardless of age. Just Dance, which is actually the number one game in our library, and DJ Hero. So here are some pictures of the first game night. And you can see over here, President Dudley playing apples to apples with students. You can see the manograms. These four people, one clenching his head, I think he's studying. So if he were over here and no pair, he'd be having a better time, right? Okay, connect four by four, premium. I'm going to wave through these sort of quickly. Fact or Prop, Jenga, Giant Shas, which we have in our library all the time. A traditional puzzle, which we usually have a puzzle going in the coffee area, and it's popular. People grab a cup of coffee in between classes, fit a few pieces in. But it really did surprise me that students came to game night and worked on a puzzle together. That was kind of neat. Our second game night, we held in January during what we call J-term. It's our three-week term in the middle of fall and spring semesters. So we tried it out during J-term since it's sometimes a lighter load. And again, it went over really well. This is Wee Mario Party, and you can see you can have multiple players. This happens to be, I hope my pointer is going, the young man in the J-hawk basketball shirt is her son, and apparently he likes to play Wee Mario Party with his eyes closed. Now that's just where I caught him. That's the camera. Just Dance, as I said, is our most popular game by far, and it has 30 fracks for those of you not familiar with it, and very few people are. My son actually gave it to me as a Christmas present last year for several reasons. He basically was mocking me because I like all sorts of music, including disco, and he had seen an advertisement for this corny game. So it was kind of like the joke was on me, like him giving it to me, except the joke is really on him. So what it is, is it has three songs, and a little animated person, or in one case a mascot dog, moves, dances, does choreography to the songs, and then however many players, I think four to six can play at a time, you follow, you hold the remote in your hand and you follow the moves, and so you get points for following exactly and whatnot. But students who don't like to dance in public don't like to be fools out of themselves. It's just amazing that this game is the most popular. And the second version came out October 12, so I'm working on getting my hands on that. Now the second game night, I put a sign up saying to prevent a certain person from having her self-humiliating just dance moves preserved for infinity. Please no cameras or video cameras. Thank you for your compliance. Noncompliance will be strictly punished. Of course by her that meant me. Of course I'm exempted from that. I can photograph people making fools of themselves, but I don't want me in there. However, as you can see right there in the middle, they don't listen.  You will exercise simultaneously while laughing and having fun. More just dance, and it cracks me up every time. It's always the men who get into it, and they're absolutely into it. So this is what a screen looks like. This is one of Spice Girls songs, and you can sort of see each bar here, and each icon represents one player, and so while you're playing the game, you can gauge how well you're hitting the marks in comparison to your dance mates. Next, we have students who like this game so much that they come prepared. I'm not sure what his cat or mask are about, but he showed up ready to game. He's got his gloves on so he does not hold, doesn't drop the remote, and he's absolutely ready for the game. In this picture, our second most avid dance player showed up. Remember, this is in January, and he had jeans on, and yes, those are his jeans on this carpet, and he said, all right, I'm ready to play, and he unzipped and unhooked his pants, and I'm like, whoa, Kirk, what are you doing?  This is DJ Hero. You can kind of see, you have a turntable and little levers that go up and down, so you are acting like DJ.  And again, this is Nerds. You can see three people, and they each have a deck of cards. I think they're playing cranium in the background. Ooh, this is really, really dark, but it's not that way on my slide, but this is a Nerds scorecard, and you can see that I kept it because I annotated that Susan was the winner, and that the others were not winners. So, you know, there's nothing like being a good sport as well. Jenga, again, please excuse the sound of my phone ringing in the background. I tried to turn it down, it won't be silent. And then our fourth game night, the first one held this semester, was Monday, December 20th, and it was right after, it was the week, third full week of school, and it, we wanted to start off pretty quickly so that freshmen could get oriented to library game, and it was a success as well. You can see Monopoly. It also coincided with the first celebration of international talk, like a pirate day, so we had various pirate stuff. This picture didn't come out very well. I should have included one with people in it, but we had a nice swashbuckling pirate laugh and pirate, and they could put their faces in the holes, become the pirates, and take pictures. And this time I made caramel corn puffs, which were also decadent, and you can see we had first stickers, some pirate coins, pirate eye patches. This bowl over to the side had pirate bouncy balls. So we kind of threw in a double, it was a two for one celebration of pirate, talk like a pirate day, and then also game night. So, my how we've grown. From the first to the fourth, we've grown in number of participants, and of course, depending on the night of the week itself, we've heard Monday, Wednesday, Thursday. We're closed on Fridays, Tuesdays. It also depends on the time of semester and other activities that are going on. But we've found that 7 to 10 is the right amount of time, and that you really can't go wrong with those hours, at least in our setting. We've acquired more Wii games, including Like the Star Wars, Mario Party 8, and Seat It. We have outside games now, so we have Botchy Ball, we have OK. We've added more board games, like Craneon. We have two that are unique to Hastings College days, which is about, it's like Trivial Pursuit, except it's based on the Hastings College campus, and then Hometown USA Hastings, and then lots of more other games. So, Spoons, Pasa, Quidditch, Card Game, and it's amazing how delighted students get when they realize Spoons. You haven't played Spoons for a long time, or Slamwitch, or Old Maid. It's amazing that they will revert back to the Shoots and Ladders stage sometimes before trying out a new, quote, adult game. Potential problems, OK. Noise, which our first floor were not big noise teachers. Our first floor is basically normal level conversation. People who really want to get intimate with their books and studies generally go upstairs anyway, which is the quieter floor. But, of course, on game nights, you can't tamp down the desire to, you know, oh, yeah, or, yeah, take that, I got it. So, it is going to be noisy. There's a fear of monopolization. When I first started, I was worried that, you know, one group of kids monopolize the Wii or, you know, monopoly or whatever all night. And it just didn't happen. We found students playing games with students, other students, that they didn't already know just because they wanted to play the same game. And they were pretty good about taking turns, you know, the bowl, and then they'd look around and say, do other people in place of the slot, let it out. A concern, of course, is theft or misuse of the games and equipment, which we are blessed in our environment. We simply do not have that problem at all. And we circulate all of our games. So, any of our games can be checked out or Wii consoles checked out. Everything is circulating except when the library is using it for game night. There's the consideration of a mess from snacks. But we are big on the food. We love the food at Perkins Library. And so, that's just something that we take as a given. Whenever we have an event, we have snacks. We're going to have crumbs on the floor.  You're going to have sticky remarks, but that's just what it is. And then, you prepare to answer why from outside. So parents or administrators or whoever the case may be. Expect reactions, questions, and comments from your user community. And then, that's when you rely on research and statistics and studies on how gaming promotes learning, creativity, intellectual pursuit, et cetera. And then, you go challenge someone to a game of paper scissors rock because that could be more creative or intellectual than that, right? Challenges and considerations include batteries. So, are you going to do rechargeable or regular? We do regular. As I said, the day of week, time span, you're always going to have conflicts. You run into the problem of having it be too short, too long. And of course, these are things you adjust. They're self-adjusting. You could do surveys, which we did. The second game night, we did a small survey. And so, I didn't include it here, but we asked things like, how did you hear about game night? Did you come alone? What games did you play? What games didn't we have that you would have liked to have played? What day of the week would you prefer it to be on? What time period would you prefer it to be on? And so, we gathered some feedback and took it for what it was worth. Games, are you going to borrow them by them or BYOG? We, of course, as I said, borrowed it first, then we bought. And now students know to bring their own games. And that works out wonderfully as well. So, last time we had someone bring, I can't remember what it was called now. But it was a freshman. So, this freshman was paying attention to the flyers when it said bring your own game. Consider whether freestyle or refereed is going to work for your particular environment and user population. For us, freestyle works perfectly where people can just organize themselves into groups and find their own place in the library where it has adequate seating and space for that particular game. But I know situations where refereed actually works better, maybe with smaller kids, but with us freestyle is just fine. And then, other, you can talk about if anyone has any experience or can think of any other concerns when we get to the question part. Benefits, lots and lots of benefits. Relaxation and recreation for all. Positive energy in and for the library. They see the library as a fun place. And I like to think that our library is a little bit higher ranking on the funometer than lots of libraries that are academic. But it's good to see all of the positive energy, and it's good to see other people who just come in to study seeing that people are having fun in the library. It's validation. As a library, it's more than just books or as the need for multiple types of literacy. It's great. You can read. It's great. But you also need to be social. You also need to have hand-eye coordination. And then also, as part of this, work-play balance, which is something everyone as an adult is going to struggle with. So it helps them moderate that balance. Of course, the connections between students and library staff and students and other students, as I said, it gives them a chance to see us in a light that is exactly that lighter. So they get to interact with us on a really fun level. And they also get to meet students that they may not have met before. Increased traffic, of course, pulling patrons in. Gabe Knight has brought us, like the Kirk, the young man who shed his jeans in order to have gym shorts and more freedom while kicking my butt at Just Dance. I had never seen him, and he was a sophomore. I had never seen him on campus or in the library before. And he came out for game night. And now he will not miss a game night. So that's great. Increased traffic, pulling patrons in. The sheer fun of it. Why not do it? It's a feel-good thing. It's a good time. And it doesn't require bucket loads of money or time to pull off successfully. I read some other presentations or kind of how we done it goods, too. And there are a ton of libraries who spend lots and lots of money on game night, and we don't. Aside from the initial outlay of buying the games, which you spend this time of year or before Christmas, you can get some really good deals. Aside from that and the snacks, it's really cheap, at least the way we do it. More benefits. We have experimented with strategically using Gabe Knight for a way to pull freshmen in as back-to-school thing as a stress reliever before finals week. So figure out a way to make it useful and worthwhile to your students. It gives us insight into millennial life, and it gives them, in some sense, as I said, into our personalities. It brands the library as a real-life social networking place, as a relevant place to students, just as relevant as interacting on Facebook. This is a real-life social networking place where you can poke people in person if they're beating you.  It's an inevitable introduction to the library's spaces, resources, et cetera, because they have to find a space to play their game. And, of course, it's not a surprise that students who are running for Gabe Knight tend to use our other services and resources while they're there. So they'll come before Gabe Knight, or they'll take a break from gaming and look up an article or do whatever it is they need to do. But in the end, Goodwill is generated for the library. All right, future of gaming at Perkins Library. We are continuing to add games to our collection, as our budget allows. We take requests from students. Of course, that's a no-brainer, because if students are playing games, then they'll want to play them here. We plan to continue to hold game nights at least twice per semester, one toward the beginning of the semester, one toward the end. We will continue to seek partners such as our peer ed groups on campus or the Student Association. So if we can have a partner in staging a Guitar Hero attorney or whatever the case may be, all the better. We listen to our students. I kind of wrap that in with adding games. And we want to try hosting tournaments, like a bowling tournament where students self-organize into teams and then go at it until the death. But most importantly, we want to keep on having fun. My personal future goals with gaming are to get someone to challenge me to Twitter. And I'm serious about this. We have Twitter. I've been stretching for like two years. No one will play Twitter with me. And my goal number two is to get this guy to take a 10-minute study break to join in the fun. This happens to be one of our international students. He's from Germany, and he's always in the library. I cannot get him to take even a 5-minute, 10-minute break. He has too much homework to do. So I think this is a senior year. I will get him to gain him before it's the end of the year. I'm just determined to do it. Ideas for Contemplation. So try hosting an event on 2010 National Gaming Day, which is coming up on November 13th. And if you go to nationalgamingdayala.org website, there are some ideas and different resources, examples of publicity. So I would encourage you to try that, even if it's something small. If you do just a soft rollout, get into the spirit on National Gaming Day. Try an intergenerational game night. When we have faculty, staff, and students, it's kind of fun because we all come from different gaming backgrounds, and it's just kind of neat to see someone in his 60s sit down with an 18-year-old and play a game of cranium. Start with a survey, formal or informal, to see if your users would be interested in the game night. You can incorporate library instruction into a gaming event. For all creative, you can easily do that. Especially if you're doing younger kids, you can also incorporate quizzes or crossword puzzles about the library or scavenger hunts that can be going on simultaneously while people are gaming. And basically, I would encourage you to start small and grow from there. And if it doesn't work, then it doesn't work. You either adapt it or you ditch it, but at least you tried it. Remember what William Shakespeare said? All the world's a game, and all the men and women are merely players. If this be true, let's play on. Are you game? Questions? All right, thank you. Move my mic. Thank you, Susan. That was great. I want to remind everybody if you've got a question, we will happily take those now. If you have a microphone, you're welcome to give a hand raise in the GoToWebinar software, and I'll turn your mic on for you. Everybody is currently muted. Or you may go into the questions area in the GoToWebinar interface and type in your question that way, and I will happily read those back out to Susan. We got one question already, and it's a really good one. I'm just going to throw in that we just did our gaming night at the NLA conference, and we found that actually the board games ended up being slightly more popular than the video games. We had card games going. We had Scrabble going. Roomful librarians. You think Scrabble's going to be popular? In fact, there were some very interesting, shall we say, variations on your traditional Scrabble rules once some alcohol appeared. We'll just get to that. I'm not sure there's any photographic evidence of that, at least none that's being posted on the internet. Anyway, it was fun. Let's go ahead and I'll read some of these questions out that have come through. The first one is actually here from some staff at the commission, and you mentioned about dealing with comments that are coming in, and basically the question was, did you get any negative comments? What were they? How did you handle them? Were there any maybe generational issues involved with library staff actually thinking whether this sort of event was appropriate? Actually, no. I live in a wonderful bubble here at Hastings College Perkins Library because as long as I can make a case that it's something that is beneficial to our students and to the library and it doesn't cost lots of money, I generally get to do it. About the only comments, I mean, some people did say why, not staff-wise. In fact, that one picture showed two of our other staff members playing banana grams. Everyone came the first time and everyone can't come all the time. I'm here all the time because I'm the one hosting it, but I don't expect the rest of the staff to be here all the time. The only really negative feedback we get even from other people in the library is that they wish they could join in. Again, I'm trying to work on some people getting them here in the first place and then getting the ones who are intently studying to break for 10 minutes. You know they're breaking for 10 minutes anyway. Why can't they come play a per game? Michael is absolutely right. The board games, the card games, out of the blue games like Nerds are way more popular. Not to say that the weeds aren't in continual and always used, but they rotate, so board games much more popular than we. I hope that answered your question. Sure, and I suppose if that's the complaint you're going to get, that's the one you want. Yes. We also had a pretty fun game that I like to play, a card game called Flux. Always fun and I will teach anybody to play at any time. Next question from Steve. Do you work with the local middle or high schools at all as that's his demographic? I do not. Hastings College had all of the middle schoolers in 8th grade on campus earlier this semester and I did a session for them in the library on library science which you can imagine how that went. I would not have enough energy to put on a game night for middle schoolers but I imagine you would want to do some refereeing and you would want to make sure that students aren't left out, that sort of thing. It sort of takes care of itself on the college level. But I do know from perusing the web and such that there are resources for holding teen gaming nights. Good luck. I know Lincoln City Libraries does it and generally opens it to public and I've seen they do have some younger individuals show up. You do kind of have that older demographic which does lead to a couple of interesting questions that have come in here. What if people bring inappropriate games and there is a younger audience and tied to that, what about shooter games? If somebody was to bring Call of Duty or something like that. You're dealing with a college audience obviously but are you kind of watching for the content or has it just not been an issue? It's not been an issue in our environment. No one has brought Call of Duty and probably, I don't know, I'm not sure what I would do. I've never played Call of Duty. I'm assuming that it's a fairly or could be a fairly long game and we try to keep the types of games we want on the Wii are concrete, beginning and ending, ten friends bowling, just dance, three dances in a set. Mario Party is a little bit different than Mario games are but usually 10, 15 minutes per game. I'm not sure I would say anything or disallow it if people were playing because it's just not an issue with my age group. Okay, yeah, completely understandable. Susan Lee has a comment here. We have a team gaming twice a month and elementary student gaming once a month at a public library and they call their program Play It Up. So that sounds pretty cool. Any other questions from the group? That's kind of the list. I'll comment. It never hurts to mention that you need money from the sounds of it because you never know where it'll come from. So that's a very good point. So let me see here if there's anything else. We've got some more time. If people have questions, just give everybody a chance to type for that. Was there anything else, Susan, you wanted to throw in or mention before we wrap up if any other questions don't come in? Back on inappropriate content or whatever. I'm sorry, I still wanted to attend your gaming session at NLA but being so close to home, I had to go home and be real and not partake in the fun. There's always next year. Good, excellent. I will be there. Game on. College students tend to have different varieties of games, like their own versions. And I did learn that there is an alternate version of Jenga. Did anyone know that? I was unaware of that. It is where college students write with Sharpies. It's like a truth and dare type of thing. So they write with Sharpies on each piece, something embarrassing for something that has to be done. And I can't remember how it logically would be. If you successfully put the piece in and you get to ask someone to do it, do that task. So the first time I brought Jenga out, one of the students yelled, dirty Jenga? No, not Jenga. They have their alternate versions, but again, we keep it fairly tame in the library. Well, like I said, that kind of happened to us at conference. And I will say, don't make any generalizations about or don't make any assumptions about the generations involved in that version of the Scrabble game they were playing. Exactly. You never know. It was wide ranging, yes. Yes. Gaming will bring out the best or the worst in people, and then when you add alcohol and plus librarians. I mean, you got a lot to them anyway. Yeah, exactly. We did get a couple more questions in. What time of day was most successful for your gaming events asks Kate? Oh, I'm sorry. I should have said that. 7 p.m. to 10 p.m. Our library is open on Sunday through Thursday, actually, evenings until midnight. At 7 to 10, it seems to be, and like I said, it starts out a little bit slow. So athletes are just being done with practice and showering and eating at 7 p.m. If I weren't so old, I would go. And if I didn't live half an hour away, I would go 8 to 11 because they think more people would stay. And also the, I have, though, in the past two times, instead of just gathering everything up when it ends, if people are still playing, I just leave them playing and ask them to turn off the Wii or put their games back on the table and deal with it in the morning. Great. Next question.  How does that work? We absolutely do circulate all of our games. They are barcoded. And we haven't had, I haven't been keeping track. We just got that in place primarily because I just got organized over the summer and so we just had one game night and then I haven't been keeping track. But I do know that I've come in and seen people playing Slamwich or is everyone familiar with Slamwich? I can say I'm not. Okay, it's a card game. It's a children's game and it's kind of like that hand-slapping game Jax or whatever it is.  And so you're building a sandwich and you play your cards and you get to the game stoppers, you get to slap your hand down and then you get to keep all of those cards. So it's the equivalent of Old Maid or something totally, totally childish and I have come into the library before and seen kids, students who have just picked it up off the shelf and checked it out but they're taking a break playing it. So that's good too. We have in-library use and also checkout use. Great. And the only other question we have outstanding is, will your slides be available? And our general rule with Encompass Live is that we do make all the material available. We'll work with Susan to do that assuming Susan, you're okay. Now that I'm putting you on the spot. Absolutely. Okay, yep. This has been recorded. Audio and video will post up as our podcast. We'll post the video up on the Encompass Live archive and we will make a link available to the slides for everybody to look at and print later. So that seems to be the end of our questions. So Susan, I want to thank you very much for doing this and working between conference and everything else. We kind of put this together for the last minute this morning but everything worked out lovely, I will say. So that is great. So I'm just going to go ahead and wrap this up and point out that next week's Encompass Live, I will be in Monterey, California and attending the Internet Librarian Conference. And if everything goes well, I will be talking live with some people about what's been going on in the Internet Librarian this next week. And then the week after that, we will have some folks from NLA coming and doing a kind of NLA NEMA 2010 wrap-up, kind of give you some of the highlights and what went in the conference for those of you who weren't able to make it. And I do know on the NLA SlideShare site that a lot of the presentations are being put up, so those will be available for anybody else who didn't get to attend or is looking for slides. And with that, I will thank Susan once again and thank you all for attending today's edition of Encompass Live. And we will see you next week. Thanks a lot. Bye-bye.


Previous lecture we have considered two-dimensional continuum, problems of two-dimensional continuum we have considered plane stress and plane strain problems, now we will continue with that discussion and extend our discussion to three-dimensional solid elements, so to quickly recall one of the element that we developed was a linear quadrilateral element having geometry as shown here, and we mapped this to a unit square, and this mapping was essentially done to evaluate these integrals, and in doing so we represented the coordinates here X and Y in terms of this new coordinates XI and eta using the same trial function that were used to represent the field variables, so this formulation is known as isoparametric formulation, so this is how we did and this was a representation, so this we showed that the edges of this master element correspond to edges of these quadrilateral elements, and we discussed how to carry out the evaluation of stiffness and mass matrices with these representations. Now in doing so what we observed was for the kind of geometries that we considered the evaluation of this mass and stiffness elements of mass and stiffness matrices required evaluation of quadratures as shown here, and we proposed that these integrals be evaluated using Gauss quadrature, and one of the issue in implementing this is to decide upon the order of Gauss quadrature, so the rule that was mentioned was that a polynomial of order P is integrated exactly by employing N smallest integer greater than 1⁄2 into P plus 1, so I outlined the rational behind making this decision, we showed that the points where we need to evaluate these integrants coincide are actually zeros of Legendre polynomials, and that formulation was discussed in the previous lecture. So the choice of order of integration needs to be made carefully, a wrong choice can immediately lead to poor estimates of elements of structural matrices. Now two references that I have been using in these discussions is books by Petit and S.S. Rao, so the details are mentioned here. Now before we take up the problem of 3 dimensional elasticity continuum elements we can raise few miscellaneous points and have some discussions. Now the first point I would like to discuss is convergence and choice of order of interpolation polynomial. So the question that we can ask is what happens if you reduce the element size successively in a given finite element model for a structure, does the finite element solution converge, so under what condition it happens, so there are certain requirements that needs to be satisfied by the interpolation functions to guarantee that this happens. The first is the displacement field must be continuous within the element domains, this is actually automatically satisfied since we are using polynomials as interpolation functions in terms of nodal values of the field variables, so within an element continuity is guaranteed, so this condition A is not a problem. Now condition B we will consider the Lagrangian T-V, all these conditions I am discussing with reference to structural mechanics problems. Now the Lagrangian would be a function of the field variables and its spatial derivatives, and also time derivatives, but we are not discretizing in time at this stage, so we need not discuss that aspect. Now if N is the highest order of partial derivative of field variable that appears in L, let us define N as that, then all the uniform states of the field variable and its derivative up to order N must be correctly represented in the limit of element size going to 0, this is one of the requirements, I will explain what it means. The next condition is the displacement field and its derivatives up to order N-1 must be continuous at the element boundaries. Now let's consider condition B, now what is condition B? If N is the highest order of partial derivative of the field variable that appears in our Lagrangian, all the uniform states of the field variable and its derivatives up to order N must be correctly represented in the limit of element size going to 0, so now if all nodal displacements are identical the field variable must be constant within the element, so that is the element must permit rigid body state, then requirement on derivative actually translates into requirement that the element must permit constant strain states, see for example we can explain with respect to a 2-noded axially deforming rod with 2 degrees of freedom U1, U2, we know the expression for strain energy is given by this, the field variable is U, now what is the highest order of derivative appearing here is 1, the interpolation used is U1 1-X by L plus U2 X by L, now if U of X, T is constant that means U1 equal to U2, I want that U should be constant, so if I put that in the assumed displacement form I get U of X, T is U0, actually U of X, T turns out to be U0 which is what we are checking, now similarly if I find the first derivative it is U2-U1 by L which is a constant, so that second condition is also satisfied, so when we use this type of element we can expect convergence of the FE solution as we increase number of elements, there is a further caveats on that I will come to that shortly. Now this also we have seen which is now this is a condition C, the displacement field and its derivative up to order N-1 must be continuous at the element boundaries, this we have seen suppose there are 2 elements 1 and 2 with degrees of freedom as named here U of X, T for the first element is given by suppose this end is fixed it is U2 into X by L1, so if I now evaluate the field variable at L1 it is U2 of T, now similarly U of X of T here is given by U2 into 1-X by L2 plus U3 of T X by L2, now at X equal to 0 for this element U of 0, T is U2 of T as you can see here, so the field variable is continuous. Now that means we have to look at continuity of field variable and its derivative up to N-1, N here is 1 therefore I should only look at continuity of the field variables, indeed this is satisfied in this element. Now elements which satisfy conditions A and C are called compatible or conforming elements, elements which satisfy B are called complete elements, the field variable is said to possess CR continuity if its ARTH derivative is continuous, the completeness requirement implies that field variable has CN continuity within the element and the compatibility requirement implies that the field variable has CN-1 continuity across the element interface, so these are the requirements that we need to satisfy. If the requirements A, B and C are satisfied the FE approximation converges to correct solution if the FE mesh is refined, that is if we use increasing number of elements with smaller dimensions following certain requirements, so what is this? When we are refining the mesh the form of the interpolation function must remain unchanged, you cannot change the form of the interpolation function and the mesh refinement must be such that the mesh with larger number of elements contains the mesh with smaller number of elements, so also the mesh refinement must ensure that all points in the structure are within an element, so what all this means? Suppose you use for a rectangular domain a mesh with four elements as shown here, so when you make a mesh with eight elements this mesh should contain these four nodes, okay, so these nodes must be there, that means I have to partition this element, okay. So in the next refinement I should partition each of these elements, okay, suppose this is now 2 by 2 mesh, if I use 3 by 3 then this mesh won't be a subset of this mesh, so when we talk about convergence we cannot talk of convergence from that point of view, similarly all points on the structure you know what it means by saying that they have to be all of the points on the structure must be within an element means, suppose you have a circular domain and you are using straight edged elements to discretize that, clearly this portion is outside the, this say if you consider this element with this discretization this point is within the structure but not within the any of the element, so this type of discretization we cannot expect convergence, so as I refine this still there will be parts of the structure which don't get into our finite element or the domain that the finite elements cover, so the remedy to this would be to use a curved element. Now what are the factors which contribute to the development of an accurate finite element model, so we can say that accuracy with which the structure geometry is represented is one of the issues, for example in that circle example that I showed this type of issue is quite evident, then choice of polynomials used for interpolation, then distribution of elements and nodes for a same degree of freedom there can be two alternative placement of nodes and different shapes of finite elements, so one mesh may be superior to the other, then details of integration used in time marching, and also one could also include how you evaluate stiffness and mass matrices using Gauss quadrature. Now given that the accuracy of the FE model depends on these features if we now ask the question how to refine the FE model to improve accuracy, here you can reduce the element size that means the same domain will be covered with more elements, so therefore the model will have higher degrees of freedom or retain the degrees of elements but increase the order of polynomial, instead of first order interpolation use a higher order interpolation, so this first refinement is known as H refinement, where H refers to the size of the element, this second one is known as P refinement where P refers to the order of the polynomial used. Next possibility locate node point differently in a fixed element topology, so this is known as R refinement, the other thing is alter the mesh having differing element distributions, next improvements to the time integration schemes if you are doing dynamics problem that also you know contributes to the accuracy that you can achieve, so alternatives involving a combination of all these strategies also can be thought of, so what are the issues in selection of the interpolation polynomial, the polynomial should satisfy to the extent possible conditions A, B and C that is one of the requirement, the representation of the field variable must be invariant with respect to change in the local coordinate system of the element, suppose in a local coordinate system you have XYZ coordinate by renaming X as Y and others similarly renaming other axis the behavior of the element should not change, okay, so then this is known as geometric invariance or spatial isotropy or geometric isotropy, next the number of generalized coordinates must match the number of nodal degrees of freedom of the element, this is you know essential, now how to achieve geometric invariance, the geometric invariance can be achieved if the polynomial contains terms which do not violate symmetry in the Pascal triangle, which I will show now in two dimension or a Pascal pyramid in three dimension, what I mean is if you expand X plus Y to the power of N in a binomial expansion you can arrange these terms as shown here, the first term is a constant it is here, the second one will have X and Y, X square, XY, Y square, X cube, X square Y, for example X plus Y to the power of 0 is 1, X plus Y to the power of 1 is X plus Y, X plus Y to the power of 2 is X square plus 2 X Y plus Y square, so this is X square, XY, Y square and so on and so forth, so the last term will be having this distribution. Now whenever you are choosing the interpolation polynomial we have to keep in mind how to do that, for example if you are for a triangle element we had 3 degrees of freedom, I mean 3 nodes and each node there were 2 degrees of freedom and U was represented alpha 1 plus alpha 2 X plus alpha 3 Y, so we needed there were 3 degrees of 3 nodal displacement values therefore I should use a 3 term expansion for U, so that would be 1, X and Y, okay that's what it means, a rectangular element how do you select? I need 4 terms 1, X, Y and when I come here I can select any one of this in principle, if I select X square it won't be alright because if I rename X and Y axis this will be Y square, so that's not right, so what we do is we take the term closest to the axis of symmetry which is XY, so this is alpha 1 plus alpha 2 X alpha 3 Y plus alpha 4 XY, so just to give this emphasize that if you are to take this or this that is either you retain this term or retain this term as a 4th you know for the 4th term that you need use this as a candidate or use this as a candidate you will get these 2, this is not appropriate because interchanging of X and Y would change the representation. Now just to again to give an example suppose you have 4 nodded element with 3 degrees of freedom per node, now how do we, you need 12 terms to represent that field variable, so how do you select 12 terms? 1, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, up to this there is no problem, but when it comes to this axis which one will you select? So you should maintain symmetry therefore you should take X Q Y and X Y Q, you could as well for geometric invariance you could have selected X square Y square, but the next term you will not be able to select symmetrically, and also you could have selected X to the power of 4 and Y to the power of 4, but as a rule we select terms which are closest to the axis of symmetry and therefore we take this term, so we'll come to this, this we'll be using when we discuss plate bending we'll see that, how about in 3 dimensions?  Now just another point which I am sure we have come across several times I just want to articulate that in clear terms, how do you decide on degrees of freedom? Okay, so the rule is inspect the functional in the variational formulation, identify the field variables and order of their highest derivatives, call it as N, so the degrees of freedom will be the field variables and their derivatives up to order N-1, see for example in actually deforming element the functional is in the variational formulation will be AE dou U by dou X whole square, so which is a field variable U, and what is the highest order N? So we need field variables and their derivatives up to order N-1, so N is 1 here it is 0, so we need only U, so U is the degree of freedom, whereas if you consider beam element, V is the field variable, highest derivative is 2, so I need the field variable and its derivative dou V by dou X, V and dou V by dou X, so they are the degrees of freedom. So as we consider more complicated problems it won't be immediately clear how to do this that's why I thought I must emphasize this fact at this stage. So similarly just to complete the discussion in plane stress element, this is a stress field, this is a strain field and this is how the stress and strain were related, so when we considered the functional we had epsilon transport D epsilon as the, in the variational formulation this was the functional. Now here therefore if you examine these relations carefully we have the field variables are U and V, what is the highest order derivative? You will see here it will be dou U by dou X and dou U by dou Y and things like that, so highest order derivative is 1, so the nodal degrees of freedom therefore will be U and V, okay. Now equipped with this now we will start discussing 3D solid elements, so quickly we will recall the various variables, this is the state of stress at a point it can be expressed either as 3 by 3 matrix or a 6 cross 1 vector, this is state of strain at a point there are 6 variables again this can be represented as a 3 by 3 tensor or a 6 cross 1 vector and we prefer the 6 cross 1 representation in finite element development, so the stress and strain are related through the constitutive law I am assuming material is elastic, linearly elastic and isotropic, so this is the constitutive law for that material behavior model. Strain energy we have seen it is integral over volume element sigma transpose epsilon DV naught multiplied by half, so for sigma transpose I will write epsilon transpose D transpose, now D is a symmetric matrix so D transpose is D I get epsilon transpose D epsilon, kinetic energy rho into DV naught is the mass of an infinitesimal element with dimension DX, DY, DZ and the kinetic energy of that in X direction is half mass into U dot square, in Y direction half mass into V dot square, Z direction half mass into W dot square and you add up this is the kinetic energy. Now we will consider the expression for strain energy, this epsilon we want to express this now in terms of displacements, so we use the strain displacement relations, so strain is given in terms of displacement, when this matrix operates on this displacement we get the strain, using that I represent UVW now in terms of the shape functions and nodal displacements which I write it as NUE and where this epsilon given this the epsilon will now be this matrix of derivatives into N into UV, because this is N into U this is UV, so this operator acting on N is known as B matrix and therefore the strain energy becomes in terms of displacement field it is given by this expression and kinetic energy is given by this, this we have seen but just I am reiterating so that we recall quickly what we need to use now immediately. Now in considering problems of three dimensional continuum various shapes become possible, so whereas in line elements there was no such dilemma it was everything was simple, in plain problems we had quadrilaterals you know rectangles, triangles, quadrilaterals, isoparametric you know quadrilaterals with curved edges and so on and so forth, similar issues will come up in solid elements now, so we can discretize a three dimensional domain using tetrahedrons or using rectangular hexahedrons or pentahedrons or in a more general situation a isoparametric hexahedron, so what we will do is we will try to develop the logic for developing the structural matrices for at least for some of these elements. Now let us start with considering a tetrahedron element, so tetrahedron element has four nodes this is a Cartesian coordinate system 1, 2, 3, 4 are the four nodes and each node has three degrees of freedom, U, V, and W, so this is four noted element with three degrees of freedom per node and hence we have 12 degrees of freedom for the element. Now the field variables are U, V, W which vary with respect to XYZ and T, so what we do is we represent the field variables in terms of we need four terms so we have to go to now the Pascal's pyramid, so the four terms are 1, X, Y, and Z, so that is what we are doing, I have alpha 1 of T, alpha 2 of T into X, alpha 3 into Y, alpha 4 into Z, so similarly I have for V and W similar representations these alpha 1 to alpha 12 are now the generalized coordinates, now these have to be selected by knowing the value of these field variables at the nodes, so at node 1 I will have U1, V1, W1, here U2, V2, W2 and so on and so forth, so at X1, Y1, Z1 I have U is U1, V is V1, W is W1 and so on and so forth. So now I will use these conditions and I will be able to evaluate those 12 generalized coordinates in terms of nodal displacements, this we have done for a triangle element, so I get the interpolation, the formula for interpolating the field variable within an element in terms of nodal displacements and the trial functions as shown here. Now in terms of the nodal coordinates we can derive the shape functions, the formulary is given here, V0 is a volume of the element and the N1 for example is a constant A1 plus B1X plus C1Y plus D1Z, so it's a linear first order polynomial in three variables. So similarly this V0 itself is the volume of the element that will turn out to be in terms of the coordinates of the nodes and there are some constant A1, B1, C1 they are all explained here, actually there is A1, B1, C1, D1 they have been described here and there is a principle for evaluating the other elements, some rules are given here that can be easily followed. So we have now got a representation like this where these N1, N2, N3, N4 are linear functions of XYZ and there is a constant term as well. So now this is a representation UVW N into UE, UE consist of 12 variables now, U1V1W1 up to U4V4W4. So N is this 3 into 12 matrix and ME is our N transpose N matrix we can evaluate this exactly, so you have to decide upon the order of the terms, N is linear N transpose N will be quadratic and you can use the appropriate order of integration and this can be evaluated exactly or you can actually carry out the integration when closed form, there is no problem. So this is a mass matrix, this is symmetric 12 by 12, now strain energy leading to the evaluation of stiffness matrix this is epsilon into U, this operator matrix into U and this is B and now B is this operator acting on this matrix. So we can evaluate B here in this case it becomes a constant you recall what happened for a triangular element in plane problems a similar thing happens here this is a constant, so then this KE can thus be evaluated exactly, there is no need for quadrature because this is simply a constant term. So once we find all this we know the strain which is constant over the volume and stress is DB into UE which is also constant over the volume that we have considered. So a tetrahedron element, formulation of tetrahedron element is straight forward and it follows the same steps that we use for formulating a triangle elements. Now how about a rectangular hexahedron element? So this element has 8 nodes 1, 2, 3, 4, 5, 6, 7, 8, so it is 8-noded element with 3 degrees of freedom per node and therefore it has 24 degrees of freedom, the field variables are UVW which are functions of XYZ and T, so at each node there will be 3 field variables so there are 3 degrees of freedom, therefore it is a 8-noded element with 3 degrees of freedom per node therefore a 24 degrees of freedom element, so all the structural matrices will be 24 by 24. Now we introduce the coordinate transformation XI is X by A, E ties Y by B and G ties Z by C so that this gets mapped to a cube of dimensions 2. Now each of these field variables now need to be, there are 8 nodes therefore each field variable needs to be represented in terms of 8 terms, okay, so each of these variables need to be represented by a polynomial with 8 terms, how do we select that? So we go back to the Pascal's pyramid we have to take 8 terms 1, XYZ, 4 or over, X square, so the term that we are taking is 1, XYZ, XY, XZ, YZ and XYZ, this is what we will select, we are again taking terms closest to the central axis and symmetry is a requirement, okay. So X square, Y square, Z square we are not taking, we are taking XY, XZ, YZ, subsequently we go to the third order term and we don't take X cube or Y cube or Z cube instead we take XYZ, so this ensures geometric invariance, so I get this representation, now these alphas are the generalized coordinates which need to be selected so that the values of U matches with its respective nodal values at the 8 nodes, so assuming that we have done that I get the representation for the field variables, now we have transformed now to XI eta, Zeta coordinate system I get this representation, and we can show that in XI, Zeta, eta, Zeta coordinate these trial functions are given by this, this is again similar to what we did for linear rectangular plane stress element. Now how do you check for continuity of field variables across the element boundaries? I claim that it is ensured and I leave it as an exercise for you to verify, so you need to consider two neighboring elements and a point lying on the interface and argue out why the field variables are continuous across the interface, so the representation is therefore now UVW is N into UE, that means I have combined all this where N is this matrix 3 by 24 and this is the 24 cross 1 nodal degrees of freedom vector, so we go back to the expression for kinetic energy, so I get the mass matrix to be given by this where an ijth element is given by this integral. Now since this is a cubic function, you will have the nonlinear term that will be present here will be products of XI eta, Zeta, second and third order products, so you can evaluate this integral easily. So if this is done in this case it is possible again to evaluate it in closed form I get the element mass matrix in this form which is shown here where this M itself is a huge matrix of this kind, so this is 12 by 12 matrix, the mass matrix will be 24 by 24 matrix, so the partitioning is in terms of 12 by 12 square matrices, now how about strain energy, so I have displacement is N into UE and strain is given by this and this is our expression for displacements in terms of nodal, strains in terms of nodal displacement values and this B matrix is given by this into this, this is operated on N matrix, so as before I get K matrix to be given by integral over the volume B transpose DB DB naught, so how do we get these terms now, so this B matrix I can carry out that differentiation operation and take it through the trial functions I get this and if we spend some effort we can evaluate all the gradients that appears here, so we can evaluate KE element as shown here or we can use Gauss quadrature to evaluate this and you can argue out that a 2 by 2 by 2 quadrature would complete the quadrature here, I mean would offer a good solution here. Now the similar logic can be used now, how about an isoparametric hexahedron element, so here I consider this as my element, so it has 8 nodes 1, 2, 3, 4, 5, 6, 7, 8, so the faces are you know not orthogonal to each other and they are not rectangles and so on and so forth, this is, this I will map through a transformation to a unit cube of dimensions 2, at lateral dimensions 2, so then we will carry out the integrations needed to implement evaluation of KE and ME in this coordinate system. So the transformation that we are looking for is X is represented in terms of the same trial function that I eventually will use for representing displacement fields, field variables, this is Y, this is Z, in terms of nodal values, so I can assemble them in a matrix form, I can write this matrix into this vector of nodal coordinates, in XI eta, Geta plane I know that this is the form of the trial functions, so I can, I have now the representation that I need for the nodal, the transformation from X to XI eta, Geta plane. Now how about displacement field, the same representation is used in the strain following this representation I get B into UE where B is given by B1, B2, B8 where each of these matrices have this form, where I is 1, 2, 1, 2, 8, okay, so we have these matrices now. Now here I have this term dou N i by dou X, dou N i by dou Y, dou N i by dou Z, etc., so that I need to evaluate, so to do that we can start by finding derivative of dou N i by dou XI and N i with respect to Geta, these are straightforward application of rules of differentiation, so N i by XI is N i by X into dou X by dou XI plus dou N i by dou Y into dou Y by dou XI, etc., so you do for all the variables I get this, and this itself I can write it in a matrix form as shown here, and this matrix is a Jacobian matrix of the transformation, so I will get J into this vector of gradients, this is J, J itself I can write in terms of X I will now use this representation, therefore I will be able to write elements of J in this form, so J is this, now since I know the form of this interpolation function I can carry out these integrations, so the differentiation with respect to XI will give me this, with respect to Geta will give me this, Geta will give me this, so that means I can evaluate elements of J matrix, see why I am doing all this is I need to find out which order terms will be present, right, so we discover that elements of J are triquodratic functions. Now this function that I am basically looking for which one, this is now given by J inverse into this, now KE is thus given by this integral over volume element now become B transpose DB determinant of J into this, now therefore if you can now see this the elements of this matrix are ratios of triquodratic functions of XI, eta and Geta, so these Gauss quadrature will not evaluate this integral exactly, so you will have to have some judgment on this and what is recommended is use a 2 by 2 by 2 Gauss quadrature, and accordingly we get this, this is not an exact evaluation, the mass matrix may get evaluated exactly but not the stiffness matrix, and also we will be needing the volume in this calculation and the volume itself can be evaluated again using Gauss quadrature, it can be done exactly but since we are using Gauss quadrature this can be done, and since the integrand here will be a polynomial this can be evaluated exactly by using 2 cross 2 cross 2 Gauss quadrature. So now with some effort we have formulated the elements, so now we can illustrate with some simple examples, suppose I consider a cantilever block which is fixed at the bottom, at these nodes it is fixed, so in the first model that we have used I have 16 elements and 108 degrees of freedom and we have used 8-noded hexahedron elements, so these are the parameters of the structure, simple structure, and we will let us try to find first few natural frequencies and more shapes, so you can easily see that this will, first mode will be a bending mode in this direction, second mode is likely to be this, and depending on the geometry the third mode could be a torsional, so indeed that happens, the first mode is bending along this direction, and the second one is bending along this direction, and third mode is torsional mode, and the frequencies we get are shown here 84 hertz, 122 hertz, 379 hertz. Now what I will do is I will refine the mesh now, again I am using the same, the refinement is such that within an element I am creating more elements, okay, so that leads to a model with 600 degrees of freedom and 128 elements, and again I am using 8-noded hexahedron element, that means I am keeping the interpolation function the same, and the mesh in the previous edition of the model is a subset of this. So here these are the modes, again first mode is bending here, this and twisting, the frequencies of course are now different numbers, so I am getting now 83.33, this is 84.8, 120, 281, 379, so if we follow all these rules that I mentioned this convergence will be from the above, okay. Now in the next part of the discussions we will consider another 2D approximation to problems of solid continuum, if you recall now we had two dimensional approximations already, in the plane stress model the object was so thin that the stresses across the thickness were neglected, and we got a plane stress model, in the next plane strain model the object was so thick that the displacement across the thickness were neglected, and we got a plane strain model. Now in the next part of our discussion we consider objects possessing rotational symmetry about an axis, and loaded and supported in an axisymmetric manner, so here also we will get a 2 dimensional approximation, so how does it work? Now this is an object with rotational symmetry, so you take a curve and an axis and rotate about this, so you take this line and this axis and rotate about Z axis and you get this first term of the cone, okay. So this is an example of an object with rotational symmetry about an axis, such structures are found extensively in many application, for example this is a cross section of a nuclear reactor vessel and the outer shell that you can see here has this type of property, it is rotationally symmetric about the Z axis here, there will be many internals that may not have this type of rotational symmetry, but still the outer dome for example has this property. So if we are analyzing this type of properties it is useful to take advantage of this simplification in formulating the problem, the dimensions of the problem, the numerical, the dimension of the equation that we need to solve reduces. Now what are the characteristics of this type of objects, geometry, there are 3 dimensional axisymmetry, axisymmetric solid, it is not necessarily prismatic and not necessarily thin or thick, by that what I mean, instead of this curve I can rotate this curve about Z axis I get different geometries, okay, so the cross sectional properties will not be the same, at different values of Z, how about the loads? Now we are going to use a cylindrical polar coordinate system, Z axis is this and this is a radial axis and this is the angle, theta axis, so we are going to use actually, suppose this is the origin, this is theta, this is R, and this is Z, that is the axis that we are going to use. Now with reference to that axis the surface tractions are independent of theta, that means they are constant with respect to theta, the body forces in the theta direction are zero, and the surface tractions in the R and Z direction are independent of theta, that means they are uniform for all values of theta, like a cylindrical, I mean a vessel like this internally pressurized for example, suppose it is closed at the bottom and top and it is internally pressurized we will have this type of model for surface tractions. Then using the property of the symmetry we will postulate that there are three displacement fields, U along R, theta is V and W is along Z, because of the symmetry and of loading boundary conditions and surface tractions and body forces it emerges at V is zero, then U is independent of theta and W is independent of theta. Now the material that we are using is linear, homogeneous, elastic and isotropic, so what we will do in the next class is we will develop a finite element model for problems that satisfy these requirements, so that would offer us another two dimensional approximation to a more complicated behavior. Following that we will consider behavior of again thin elements of a different kind, we have now considered in plane stress models prismatic objects which carry loads in their own plane. Now we want to consider what are known as plate bending problems, so suppose you have a folded plate structure and it is loaded, then this plate for example there will be both transverse loads and in plane loads, okay, this could be a wall or a panel in a structure also, so we consider objects like this whose thickness is constant, right, initially they are flat, in addition to the in plane loads we now consider transverse loads like a slab in a building deforming under its own weight, so that is a plate action. Now a problem like this has two components, one is what is known as membrane action where we consider the behavior of the structure only under in-line, in-plane loads, and the bending action which is behavior of this type of structures under transverse loads, the bending action is known as plate action and the response due to in-line loads or in-plane loads is known as membrane action. The analysis of membrane action can be carried out using plane stress models, so we need to next analyze the behavior under transverse loads, this requires generalization of beam, actually it's a generalization of grid, if you recall we analyzed problems grid structures consisting of beam elements and we, it was pointed out that bending in this member is twisting in this member, so a plate can be considered as a continuous analog of a grid where bending in one direction causes twisting in the other direction, so the stress resultants will consist of apart from bending moment and shear forces there will be a twisting moment, so what we will do in the subsequent class is we will consider these two problems, problems of axisymmetry and problems of plate bending, and this we will develop based on two-dimensional theory of velocity, and this we will develop by developing theory based on Kirchhoff-Lauw assumptions and Midlin's assumptions, so in Kirchhoff-Lauw's assumption the thickness of this member is taken to be small and certain assumptions on how a line element like this behaves will be made, whereas in Midlin theory which is generalization of Timoshenko beam theory the beam can be thick and we will include shear deformation and also while computing inertia we will compute, include effects of rotary inertia, so these two problems we will consider in the next class and we will conclude the present lecture at this stage.


You guys are still on horizon. What is the new meta drift car that everybody's been doing? I'm very curious to see what cars everybody's drifting in Nope, and oh There it was I knew that was gonna happen. I knew that rock was there because I've hit that rock before Man hello everybody I'm a wherever we're here back on Horizon 5 to see if we can still drift here in horizon 5 We got the moza r9 with the energy innovations wheel here She does fall man all social media all which found in the description box below Let's do it. So very curious if I can actually still trip here in horizon It's actually apparently a wet course. Oh, we're gonna be doing some tandems, baby Looks like we got Somebody else ripping up the mountains. Oh boy the nice wet road All my wheel settings and everything apparently got refreshed after I accidentally uninstalled this game and then reinstalled it So we're trying to see If we can still Get the sideways and this is apparently the last car I drove Because we just hopped right into it was animals these RTR Well, yeah, definitely not doing the greatest right now Gotta get back into the swing of things No pun intended But we're slowly getting back It's like that's our hood of corn Horizon 5 is definitely something I've been missing and definitely feeling bring it back to the channel more horizon content So we guess what keeps seeing horizon. Let me know down in the comments That was a really long e-brake grab Seems to be drying up though. I think we're gonna switch to our RS 2.5 wheel or RS V2 wheel up for the downhill section I mean, we're still managing to keep our drift score.  There we go Little touch of gravel Okay, let's kick So much wheel movement in horizon But it's super nice at all my controls and everything. We're still linked It's lost all my presets because we're on my a set of Corsa Drift settings for the moza R9 base And some factory settings for here in horizon I mean the fact that we've kept our drift chain alive is Impressive feet for myself in my mind. That's gonna be not right. Here we go Wheel just feels super light compared to what I'm used to in a set of obviously Can't really compare horizon to a set of but you know, I want to lose that train or Chains, I don't know why I kept saying train. Hey, that was on the gutter or guard rail Too soon That was quite nice. This is where I forgot how long this road is. Oh We getting it now. Oh, yeah, we back in it. Oh too soon getting close to the top, though And we're gonna switch and go downhill with the other wheel. Oh This is a long turn or a long uphill section. We'll find out. Oh Almost died At the end of this So overall not too shabby seven hundred thousand. I'll take it. So now we're gonna take this off But hopefully my wheels doesn't start freaking out Don't bump the wheel or it might start freaking out Let's grab our RS V2 Neff on RS V2 then we're gonna go full send downhill See what we can do going downhill now off that thing to fourth Guard rails have I'm surprised. We've been done oscillate ourselves out of that Kind of like the feeling of this with the RS V2 better than running my energy wheel could just be Extra weight Okay, this time we took the guard rail out Try to keep this drift this drifting alive For the all the way down definitely Enjoying coming back here on to horizon you guys want to keep seeing horizon content or maybe some new drift builds and Drifts challenges in horizon. Let me know down in the comment section down below You guys are still on horizon. What is the new meta drift car that everybody's been doing? I'm very curious to see what cars everybody's drifting in nope and oh There it was I knew that was gonna happen. I knew that rock was there because I've hit that rock before Oh Man well That's uh, oh geez I Mean we father fell back onto the dirt road, but pretty far down already I knew that rock was there because that rock tends to get me all the time We're gonna finish this road up Make sure you guys follow me on social media all which found in the description box below Do appreciate all the support you guys come back for more episodes here on the channel switching it up gonna be doing some different games and stuff like that to Drawed in the spectrum of videos here on the channel. So you guys have a specific Style of content or game you guys want to see let me know down below because the new year is coming A lot of new things are gonna be happening So we want to start the new year off with a bang. So going into this holiday season gonna be Changing up a lot of things and doing a lot of fun stuff here on the channel So make sure you guys follow me on all social media all which you found in the description box below As always thank you guys for coming by. I'll see you guys on the track Oh


Hello everybody, welcome back to another AI video. In this one, I'm in ChatGPT4, ChatGPT Plus, and it's the paid subscription, and I'm gonna show you how to create your own GIF inside, or GIF inside ChatGPT. You don't need to use any external programs anymore. And this is an example of a zoom-in on Margot Robbie. I selected her for scientific purposes only, I swear. All right, how did I do that? You'll see here I even downloaded it. Let's start from scratch, it's very quick and easy. All right, I'm gonna click on new chat, and then when you click on new chat, you get the option to select GPT. I'm gonna go ahead and select GPT4, and then very crucially, you need to make sure there's a check mark beside code interpreter. It's currently in beta, but it should be coming out of beta pretty soon. If you do not see that, just go to the bottom left here where my mouse is, and then click on settings, go to beta features, and then make sure code interpreter is selected and turned on like it is. All right, here we go. Now in the prompt, copy and paste in, or just type in whatever you want it to say. So in this case, I've got create a GIF or GIF of this image, slow zoom in five seconds long, 512 by 512 pixels, five frames per second. I just randomly selected a slow frame per second. No talk, just do. And before I hit on the go button there, I'm gonna go into Finder or into Windows Explorer if you're on a PC, grab the image, and then just hover over top of it, and you'll see that it says upload file. So I'm just gonna upload it. It's gone ahead and done it, and then presto. I'm gonna go ahead and click on the little purple button, or you can just hit enter, and it's gonna do its thing. Excuse me. Now, while it does its thing, you'll see here that the code interpreter is working. You know it is, because that little purple square with the code symbol in it is code interpreter. So it's doing its thing, it's finished working, and it has created the GIF as requested. If you wanna see what it did, you can drop that triangle down, and then you'll see here that this was created in Python, and these are the exact steps it took, and then you can just click on download the file, and presto, it's download zoomimage.gif, and if I was to go in and check that, I would just go show and find her, or show and work, and then presto, there she be, and then I can either right click on this, open it with, I don't know, Google Chrome, and let's see what we got. Ho-ho, we've got a zooming out, actually. Zoom out in this case, in this one I zoomed in, whatever. Either way, this is how you create GIFs inside chat GPT. Thanks for watching.