CDFAM Berlin 2024 · Berlin · 7–8 May 2024
Simulation-Driven Design of Lattice Structures
Abstract
The world of additive manufacturing is constantly evolving, and we are fortunate to witness its growth with new machines, faster processes, and an abundance of new materials. Design practitioners are now enabled to unleash the full potential of AM using Generative Design and Lattice structures.
Lattice structures are topologically ordered, three-dimensional, open-celled structures used by nature. Lattice structures are observed in insects, birds, bones, and plants. Lattice structures are very effective for lightweight structural panels, energy absorption devices, thermal insulation, high-performance heat exchangers, ballistic protection, and porous implants.
Transcript
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0:02 Well, good morning. My name is Andreas apparently I’m the oldest person in this room, and I can’t stop working because these things are so much fun. We live in really exciting times, we do things we couldn’t even dream or imagine before. Okay, so very exciting stuff. My first two decades I was a professor at the University of Colorado, but I work all the Summers for the industry, so I was practical. In the last 20 years I do Consulting for defense and Aerospace, especially solving new, unique and difficult problems for SpaceX, Lockheed Martin, General Dynamics, BAE, practically all defense and our space contractors in US and some in Europe, like right here in Germany, Italy, Norway. I mean all over the place, because it’s fun, I enjoy the stuff, and this is sort of you can pass the enjoyment to to others. We have a three-day master class on this, things that’s the only commercial, because I don’t sell software, I don’t sell Hardware, I don’t sell Powders or anything else.
1:30 There are six recent enhancements in computational design, I learned the term here. What are they? First, generative design, say wow, that topology optimization has been around for 30 years, what’s the big deal? It is a big deal, because you can do cut reconstruction with a push of a button, you can do DOE, design of experiments, on the factors we use to tune up and you need the expert and the PHD guy to do it, you know, like element size, minimum element thickness, spreading, and Etc. So you do DOE, so you can generate hundreds and hundreds of optimum feasible designs. So the task is which one do I need. After that, and of course we now we have manufacturing con strange, we couldn’t dream having print orientation Direction with 45° 6 years ago, okay. So super exciting, I won’t talk about it.
2:40 Generation of lattice structures. Lattice structures are used in nature for a long time, but nature is a very good designer, okay, he has a lot more experience, failures, and Etc, but nature is a very good designer and uses lattice structures. We couldn’t use them before six years ago, we couldn’t even imagine that. Why? Because we couldn’t manufacture them, we couldn’t even build them in CAD, now we can. Super exciting, amazing geometries, and also we have now custom lates, you can visualize a dream of a lattice unit cell, make it custom, and use it. And the other one, architected materials, wow, you say, what, what’s a big deal? The big deal is you can get properties for response, like mechanical properties, like stiffness and thermal conductivity, porosity, and Etc, which they don’t exist in nature. See, if they don’t exist in nature, how do you get them? Well, it’s combination of the material, so we can get zero coefficient of thermal expansion will be that exciting for the people, they fight thermal stress, you know, stuff like that.
3:52 Then the next big deal out of the six is realtime simulation tools. I’m in the industry for 40 years, I never thought I will be able to do real time simulation. Let’s say conjugate heat transfer, say what is real time, oh, you have big computer? No, no, they use the GPUs, and they don’t use finite elements, they use voxels, so what? Well, now I can do static, model, thermal, CFD, conjugate he transfer, so big deal, okay, you can see it fast, but is it accurate? We’ll talk about it. Simulation results become features on the model tree, because it’s fast, if I regenerate the model I can see the pressure drop. So, so what? Well, if it’s feature I can do sensitivity, I can do optimization, I can do multi-objective design studies, I can do statistical design studies on the fly, I don’t need additional software, and if you can do optimization, you don’t just do good designs, you do great designs. I won’t talk any about these things, if you need this stuff you take the class.
5:14 Simulation driven structures, lat structures, there are a lot of challenges there. We can generate amazing geometries, so we can grasp the form and the fit, but how about the function? Will it work, will it break, will it overheat, will it vibrate, will it flow? I don’t know, we we need to go beyond that. Looks really good, is it Optimum, will it work, does it have the minimum weight, questions like that. And then who defines what is the size of a lat structure? Usually, usually the user says the gyroid thickness is 1 mm. Well, there are other options too, you can based on proximity to surfaces in, or any geometry in end toop, they call them ramps, or you can do even better, have a set of simulation results and say would you please go to the areas of high stress and make those thicker or thinner appropriately.
6:22 Then the next big thing is robustness assessment of the uncertainty in 3D printing. Can we do something in the design to overcome the uncertainty in 3D printing? What uncertainty are you talking about? It looks so beautiful, look the stuff in the back, well, look at them closer with a magnifying glass, or a, you know, microscope, and say oh my God, okay. And finally, manufacturing process simulation, can I build something, can I, can I optimize the supports or the Setters, if you do binder jet for example, the droop, they shrink 20%, can I put a Setter part under, they we don’t have supports in binder jet, but then how do I optimize that without manufacturing process simulation? It, the TRL level, it’s not quite there yet for for the manufacturing proc, but useful tools, you should explore them. And also I want to avoid build failures, I want to build it the first time without cracking at the end and say oh, what, what did we miss here, oh, you have a very thick plate and very thin support, of course it will crack there.
7:46 And then the other big deal is Distortion compensation. We can find out, we can optimize it, but it still distorts, okay, residual stresses are there, it distorts, what can we do? We want it to be perfect. Well, design it the other way, okay, do a compensation, compensation on the Distortion, so when you print it will be straight. Can I capture this back to the model so I can morph my card model, so when I have one single part, one good source of Truth, and say print that. Okay, we’re going to focus only on this talk, because we don’t have three days, the on simulation of of L structures and robustness. What are the challenges in simulating the lattice structure? The first one is massive element size, for tetrahedrons, you know, required to capsule the details, if I have a unit cell like that and it has a lot of elements.
8:48 The other one is interoperability with, we have all these beautiful powerful tool tools, they can generate TPMS and gyroids and diamonds, and and then what, we ed to do save it as a step and go to ANSYS and bring the step and solve it. We can save this as steps, so what happened? Why? Well, it’s totally different geometry, is implicit or voxel based, so I can do that, ouch, so how do I deal with that? And the other one, can I use my TPMS as a starting point for generative design, or how can I combine generative design and L structures? I’ll go a little bit quickly on that, on some of the current Solutions. We try to fight the wars with the Army we have today, not the Army we’re going to have 5 years from now. We need we have we want the CADvendor, and some of them listen, and they do it, and I’m really excited working with them.
9:51 We have full geometry representation, so if I have a stupid little bracket like that and I load it, and I have a little unit cell, and it’s about 5,000, okay, I can do it with full geometry, b, a lot of elements, but this FA solvers are fast, so if I have a single unit cell who looks like that and I mess it accurately, I have about 200,000 notes, 241 unit, some. Now if I have a 10 by 10 by 10, I have 200 million notes, totally impractical for realistic problems, which I have several million of those, okay, if you can see the engine at SpaceX for the crew capsule. So the other option, we want them not don’t give me full geometry representation, give me a simplified representation, like let’s say, so I can use it for beam and cell elements. So really give me the beginning and end of the beam, say, how can you design this? You can even see the intersection, you cannot see the balls and the fillet, it doesn’t matter, the human cannot see it, but 3mf can send it to the printer and the printer knows what to do, and the simulation software understands beams and cell elements.
11:16 So if I have something like that, and it’s a parabolic beam, it breaks it in three and makes trapezoidal beam elements, and add a mass element of the appropriate size at the center. So if I have something like that, non uniform sections, I can do trapezoidal beams. So if I have a latest structure with a bunch of beams like that, I don’t do full geometry, I do simplified geometry, so now I have a bunch of beam elements. This shows the coordinate system of a beam element, but the beauty is the user does not need to transfer the nodes and elements, it’s automatically transfers beams in the simulation software. So if you look at it closely you will see beams and solid elements wherever they interacting, so that’s much more reasonable to do. So you can load it and find your deflection, you know, accelerations, velocities, if it moves, natural frequencies, but don’t expect to find stress concentration at the corner between this and this, okay, sub sub modeling needs to be happen there if you really interested in that, so you need to understand that, oh, I can capture really the stress level at that corner, but I can use it to do rapid optimization, so I can find the optimum ltis structure to generate that desire natural frequency.
12:38 And if I have two and a half beam, two and a half D structures, I want them to become cells, I want to extract automatically the M plane, and that happens today, whatever I saw you today release software. I’m not paid by any software ventor, so I’m not going to tell you the software tools we use, but you can see the cells in the beams interacting, and it’s very easy to do that now. He said, yeah, but if you have a million cells even that would cut it? Yes, then we use homogeneization. Homogeneization, we take a unit cell, we squeeze it in all three directions, we find the equivalent material properties, and we set up a solid element with this material material properties, and we solve for that, of course, don’t expect to find stresses here, okay, but you can find natural frequencies, you can do optimization.
Now let’s talk about how do we simulate, okay, we saw that, but let’s say if I have a little heat exchanger for a chip with variable thickness from the top to bottom, if I look at it like that, that’s where I put the fan. How, how do I analyze that? Believe it or not, there’s some tools today which they provide you real time simulation tools. What do you mean real time? Well, once upon a time we had four viewing modes in the cut system: hidden lines, hidden lines removed, shade it, shade it with edges. Now we have one more, simp simulation results, because the simulation is fast, you can see the results in real time, it takes more to regenerate the cut geometry than solve it, I’m not kidding, whoever doesn’t believe me I’ll show you.
14:40 So in real time, you can change let’s say the size of the unit cell and find a new temperature, change the the diameter of the unit cell and find the temperature. Super exciting stuff, it’s it’s really spell checking or grammarly for design, you do it real time. It’s like have over your head somebody with a let’s make it foam hammer, every time you make a mistake, bing, oh, you exceed the yield, all right, let’s make it back to that, or don’t add that whole, and Etc. And say yeah, the structural thermal are easy, I know, I believe you. Also you can do real time CFD, how? Well, automatically computes the fluid M and it does it how? What is the secret? There are two secrets, don’t tell anybody, okay, one, one, he uses the GPUs, and the other doesn’t use finite elements, you use voxal based, and because those most of these geometries are voxal based and implicit, the transfer is very fast, so you can find the velocity distribution and the pressure distribution, and you can cut it in various planes, and you can see, this is real time stuff, okay, I’m not talking to you who need to send it to the cloud and wait for a week and get it back and Etc.
16:10 Real time on your machine, change viewing mode if you want to see the Cod model, so you can see it in different planes, you can have the unit cell because parametric, you can change anything, and you can see the flow lines, and if you add a little bit extended fluid you can see a better accuracy on the results. And say yeah, but that’s too good to be true, there’s no way you can have that speed with accuracy, and of course most of our customers, they fly things in space, so they can take the risk of having a software tool which looks good but it’s not accurate. So what we did, in a comparison for this particular problem, we it has 7 million cells you have choice of speed and accuracy, we go always on accuracy, because it’s that fast, what is between 10 and 20 seconds, doesn’t matter. So 7 million unit cells for voxels and 13 million finite elements in fluent, less than 1% difference, this is super exciting, okay, because the customers, like the Lockheed and General Dynamics as well, can you please show me some verification problems? Man, those are simplistic, they’re solved by mechanics, they’re not practical, let’s do real problems, okay.
17:36 I had to show a heat exchanger, because you know that’s the one we’re printing today, actually, as we speak, so we can very easily find in gyroids, because it’s voxel to voxel, the simulation results, and find how they behave. And also you can say, how can I you told me of all these things, but how can I combine generative design and lates? Well, one simple Technique we use, we take the initial design domain, we identify the preserved geometry, and we comp we select an appropriate unit cell to use, we don’t know which one, but we select one and we do homogenization, so we try to do generative design with the homogenized material properties, okay, so it’s not as strong as, still it’s let’s say 20% because it’s the homogenized geometry, but I get that.
18:38 Then the next step is, before you do anything, you go find the stress field, you do a stress analysis, and you find the high stress and the low stress areas, and you you save it as a point cloud, XY Z, VES, let’s say, but it doesn’t need to be mesh, it can be temperature, it can be a lot of other cool things which I don’t have time to show you now, but take the class anyway. And then you say okay, let me infill the lattice structure based on the simulation result, more dense they, less dense they, and Etc. I think nTop introduced that concept a few years back, and a lot of people follow.
19:22 In summary, the challenges are massive element size and interoperability of TPMS and implicit, and interaction, inter integration between generative design. And how would the solutions are, have various geometric representations of your lattices, so they’re not only for the human eye in visualization, but for the downstream applications like printers, we have structures which the STL doesn’t work, we have to bypass STL, so if they’re beams we use 3mf, if they’re complex lat structures we use CLI, you know, Common layer interface files, we slice it in the cut system and then send it down. Or homogenization, in real time simulation tools understand voxels and understand implicit geometry, so you can do amazing things with that, and in the generative design use homogenized material properties and simulation driven latices for for infill.
20:31 If I do the same summary graphically, if I have between let’s say 1,000 and 5,000 unit cells, regular full representation geometry will work great, if I have between 5,000 and half a million, simplified, like beams and cells, will work fine, if I have up to 100 million, well, you need homogenization with uncertainty. What heck is uncertainty? Everything is perfect here, we specify what we want, we’ll see that in a few minutes, so typically the simulation driven lattices, we have a field, and we can either put more dense field, put more material where you need it if it’s stochastic, and if it’s regular you adjust the thickness. Here some people, like an nTop, can do both, and some can do either. Okay, so this is really exciting because I don’t need to specify the user to specify what is the the diameter of the lattice, it’s the simulation tells you, and here you can combine load cases, so you can say okay, combine these load cases and give them some weight factor.
21:51 The other thing, in the if it’s a feature in the model tree, the outcome, in this particular case you have the pressure drop here, you say could you please capture the pressure drop, or or the maximum pressure drop on the surface, and it gives it to you, but because there a feature on the model tree you can say can I plot the this is a real problem for a conformal cooling, you know conformal cooling, you saw some examples yesterday, you have a part and you put a bunch of paths around the, so you can cool it quickly, so you can open up and the next one comes in, but can we get better than that? Yes we can, infill it with lattice structure, so we don’t have so much pressure drop, and then how do we size the lattice structure. That’s one example, that we had the target for pressure drop, what is the gyroid unit cell size, you plot gyroid unit cell size here, pressure drop, and aha, that’s the good one, I’ll do this one, okay.
22:55 So that’s about simulating lat structures, it’s super exciting tools to generate IM. The only thing you need to learn from the first part of the talk, imagination is the limit for generating lattice structures, use simulation driven latices to size it. Now a few more questions, can we manufacture accurately this perfectly optimized designs? What do you think? Yes, no, can we, is 3D prone to any defects? They’re very difficult to avoid, yes. How do we apply robustness in design to overcome the uncertainty in manufacturing, what you owe me, the designer, to take care of your problem, because you can do something accurately, you know, yes. And can we design for Six Sigma quality level? The idea is okay, in the good old times, when money and cost wasn’t the issue, you say okay, go to the minimum possible diameter, the minimum possible thickness, the worst material, and the maximum possible load, and design for it, you overdesign, because not all bad things happen at the same time, so we need to introduce statistics and say I can live with three parts per million units failing, or you know, I can live with none, so not all bad things happen at the same time. How can I deal with that? Okay, and I searched on the web, by the way, designed for Six Sigma quality with CA, and a freaking paper of mine came the top thing, which I did 25 years ago with Ford Motor Company, okay, so there’s not a lot of new things there, these techniques have been out for a long time.
25:04 How do we deal with them? Well, let’s say I have a primitive, a gyroid, and a diamond, and I can plot the aspect ratio, where is the volume fraction, so I can have the same volume fraction, so I can find, oh, this is 853, this 5.52 mm, that’s exactly what I want, and that’s exactly what I expect, expect, and then you print it, and from far away it looks good, but then if you look at it a little bit closer, you say what are these steps here, well, those are the layers, okay, and why? This is not exactly that, wait a minute, you mean the printed part, it’s not exactly identical to my C model? Yeah, it’s not, it’s that’s the reality. Oh, sh, you say something, something, you know, oh my God, you know, and you can see how there is difference. And oh, this is polymers, don’t worry, let’s go to, you know, test it. You test it and you realize that you have different performance, the diamond outperforms the other guys, if you test them, you know, in compression, but the real lo is not compression only, okay, you have torsion, you have buckling, you have a lot of stuff.
26:21 Let’s go to metals, man, this plastic stuff that, and you go to selective laser sintering for 316 stainless steel, and you look at it closely and say darn, I thought this was a cylinder, what is this roughness here? You tell me I can predict the fatigue if it’s a smooth surface, and the fatigue depends a lot on the surface roughness, and now this is inside, oh, you don’t want to see it, if you’re a designer this is too rough, or you try TR to see the porosity, if you do, you know, a city scan, and you see there’s a lot more porosity at the Jones, and there, oh my gosh, and I was assuming modules of elasticity, you know, for steel, what is this, you mean this is not uniform inside, he has porosity, did you, you know, do thermal treatment afterwards, did you do any hipping? Yes, and he still has that, oh gee, what am I going to do about with this?
27:29 So if you see another one, you say oh all right, I can see for different levels I can get different roughness on the surface, so I can model this as a sine wave on the unit cell, and I can assume variation based on the period of the sign and the amplitude of the sign. Man, that’s too academic, too difficult, because if I change the power I can get different ones, so that would work. Wait a minute, now now you scare me, I have a nice design, I have a fast simulation, I do this, and now you tell me I can even model the variation and the imperfections. Well, here what you can do, you can come and do a CT scan on 316 L, and find the thickness here, and the thickness here, and the thickness, or the diameter here, and you can do a statistic ical analysis of the thickness, and you can give me the mean and standard deviation of the thicknesses. So what, so now you know that it was 099 with standard deviation on 001, so what, what can you do?
28:38 Well, now there is a fear on the designer, an engineer, and he asks the question, is my optimized design safe at the presence of variation? That that’s the question, so he’s really nervous now, I optimize the stupid thing, like what I’ll give you a simple example we use in the class, let’s say if you have a landing gear cylinder, there are two parameters, the radius of the tube and the thickness of the tube, and what we do, we have build constraints, stress constraints, and physics visibility constraint, visibility, the radius needs greater than the thickness, okay. If you don’t say these things, the optimizer gives you crazy results, but that was so you draw that line, R equals T, this is the design space, radius and thickness, we need to understand this concept so we can go to the robustness.
29:42 Then you can plot the equation for buling, you know, the buling load is, you know, P KL EI, so you solve this equation and you plot it, everything above the red line W buckle, everything below it will buckle, then you say okay, let me print the other line, which is the stress equal to the yield stress times the safety factor, and you have that blue line, so everything below the Blue Line it will fail, everything above the blue line is good. So say wait a minute, you’re taking all my real estate out, I really want zero thickness and Z radius, but I can’t get there, okay, that will be the optimum, because his, you know, minimum weight, so really I need to go as close as possible to zero, what is that point, that’s how, what we do in optimization, so really is that point, you say good.
30:38 Now I did my due diligence, I had my manufacturing constraint, and the optimization problem was minimize weight but make sure you don’t buckle, you don’t yield, and it’s manufacturable, so that’s the point, great, so that’s the one. Well, if there is variation present, and there is a scatter on loads, material properties, dimensions, and Etc, what happened, there’s a scatter around that point, so if you design right at the optimum, half of them will fail. So oh no, you could say something else, on half of them will fail, and I was on the optimize, what, what the heck, I did all this optimization for, what, I should go the good old times, we use safety factors, and you know, the we had supply and demand curves and we try to make sure they’re far apart, yeah, but that’s not really optimized, so what do you want me to do here.
31:51 Well, what I want you to do, shift the optimum little bit away from the theoretical optimal to account for V for variation. Man, how do you want me to do that, sift, okay, I’m an automatic guy, I don’t like sift, so let’s see how we can do that, okay, it’s not that big deal. You have performance requirements, performance targets, up, upper and lower specification limit, in other words, the stress, the safety factor needs to be greater than 1.2, the natural frequency should be more than 200 Herz, the buckling load should be 1.8 times the actual load, stuff like that, performance targets, and then how, how, I don’t know where to start, where you identify the parameters, they have variation, such what the loads, the materials, the dimensions, and the range, and we know from a a lot of studies that the loads follow log normal distributions, the materials follow table distributions, in the dimensions follow normal distributions, two as years at Ford to do that study, but we identify.
33:29 Okay, loads do that, because you can say to I design a car, but would you please avoid pot holes, because otherwise your, you know, lower control arm may fail, if you in Detroit you don’t have a choice, but you know you can do that, so you need to account for variation for these extremes, but don’t penalize yourself to go for the worst case. Then what you do, you set up a design of experiments with his parameters, since you know the range, so you have a bunch of variables and you know the range, so you can do a DOE study, I use one technique called solvable, but you can use Central Composite box sampling techniques, if you don’t know anything use Monte Carlo, is just take a bunch of point random points between them, how many depends how much is how costly is your simulation.
34:28 If it’s a CFD and takes you two days, you will do four, if it if it’s something real time simulation, it won’t take that much, and then you generate the experiments. So so far I specify the design variables, I do the DOE, generate the experiments, and then I execute a bunch of C runs, how many, as I told you, depends on C, you take the available time to to produce the project, divided by how much is a single run, and you select that many, and then you build a response surface approximation, you know that’s how I call nowadays, they call it machine learning, my dad used to call it care fitting, okay, so it’s all the same thing, don’t be panick, oh my God, machine learning, it’s just the response surface approximation, you sprinkle some inputs, you crank it up, and you get some outputs, so that’s machine learning, okay, but it’s fancy term now.
35:25 As I told you, my poor dad had curve fitting with splines, physical splines, you take it and bend it to two points and draw the curve, that’s the next minimum, all right, but now it’s fully automated, because we have the power to do that. So if you specify bunch of inputs and a bunch of output, you can generate multivariable response surface approximation, then you need to check the goodness of the fit, because you can be full, is that approximation good, how we do that, I can explain you another time, because, you know, we plot the predicted versus computed and we see if they’re around that diagonal, one simple technique, so visually you can say okay, that’s good, I’m within 3%.
36:18 After that, it’s trivial, because you have the mean standard deviation, you measure from the variation, and you can generate, go to Light and Hyper Q, make a big sampling, let’s say 10,000 random experiments, pass them now through the response surface, which takes no time, and you generate probabilistically the response, so I have now, you know, a bunch of numbers for let’s say stress level, so what, what are you going to do with them? Well, I’ll find the mean and standard deviation, and then what I will do, so I’ll find the mean and standard of the response variables, and I have down there the targets, so what I’ll do, I’ll find the sigma quality level, which is really how many standard deviations do I need to move from the mean value to reach my Target, and then you find your sigma quality level and you design for uncertainty.
37:22 Now for some of you with their generating nerds, you can see that, oh, if that’s the input, oh, let me annotate, I think I can annotate, if that’s the input and that’s the output, oh, I can put this in optimization loop, so I can find find the optimum mean and standard deviation to generate the sigma quality level, that’s for the nerds in the audience, I don’t do this because they give me a day or two per project like that. So if I go back to this particular example, and I have uncertainty quantification, I can do something simple, I can find the red beams and the yellow beams, what red beams, well, reds are from zero slope to about 30° slope, and from 30° to 45 dees I can call them yellow, okay.
38:27 So I have yellow beams and red beams, and what do I do with them, I assign the right mean and standard deviation, we measure on the CT scan for the yellow and red beam, so the red beams have wider spread, the yellow beams smaller spread, and the rest of the beams no spread, so now I have the mean and standard deviation of the input, so will be trivial to do the outputs, so I can have let’s say for the temperature I can get do the process I saw you before, which, by the way, don’t get scared, is fully automated, fully automated, within the freaking good Cod NCA systems, so if you use let’s say Creo or nTop or Anis, those things are there, they have different names, they call it design Explorer or statistical design studies, or I forget, in end top-op they have a box block that that, so don’t be scared, as long as you understand what you need to do, it’s not big deal, it can happen automatically.
39:34 And you can come down here, and if I annotate again, you can show, oh, the sigma quality level is 1.6, that’s not really good, and you can put the upper and lower specification limits, and you can find out the temperatures and the variations. I think I’m out of time, so I had to show inside the heat exchanger, okay, everybody se heat exchanger, this is the one we’re printing as we speak, with Chelsea here, is a diamond heat exchange, and it comes in. But there is a misconception, they tell you gyroids and diamonds and TPMS don’t need supports, yes, if you build blocks, but if you undercut them and you have local minima, they there and there, you bet they need supports, so we put screens, because you can’t, those heat exchanges are that much, so you can go inside and remove the supports, they’re tiny, so we put some screen, so you can see a screen there, but you see variable cross section for the flow, so it will have uniform flow going in, the same thing here.
40:49 And there’s one underneath, there is a nice cone here of supports, so you can you need to pay attention to support the local minima, and of course little bit outside, and here it’s a beautiful design which has no matter where you look at it, it’s 45°, no supports, because it’s 45° block like that, and it has inside a lattice with 45°. So in summary, optimization techniques are great, but robustness evaluation required to provide proof or evidence of quality. Andre will love this, because now that’s what he sounds apply robustness in design to overcome uncertainty in quantification, so we need to oversize a little bit the the mean and standard deviation of our parameters to overcome that.
41:42 In live simulation, what a joy to work with it, it promotes Innovation, because making simulation experience interactive, you see it real time, if you don’t believe me, at the break give me a problem, we’ll do it together, it’s fun, and a bigger audience can understand that. And he has some AI, for example, in the heat exchanger, if you apply heat on the bottom, you don’t need to specify heat transfer coefficient in the rest of the surface, it assumes okay, I will give you 20c and 10 watts per met square Kelvin as heat transfer coefficient if you don’t tell me anything, so you apply heat, boom, and you see the temperature, amazing stuff, this is by ANSYS, by the way, okay, I don’t get paid by them, right, but it’s ANSYS Discovery Live, and it’s embedded within cut systems.
42:40 And also start thinking a little bit more, what design limitations do you inspire to overcome using these tools, think of your current design limitations, how can I overcome this, be daring and bold, because knowledge is power, so if it’s so fast to get a response, don’t afraid to say how about if instead of diamonds I use IWP, how about instead of beam lattice I will use two and a half beam lattice, how about if I make my design weird like that, and you know, whatever, you’re not afraid to try a lot of things fast, which accelerates Innovation. Thank you very much.
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