Multi Physics Topology Optimization Part 2

This video is an introduction to topology optimization. There are three videos in this series
1. Topology optimization
2. Multi physic optimization
3. Using Blender

[@himalgurung2902]

Hi, at 0:12 , the strain energy formula, I understand that strain energy is 1/2 (F u) and that you have expanded F = Ke Ue and replaced as 1/2 (U(T)e Ke Ue). Could you please help me clarify what the UTe represent here? Thank you.

[@Luchsio]

Hi, the strain energy is 1/2 u ^TK u or 1/2 u^T F or in your way 1/2 F u. Its just the similar expresion by inserting the FE-System. With u^T_e i mean the transpossed (for matrix multiplication) displacemenets according to the element e with the distributed Material Properties K_e. So you first push the material in K_e by using the normalized density. Then you calculate the displacements u_e on that system with distributed material properties. For the sensitivity you requiere the full Stiffness matrix, so that you just need to multiply the displacements u_e of the distributed material with the full stiffness matrix. u^T_e is the same as u_e, its just a transposed vector of u_e. So to sum up u_e represents the displacements of the FE-System of the distributed stiffness matrix K_e, which needs to be multiplied later with the full stiffness matrix K_0 for the sensitivities.

[@himalgurung2902]

DMST Thank you very much for the clarification. 👍🏼

[@Luchsio]

@@himalgurung2902 Hi no problem, if you need more help just ask for it :). If you need some code example (Python, C++, Matlab) i can send you some links. If you requiere any help for some research paper I can also help you.

[@himalgurung2902]

DMST Hi, Thank you so much for your assistance. I will definitely contact you if I need any help.

[@santoshmaharana4020]

@@Luchsio I need to code in Matlab what you explained in video, here is my email [e-mail] I appreciate your time and consideration 🙏😊

[@guillermonunezmuguerza271]

Hi, Would you mind sharing the sources or bibliography where all of this development comes from? Thanks

[@Luchsio]

Sure i ll give you the dois doi.org/10.35199/dfx2020.10 And doi.org/10.1017/pds.2021.486 If you have any further questions just let me know

[@atulwithsmile]

can you make a demonstration using blender?

[@Rene_Christensen]

Why not just make an objective function that is part mechanical, part thermal, and let the two physics share the same density field? Or is that the same as the Sensitivity weighting?

[@Luchsio]

hi rene its the same as sensitivity weightening. if you weight the thermal objective and the mechanical objective to one global objective and if you calculate the sensitivity of that global function you get the same expression. and you are right in these cases also in the case of the video you have only one density field for both objective.

[@sachinkandharkar3893]

Hello Sir, Thanks a lot for making videos on topology optimization. I'm more concerned about the mathematical solution of the problem based on which the computer program is generated. It will be great help if you suggest me something

[@Luchsio]

Hello Sachin, sorry for the late response. Topology Optimization "Theory Methods and Applications" (Book)

[@nileshchandrapikle1946]

Hello sir, Thanks for making this concept look so simple. I am from computer science background my area of research is parallelization of FEM. Can you suggest any book or material so that even I can understand basic concepts of topology optimization. Any background knowledge is required? I know the basics of static analysis of the FEM. Thank you.

[@nileshchandrapikle1946]

Thanks a lot.

[@Luchsio]

Hi Nileshchandra, just one remark: Try to use GPU based FEM analysis on OpenCL or via CUDA :)

[@aadithyasathyanarayanan9397]

Hello Sir, I am a student at Germany currently studying Computational Material Science . Thanks for making one of the best videos for people who would like to know the behind the screen works that is happening during a topology optimization . I would like to take up a small programming project in this field . I have a decent knowledge of programming in Matlab and Python and I am a Mechanical Engineer with knowledge on Nonlinear FEM as well. Could you suggest me any project topics that can be converted into a program (I mean like a Mini project).

[@Luchsio]

Hi Aadithya, on which University do you study? First please answer several questions, so that I can define a proper topic. 1. How much ECTS do you plan to invest? So for example most german universities use the following configuration: -Bachelor Thesis (12 ects) -Master Thesis (30-60 ects) -Project Work (6-12 ects) -Research Paper (15 ects) 2. What should be your main focus - Computational Science (Implementation, faster optimization, better convergence) - Computational Engineering (Pareto Optimization, Multimaterial, New Material Penalty law) - Applied Engineering (Reconstruction, Shape Optimization, Mesh Morphing) 3. Which software do you want to use - Commercial (Abaqus, Ansys, ...) - Open Source (ToOptix, Z88, FreeCAD, Blender ...) - Package-Level (ToOptix, numpy, scipy, matlab) So for example I am programming on the Python Module "ToOptix", which has quite a hard learning curve. github.com/DMST1990/ToOptixCore/ Best Regards Martin

[@sywang4623]

​@@Luchsio Hi Sir, thanks a lot for your videos. I am a novice and student, and I want to do conjugate heat transfer of TO with fluid, can I use ToOptix to develop a solver to implement? what is the difference between ToOptix and python codes of DTU? What are your suggestions? Thank you so much.

[@Luchsio]

@@sywang4623 Hi Qiao, yes you can implement a flouid approach. I use CalculiX for solving the finite element system. CalculiX is capeable on several speicifc type of flouid flows (laminar, turbolent ....). The reason why I use CalculiX is that it can handle a huge amount of different finite elements (Shape and Physics). The Implementation itself is not quite handy. You have to wrap around CalculiX or for speacial cases you have to write a FORTRAN routine (umat). If you do some stuff for only research purpose i would recommend DTU. Thier code has round about 100 lines of Code while ToOptix has round about 20 000 lines of code. Extending DTU requieres knolwedge in how to generate Stiffness Matrixes for Fluid Simualtions. If you need some help dont hesitate asking for help. Why do you requiere heat transfer and fluid? Best Regards

[@sywang4623]

@@Luchsio Hi DMAST, thank you so much for your reply and help. I want to do thermal TO of a plate with external forced convection heat transfer, just for research. So it is expected to have both thermal and fluid solver. I don't know if there exists a fluid solver with python. Does that mean if I can find heat transfer solver and fluid solver, I only need to develop TO model of fluid and compile them together to do what I want? Is that right? Best wishs Qiao

[@Luchsio]

​@@sywang4623 Hi Wang, yes if you have direclty access to a fluid and heat transfer solver, you can just compile both by weight factors. Therfore you have to solve the FEM- System of the heat transfer case and the FEM-System of the Fluid Case. Then you have to multply the Temperature and Velocity with the cooresponding stiffness Matrix. For example heat transfer you need t K t and for the flouid you need v K v. Everything else is just standard topology optimizaiton. Which can be handeled by the code of DTU. There you just have to replace u K u with w_1 t K t and w_2 v K v where w_1 is the weight factor for heat transfer and w_2 is the weight factor for fluid analysis. If this topic is part of a publication/paper I can help you directly. So the main problem is to get access to a fluid solver within a small amount of effort. (CalculiX has a fluid solver but requieres a lot of code to wrap around it). Best Regards