POPULARIZATION
https://www.linkedin.com/pulse/possible-build-aircraft-wing-lego-joseph-morlier/
Jun Wu's channel on Youtube
https://www.youtube.com/watch?v=5ocnVS_HvdY
LECTURES
But how do you compute sensitivity of the compliance?
Some OptiStruct tutorials https://altairuniversity.com/13907-topology-optimization-tutorial-3-point-bending-of-a-beam-1d-2d-and-3d/#
COMPUTER LAB using SIMP
The highlights for FA & TOPOPT
You can find in top88 repository all the files, paper, and ...
The 3 point bending projected corrected using top88
for people wondering about how linear elasticity of top88.m is working
Prof, can you help to us understand how to compute the stiffness matrix of 2D membrane? Explictely ? Membrane2D_K
Have a look in the top3D repository to do the same but in 3D !!!
MORE ADVANCED STUFF
Last but not the least a MATLAB tutorial Advanced Topology Optimization.
Part A: Constraints Agreggation Thanks to my PhD Simone.
Part B: Stress Based TopOpt Thanks AGAIN to my PhD Simone. Before you can use Method of Moving Asymptotes (MMA) as an optimizer in our stress based topology optimization program, you need to obtain the Matlab implementation of MMA from Prof. Krister Svanberg ([email protected]) from KTH in Stockholm Sweden.
RECAP
This note introduces the basic concept of finite element analysis (FEA) and topology optimization (Topopt), and hopefully convince you that these are important topics to learn about for future engineers
We showed that the deflection or deformation of a structure U can be solved through a algebraic equation
KU=F.
It can be further shown that the strain energy due to the deformation is 0.5U^TKU. Minimizing this energy is equivalent to minimizing the compliance of the structure under the given loads and boundary conditions, leading to optimal topologies.
We explain some technical details below. A good tutorial can be found from Dr. Sigmund's group (see e.g., this code and this paper).
For those interested, A good introduction can be find here
While the theories behind topology optimization were developed during the 1980s, the value of this technique only started to show after manufacturing and in particular 3D printing technologies become more matured in the last two decades. Today topology optimization has many industry applications, from light-weight vehicle bodies, to artificial bones and implants, to biomemetic airplane wings, to various sensors and actuators.
Image from Aage et al. (2017) "Giga-voxel computational morphogenesis for structural design"
Image from Wu et al. (2018) "Infill Optimization for Additive Manufacturing - Approaching Bone-like Porous Structures"
Image from Dassault Systems
CAD from Tesla
Previous Manufacturing from Tesla
3D printing from Tesla