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README.txt
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% %%%
%%% Topology Optimization Toolbox %%%
%%% %%%
%%% Solid Isotropic Material with Penalization (SIMP) %%%
%%% Bidirectional Evolutionary Structual Optimization (BESO) %%%
%%% %%%
%%% Vicente Cholvi Gil %%%
%%% February 10th 2021 %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The folder /TopologyOptimizatoinToolbox contains all the Matlab functions
The folder /Examples contains files required for some of the examples
The matlab files strarting with MI are examples in which the mesh files
are imported from the /Examples folder.
The matlab files starting with MG are examples in which the mesh is
generated by the topology optimization toolbox. These take longer to run
as the mesh has to be generated. It is not recomended to generate meshes
with more that 200 000 nodes as the optimization might take too long.
The most complete example is MG_simpleHinge.
The fastest example(with a reasonable number of elments) is MI_thinBeam.
Each time the optimization is run, two folders will be created under
/RESULTS/<folderName> and /ITERATIONS/<folderName> with the optimization
results and with figures of each iteration.
Some more information and sources :
1.1 Importing the Mesh
The mesh is imported through a python script(transformData.py)
which generates two text files: connectivity.txt and
coordinates.txt these are then imported into matlab. Takes in
Optistruct .fem files. When exporting, do not remove E real
values.
1.2 Generating the Mesh
The mesh generation algorithm is based on the general idea from
Per. Olof. Persson and Gilbert Strang. “A simple Mesh Generator in
Matlab”. In: SIAM Review 46 (2 2006), pp. 329–345. doi: 10.1137/
S0036144503429121
2.0 Finite Element Analysis
Much of the information for the development of the finite element
analysis functions was obtained from three sources:
- Richard H. Galagher.Finite Element Analysis: Fundamentals.
Prentice-Hall, 1975.isbn: 978-0133172485
- K. J. Bathe.Finite Element Procedures for Solids and
Structures-LinearAnalysis. Online Lecures. https://ocw.mit.edu/
resources/res-2-002-finite-element-procedures-for-solids-and-
structures-spring-2010/linear/: MIT-OCW,1982.
- Young W. Kwon and Hyochoong Bang.The Finite Element Method using
MATLAB. CRC Press, 1997.isbn: 0-8493-9653-0.
3.1 BESO Optimization
The main source on information on this topic was:
- X. Huang and Y.M. Xie.Evolutionary Topology Optimization of
Contin-uum Structures, Methods and Applications. John Wiley
and Sons, 2010.isbn: 978-0-470-74653-0.
3.2 SIMP Optimization
Other than Huang et Xie 20120, the following was very useful:
- Wenjie Zuo and Kazuhiro Saitou. “Multi-Material Topology
Optimization using Ordered SIMP Interpolation”. In:Structural
and MultidisciplinaryOptimization 55 (2016), pp. 477–491.
doi:10.1007/s00158-016-1513-3.
0.0 "Not quite 99 lines though"
This was all inspired by:
- O. Sigmund. “A 99 Line Topology Optimization Code written in
Matlab”.In:Structural and Multidisciplinary Optimization(2001).
doi:10.1007/s001580050176.