ch10 - Educational article Struct Multidisc 27...

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Educational article Struct Multidisc Optim 21, 120–127 Springer-Verlag 2001 A 99 line topology optimization code written in Matlab O. Sigmund Abstract The paper presents a compact Matlab im- plementation of a topology optimization code for com- pliance minimization of statically loaded structures. The total number of Matlab input lines is 99 including opti- mizer and Finite Element subroutine. The 99 lines are divided into 36 lines for the main program, 12 lines for the Optimality Criteria based optimizer, 16 lines for a mesh- independency ±lter and 35 lines for the ±nite element code. In fact, excluding comment lines and lines associ- ated with output and ±nite element analysis, it is shown that only 49 Matlab input lines are required for solving a well-posed topology optimization problem. By adding three additional lines, the program can solve problems with multiple load cases. The code is intended for edu- cational purposes. The complete Matlab code is given in the Appendix and can be down-loaded from the web-site http://www.topopt.dtu.dk . Key words topology optimization, education, optimal- ity criteria, world-wide web, Matlab code 1 Introduction The Matlab code presented in this paper is intended for engineering education. Students and newcomers to the ±eld of topology optimization can down-load the code from the web-page http://www.topopt.dtu.dk . The code may be used in courses in structural optimiza- tion where students may be assigned to do extensions such as multiple load-cases, alternative mesh-independ- ency schemes, passive areas, etc. Another possibility is to use the program to develop students’ intuition for optimal design. Advanced students may be asked to guess the op- timal topology for given boundary condition and volume Received October 22, 1999 O. Sigmund Department of Solid Mechanics, Building 404, Technical Uni- versity of Denmark, DK-2800 Lyngby, Denmark e-mail: [email protected] fraction and then the program shows the correct optimal topology for comparison. Intheliterature,onecan±ndamultitudeofapproaches for the solving of topology optimization problems. In the original paper Bendsøe and Kikuchi (1988) a so-called microstructure or homogenization based approach was used, based on studies of existence of solutions. The homogenization based approach has been adopted in many papers but has the disadvantage that the deter- mination and evaluation of optimal microstructures and their orientations is cumbersome if not unresolved (for noncompliance problems) and furthermore, the resulting structures cannot be built since no de±nite length-scale is associated with the microstructures. However, the ho- mogenization approach to topology optimization is still important in the sense that it can provide bounds on the theoretical performance of structures.
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ch10 - Educational article Struct Multidisc 27...

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