Implementation of the harmonic transformation method in shape optimization
Abstract
The paper describes an implementation of the variant of the speed method in shape optimization for plane elastic structures, based on harmonic transformations. It is coupled with special method for solving the singular elliptic problems resulting from geometric features like e.g. reentrant corners. Both approaches are based on the works of the author. The interactive system has been built, based on MATLAB environment, and the examples showing the robustness of the algorithms were solved.
References
[1] D. Chenais. On the existence of a solution in a domain identification problem, J. of Mathematical Analysis and Appl., 52: 189-219, 1975.
[2] R.G Cooke. Infinite Matrices and Sequence Spaces, MacMillan and Co., London 1950.
[3] K. Dems, Z. Mróz. Shape sensitivity in mixed Dirichlet-Neumann boundary value problems and associated class of path independent integrals, Eur. J. Mech., A/Solids, 14(2): 169-203, 1995.
[4] K. Oems. Shape and materials parameters sensitivity analysis in quasi-harmonic problems, Control and Cybernetics, 25(5); 969-1000, 1996.
[5] P. Grisvard. Elliptic Problems in Nonsmooth Domains, Pitman, 1985.
[2] R.G Cooke. Infinite Matrices and Sequence Spaces, MacMillan and Co., London 1950.
[3] K. Dems, Z. Mróz. Shape sensitivity in mixed Dirichlet-Neumann boundary value problems and associated class of path independent integrals, Eur. J. Mech., A/Solids, 14(2): 169-203, 1995.
[4] K. Oems. Shape and materials parameters sensitivity analysis in quasi-harmonic problems, Control and Cybernetics, 25(5); 969-1000, 1996.
[5] P. Grisvard. Elliptic Problems in Nonsmooth Domains, Pitman, 1985.
Published
2023-05-31
Issue
pp. 285-298
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Żochowski, A. (2023). Implementation of the harmonic transformation method in shape optimization. Computer Assisted Methods in Engineering and Science, 5(3), 285-298. https://cames3.ippt.pan.pl/index.php/cames/article/view/1345
