The Concept of Topological Derivative for Eigenvalue Optimization Problem for Plane Structures
Abstract
:1. Introduction
2. Topological Derivative
2.1. Plane Structures
2.1.1. Existence of the Topological Derivative
2.1.2. Topological Sensitivities
2.2. Eigenvalue Problem
3. Numerical Results
First Eigenvalue Maximization
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Topological Asymptotic Analysis
Appendix A.1. Proof of Theorem 1
Appendix A.2. Proof of Theorem 2
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Cases | Grid | Elements | Nodes | ||
---|---|---|---|---|---|
A | 10,800 | 5521 | 0.25 | 1.4 | |
B | 21,600 | 11,011 | 0.3 | 0.7 | |
C | 1600 | 851 | 0.3 | 1.5 |
Case D1 | Case D2 | Case D3 | Case D4 | |
---|---|---|---|---|
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Carvalho, F.S.; Anflor, C.T.M. The Concept of Topological Derivative for Eigenvalue Optimization Problem for Plane Structures. Mathematics 2024, 12, 2762. https://doi.org/10.3390/math12172762
Carvalho FS, Anflor CTM. The Concept of Topological Derivative for Eigenvalue Optimization Problem for Plane Structures. Mathematics. 2024; 12(17):2762. https://doi.org/10.3390/math12172762
Chicago/Turabian StyleCarvalho, Fernando Soares, and Carla Tatiana Mota Anflor. 2024. "The Concept of Topological Derivative for Eigenvalue Optimization Problem for Plane Structures" Mathematics 12, no. 17: 2762. https://doi.org/10.3390/math12172762