On numerical resolution of shape optimization bi-Laplacian eigenvalue problems

Abdelkrim Chakib, Ibrahim Khalil and Azeddine Sadik

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 230, issue C, 149-164

Abstract: In this paper, we deal with the numerical resolution of some shape optimization models for the volume-constrained buckling and clamped plate bi-Laplacian eigenvalues problems. We propose a numerical method using the Lagrangian functional, Hadamard’s shape derivative and the gradient method combined with the finite elements discretization, to determine the minimizers for the first ten eigenvalues for both problems. We investigate also numerically the maximization of some quotient functionals, which allows us to obtain the optimal possible upper bounds of these spectral quotient problems and establish numerically some conjectures. Numerical examples and illustrations are provided for different and various cost functionals. The obtained numerical results show the efficiency and practical suitability of the proposed approaches.

Keywords: Shape optimization; Gradient method; Clamped plate; Buckling plate; Eigenvalue problem; Bi-Laplacian; Shape derivative; Quotient problems (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:230:y:2025:i:c:p:149-164

DOI: 10.1016/j.matcom.2024.11.007

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