Review of computational approaches to optimization problems in inhomogeneous rods and plates

Numerical optimization and variational techniques (65K10) Rods (beams, columns, shafts, arches, rings, etc.) (74K10) General topics in linear spectral theory for PDEs (35P05) Plates (74K20) Estimates of eigenvalues in context of PDEs (35P15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) PDEs in connection with control and optimization (35Q93)

Cites Work

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Maximization of the first eigenvalue in problems involving the bi-Laplacian
Bounds for the eigenvalues of some vibrating systems
A hinged plate equation and iterated Dirichlet Laplace operator on domains with concave corners
A boundary integral equation method for mode elimination and vibration confinement in thin plates with clamped points
High precision solutions of two fourth order eigenvalue problems
Efficient rearrangement algorithms for shape optimization on elliptic eigenvalue problems
Localization of eigenfunctions in a narrow Kirchhoff plate
The optimal order convergence for the lowest order mixed finite element method of the biharmonic eigenvalue problem
Extremal principal eigenvalue of the bi-Laplacian operator
Minimizing eigenvalues for inhomogeneous rods and plates
The limiting speeds of characteristics in relaxationhydrodynamics
C 0 Interior Penalty Galerkin Method for Biharmonic Eigenvalue Problems
Chladni Figures and the Tacoma Bridge: Motivating PDE Eigenvalue Problems via Vibrating Plates
Asymptotic Analysis of Localized Solutions to Some Linear and Nonlinear Biharmonic Eigenvalue Problems
On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability
Optimization of the first eigenvalue in problems involving the 𝑝-Laplacian
A Mixed Finite Element Method for the Biharmonic Equation
Über das Gleichgewicht und die Bewegung einer elastischen Scheibe.
Symmetry in the composite plate problem
Eigenvalues of Inhomogeneous Structures
Optimal Localization of Eigenfunctions in an Inhomogeneous Medium
Localization of eigenfunctions via an effective potential
Leonhard Euler: His Life, the Man, and His Works

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