Eigenfrequency optimization in optimal design
From MaRDI portal
Publication:5935675
DOI10.1016/S0045-7825(00)00284-XzbMath1004.74063MaRDI QIDQ5935675
François Jouve, Sylvie Aubry, Grégoire Allaire
Publication date: 26 June 2001
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
homogenizationcomposite materialeigenfrequency optimizationoptimal shape designrelaxation theoremsaddle-point theoremtopology optimizervolume constraint
Brittle fracture (74R10) Composite and mixture properties (74E30) Homogenization in equilibrium problems of solid mechanics (74Q05)
Related Items
A multilevel, level-set method for optimizing eigenvalues in shape design problems ⋮ A level set method for Laplacian eigenvalue optimization subject to geometric constraints ⋮ Finite element analysis of free material optimization problem. ⋮ Simultaneous isogeometrical shape and material design of functionally graded structures for optimal eigenfrequencies ⋮ A two-grid binary level set method for eigenvalue optimization ⋮ Optimal design of multiphase composites under elastodynamic loading ⋮ Nonlinear structural design using multiscale topology optimization. II: Transient formulation ⋮ A two-grid binary level set method for structural topology optimization ⋮ Convergence analysis of Galerkin finite element approximations to shape gradients in eigenvalue optimization ⋮ Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures ⋮ An efficient transient dynamic topology optimization framework based on successive iteration of analysis and design ⋮ Optimal non-homogeneous composites for dynamic loading ⋮ Effective shape optimization of Laplace eigenvalue problems using domain expressions of Eulerian derivatives ⋮ Optimization of the first Dirichlet Laplacian eigenvalue with respect to a union of balls ⋮ Binary level set methods for topology and shape optimization of a two-density inhomogeneous drum ⋮ Greedy algorithms for eigenvalue optimization problems in shape design of two-density inhomogeneous materials ⋮ Minimization of the elliptic higher eigenvalues for multiphase anisotropic conductors ⋮ Mathematical analysis and solution methodology for an inverse spectral problem arising in the design of optical waveguides ⋮ On accuracy of approximate boundary and distributed \(H^1\) shape gradient flows for eigenvalue optimization ⋮ A phase field method based on multi-level correction for eigenvalue topology optimization ⋮ Numerical Minimization of Dirichlet Laplacian Eigenvalues of Four-Dimensional Geometries ⋮ Finite element approximation to the extremal eigenvalue problem for inhomogenous materials ⋮ Optimal design of sensors for a damped wave equation
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Homogenization and optimal bounds in linear elasticity
- Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materials
- Generating optimal topologies in structural design using a homogenization method
- Regularization of optimal design problems for bars and plates. I
- Regularization of optimal design problems for bars and plates. II
- A homogenization method for shape and topology optimization
- Contre-exemples pour divers problèmes ou le contrôle intervient dans les coefficients
- A saddle-point theorem with application to structural optimization
- Extremal eigenvalue problems for two-phase conductors
- Optimal design and relaxation of variational problems, III
- On the Convergence of the Energy, Stress Tensors, and Eigenvalues in Homogenization Problems of Elasticity
- Optimal design and relaxation of variational problems, I
- Optimal design and relaxation of variational problems, II
- Optimal Bounds and Microgeometries for Elastic Two-Phase Composites
- Solutions to shape and topology eigenvalue optimization problems using a homogenization method
- The homogenization method for topology and shape optimization. Single and multiple loads case
- Optimal bounds on the effective behavior of a mixture of two well-ordered elastic materials
- Topology design with optimized, self‐adaptive materials
