Shape and topology optimization involving the eigenvalues of an elastic structure: a multi-phase-field approach
From MaRDI portal
Publication:1983841
DOI10.1515/anona-2020-0183zbMath1475.35217arXiv2005.13497OpenAlexW3182771416MaRDI QIDQ1983841
Patrik Knopf, Paul Hüttl, Harald Garcke
Publication date: 10 September 2021
Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.13497
General topics in linear spectral theory for PDEs (35P05) Classical linear elasticity (74B05) Optimization of shapes other than minimal surfaces (49Q10) Topological methods for optimization problems in solid mechanics (74P15) Compliance or weight optimization in solid mechanics (74P05) Variational methods for eigenvalues of operators (49R05)
Related Items
A three-term CGPM-based algorithm without Lipschitz continuity for constrained nonlinear monotone equations with applications, Kohn-Vogelius formulation for plasma geometry identification problem, Topological sensitivity analysis for the 3D nonlinear Navier–Stokes equations, Determination of rigid inclusions immersed in an isotropic elastic body from boundary measurement, On the topological gradient method for an inverse problem resolution, Phase field topology optimisation for 4D printing, Analysis of a combined filtered/phase-field approach to topology optimization in elasticity, Sharp-interface limit of a multi-phase spectral shape optimization problem for elastic structures, Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies, Eigenvalue inequalities for the buckling problem of the drifting Laplacian of arbitrary order, Two-scale topology optimization with heterogeneous mesostructures based on a local volume constraint, Phase-field methods for spectral shape and topology optimization
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Linear functional analysis. An application-oriented introduction. Translated from the 6th German edition by Robert Nürnberg
- Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition
- Isogeometric analysis for topology optimization with a phase field model
- A computational approach to an optimal partition problem on surfaces
- Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
- An existence result for a class of shape optimization problems
- An optimal design problem with perimeter penalization
- A framework for the construction of level set methods for shape optimization and reconstruction
- Continuité et différentiabilité d'éléments propres: application à l'optimisation de structures. (Continuity and differentiability of eigen-elements: Application to the optimization of structures)
- The gradient theory of phase transitions and the minimal interface criterion
- An introduction to continuum mechanics
- Shape and topology optimization based on the phase field method and sensitivity analysis
- Graded-material design based on phase-field and topology optimization
- A level-set method for vibration and multiple loads structural optimization
- Relating phase field and sharp interface approaches to structural topology optimization
- Multi-material Phase Field Approach to Structural Topology Optimization
- Phase-field Approaches to Structural Topology Optimization
- Shapes and Geometries
- A phase-field model for compliance shape optimization in nonlinear elasticity
- Structural Topology Optimization with Eigenvalues
- Differentiation with Respect to the Domain in Boundary Value Problems
- Design-dependent loads in topology optimization
- 6. Optimization of eigenvalues and eigenmodes by using the adjoint method
- A phase-field-based graded-material topology optimization with stress constraint
- Free Material Optimization with Fundamental Eigenfrequency Constraints
- High Frequency Oscillations of First Eigenmodes in Axisymmetric Shells as the Thickness Tends to Zero
- Phase‐Field Relaxation of Topology Optimization with Local Stress Constraints
- Phase-field methods for spectral shape and topology optimization
- Mathematical Modeling
- Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum
- Shape optimization by the homogenization method