Eigenfrequency constrained topology optimization of finite strain hyperelastic structures
Abstract
This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.
- Authors:
-
- Lund Univ. (Sweden)
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1827513
- Report Number(s):
- LLNL-JRNL-815166
Journal ID: ISSN 1615-147X; 1024334
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Structural and Multidisciplinary Optimization
- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 6; Journal ID: ISSN 1615-147X
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Topology optimization; Eigenfrequency optimization; Finite strain; Nonlinear hyperelasticity; Element removal; Degenerate eigenfrequencies
Citation Formats
Dalklint, Anna, Wallin, Mathias, and Tortorelli, Daniel A. Eigenfrequency constrained topology optimization of finite strain hyperelastic structures. United States: N. p., 2020.
Web. doi:10.1007/s00158-020-02557-9.
Dalklint, Anna, Wallin, Mathias, & Tortorelli, Daniel A. Eigenfrequency constrained topology optimization of finite strain hyperelastic structures. United States. https://doi.org/10.1007/s00158-020-02557-9
Dalklint, Anna, Wallin, Mathias, and Tortorelli, Daniel A. Sun .
"Eigenfrequency constrained topology optimization of finite strain hyperelastic structures". United States. https://doi.org/10.1007/s00158-020-02557-9. https://www.osti.gov/servlets/purl/1827513.
@article{osti_1827513,
title = {Eigenfrequency constrained topology optimization of finite strain hyperelastic structures},
author = {Dalklint, Anna and Wallin, Mathias and Tortorelli, Daniel A.},
abstractNote = {This paper incorporates hyperelastic materials, nonlinear kinematics, and preloads in eigenfrequency constrained density–based topology optimization. The formulation allows for initial finite deformations and subsequent small harmonic oscillations. The optimization problem is solved by the method of moving asymptotes, and the gradients are calculated using the adjoint method. Both simple and degenerate eigenfrequencies are considered in the sensitivity analysis. A well-posed topology optimization problem is formulated by filtering the volume fraction field. Numerical issues associated with excessive distortion and spurious eigenmodes in void regions are reduced by removing low volume fraction elements. The optimization objective is to maximize stiffness subject to a lower bound on the fundamental eigenfrequency. Numerical examples show that the eigenfrequencies drastically change with the load magnitude, and that the optimization is able to produce designs with the desired fundamental eigenfrequency.},
doi = {10.1007/s00158-020-02557-9},
journal = {Structural and Multidisciplinary Optimization},
number = 6,
volume = 61,
place = {United States},
year = {Sun May 17 00:00:00 EDT 2020},
month = {Sun May 17 00:00:00 EDT 2020}
}
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