Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

TY - JOUR

T1 - Eigenfrequency constrained topology optimization of finite strain hyperelastic structures

AU - Dalklint, Anna

AU - Wallin, Mathias

AU - Tortorelli, Daniel A.

PY - 2020/6

Y1 - 2020/6

N2 - 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.

AB - 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.

KW - Degenerate eigenfrequencies

KW - Eigenfrequency optimization

KW - Element removal

KW - Finite strain

KW - Nonlinear hyperelasticity

KW - Topology optimization

UR - http://www.scopus.com/inward/record.url?scp=85084805170&partnerID=8YFLogxK

U2 - 10.1007/s00158-020-02557-9

DO - 10.1007/s00158-020-02557-9

M3 - Article

AN - SCOPUS:85084805170

VL - 61

SP - 2577

EP - 2594

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-1488

IS - 6

ER -