Topology optimization considering contact and stress constraints

This work advances stress-constrained topology optimization for frictionless unilateral contact problems involving large deformations and hyperelastic material behavior. The objective is to minimize the mass of a contact-constrained structure while enforcing stress constraints through local or global stress measures. Different contact coupling techniques based on Lagrange multipliers and penalty methods are investigated with respect to their applicability in stress-constrained optimization. The results show that stress-constrained optimization is considerably more sensitive to discretization errors at curved contact surfaces than common objectives such as compliance. Such errors may introduce artificial stresses that mislead the optimizer towards poorly performing designs. To address this issue, blending functions are used to retain the physical contact geometry during finite-element-based optimization, thereby avoiding the computational cost of very fine contact-surface discretizations. Furthermore, node-to-segment and segment-to-segment contact coupling are compared directly in stress-constrained topology optimization. The smoother contact-pressure and stress distributions provided by segment-to-segment coupling improve the optimization performance and lead to lighter feasible designs. Finally, local and global stress constraint formulations are compared, and an extension of the augmented Lagrangian approach is proposed to address convergence issues in challenging contact scenarios.

Content

Subjects

Topology optimization

Stress constraints

Unilateral contact constraints

Node-to-segment contact

Segment-to-segment contact

DDC Class

620.1: Engineering Mechanics and Materials Science

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Funding(s)

Simulation-based objective of dynamic systems under the aegis of uncertainties

Projekt DEAL

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https://creativecommons.org/licenses/by/4.0/

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publishedVersion

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