Topology optimization of quasistatic contact problems

Abstract

This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied by the body in unilateral contact with the rigid foundation to obtain the optimally shaped domain for which the normal contact stress along the contact boundary is minimized. The volume of the body is assumed to be bounded. Using the material derivative and asymptotic expansion methods as well as the results concerning the differentiability of solutions to quasistatic variational inequalities, the topological derivative of the shape functional is calculated and a necessary optimality condition is formulated.

Topological Optimization of Under-Platform Dampers With Moving Morphable Components and Global Optimization Algorithm for Nonlinear Frequency Response

“…Gradient-based optimisation is used for the optimisation. Considering contact problems, the problem of TO has been addressed in a quasi-static context in [30][31][32]. The objective of this study is to perform TO for the optimisation of nonlinear dynamic systems in the presence of a friction interface, which has never been done before according to the knowledge of the authors.…”

Topological Optimisation of Friction Dampers for Nonlinear Resonances Mitigation

“…In [8], the cross section of a beam with a geometrical nonlinearity has been optimised to reduce the nonlinear resonant response using a gradientbased approach. Contact problems have been addressed mostly in a quasi-static context [9] using both LSM and density-based approaches. In [10], the MMC framework coupled with kriging-based optimisation was employed to optimise the nonlinear frequency response of blades with an UPD.…”

A verified method for solving piecewise smooth initial value problems

“…Such situations occur, for example, when engineers describe systems with friction, take into account saturation effects in quantities of interest or simply express naturally arising conditions such as non-positivity of variables (Patton et al, 2012;Myśliński, 2012;Barboteu et al, 2013). The task becomes especially complicated if non-smooth Initial Value Problems (IVPs) are considered.…”