Phase field approach to topology optimization of elasto-plastic contact problems
Tom 127 / 2024
Streszczenie
The paper is concerned with the analysis as well as the numerical solution of the topology optimization problems for elasto-plastic rather than elastic structures in bilateral frictional contact with a rigid foundation. The small strain plasticity model with linear hardening and a von Mises effective stress is used. The displacement and stress of this structure are governed by the system of coupled variational inequalities. The structural optimization problem consists in finding such material distribution of the domain occupied by the body in contact to minimize the contact stress. Using the regularization of the stress projection operator as well as of the friction this original structural optimization problem is replaced by the regularized ones. The phase field approach is used to approximate sharp interface formulation and to calculate the derivative of the cost functional. The Lagrange multiplier technique is used to find the set of necessary optimality conditions. Gradient flow approach in the form of modified Cahn-Hilliard boundary value problem is used to evaluate optimal topology domain. The evolution of the structure topology is governed by the cost functional derivative. The examples of minimal contact stress topologies are provided and discussed.
