Unified primal-dual active set method for dynamic frictional contact problems

Abstract

In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset $\mathcal{A}$ A of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method.

Swarming procedures to solve the novel perturbed delay third order singular model

“…The best PSO performances is executed as an initial input in the process of ASM, which is implemented to provide the numerical performances through the constrained/unconstrained networks. ASM is applied in frequent submissions, e.g., real-time optimal control [50], fast model predictive control [51], a quasi-monolithic phasefield account for orthotropic anisotropic fracture [52], pressure dependent model of water distribution systems [53], monotone operators [54], dynamic frictional contact problems [55] and ultrasound images of breast abnormalities [56].…”