Motion analysis method of multibody system with contact and plastic deformation using linear complementarity problem

Abstract

Abstract This study proposes a method to analyse the motion of a multibody system with components subjected to large plastic deformations by contact and collision. The method is based on the mathematical similarity between the non-smooth behaviour of the contact and collision phenomena and the complementarity associated with the nonlinearity of plastic deformation. The material nonlinearity of plastic deformation is described by the complementarity condition for stress and strain. An analysis method of rigid non-smooth contact and collision phenomena was previously reported to solve a linear complementarity problem by using the complementarity condition for state transition. In this study, by extending the concept of state transition in the previously reported method, the complementarity of stress and strain related to plastic deformation is expressed as a dynamics problem and formulated as a linear complementarity problem incorporating contact. Hence, the problem can be analysed considering both contact and yield phenomena by solving one linear complementarity problem. The proposed method is evaluated using numerical analysis. Article Highlights Mechanical system with contact and collision and plastic deformation phenomena is formulated in a unified manner. The proposed method is based on an efficient formulation and analysis of the conventional contact problem. The effectiveness of the proposed method is demonstrated by numerical analysis for different cases and different time steps.

Keywords

• Contact problem
• Plasticity
• Linear complementarity problem
• Unilateral phenomenon