線形相補性問題に帰着した接触挙動と塑性変形を伴うマルチボディシステムの運動解析手法

抄録

This research proposes a method for analyzing the motion of a multibody system with members that are subject to large plastic deformation by contact and collision. This analysis method is based on the mathematical similarity between the non-smooth behavior of contact and collision phenomena and the complementarity about the nonlinearity of plastic deformation. The material nonlinearity of plastic deformation is described as a complementarity condition regarding stress and plastic strain as a yield criterion. On the other hand, Pfeiffer et al. developed an analysis method of rigid non-smooth contact and collision phenomena to a linear complementarity problem by using the complementarity condition for state transition. In this research, the transition to the yield state is introduced into the concept of contact and collision state transition in the method of Pfeiffer et al.. Thereby, the complementarity conditions of contact problem and plastic deformation are integrated into one complementarity condition. Furthermore, the linear relationship is derived from equation of motion, and formulated as a linear complementarity problem. As a result, by solving one linear complementarity problem, it is possible to analyze considering both contact phenomenon and yield phenomenon. In order to verify proposed method, a numerical analysis using a model consisting of basic elements is performed. In proposed method, contact phenomenon and yield phenomenon comes down to contact force, so these phenomena can analyze as dynamics. Furthermore, since the same numerical analysis as the conventional rigid body contact problem is possible, efficient analysis is expected.