单-双边约束多体系统的线性互补建模与数值积分方法

LINEAR COMPLEMENTARITY MODEL AND NUMERICAL INTEGRATION SCHEME OF MULTIBODY SYSTEM WITH UNILATERAL AND BILATERAL CONSTRAINTS

求解受双边约束或者单双边约束共同作用的多体系统动力学问题时,可能发生约束方程的违约问题。为避免处理违约问题,在现有单边约束多体系统动力学的研究成果基础上,给出了一种同时包含单边约束和双边约束的多体系统的动力学建模和计算方法。将双边约束分解为两个单边约束,建立多体系统的动力学模型;通过试算法筛选出起作用的单边约束并给出数值积分算法,并将对未知约束冲量的求解问题转化为等价的线性互补问题;最后通过数值算例验证了方法的有效性。

Considering the fact that the direction of normal force can be determined by the constraints, the methods of modeling and solving the constrained multibody systems with both unilateral and bilateral constraints were presented. Multibody systems were modeled by means of decomposing one bilateral constraint into two unilateral constraints. The active unilateral constraints were screened out by trial and error method, then an integration scheme in the form of the Euler scheme was presented, and the problem of calculating the unknown impulses was equivalently transformed into a linear complementarity problem. The method was validated through numerical example.