多点摩擦接触问题的离散动力学模型及数值求解

摘要

Aiming at multi-rigid-body with multiple friction and contact,a multi-rigid-body dynamics model expressed by complementary equations was firstly given.Secondly,dynamics models for multi-rigid-body with multiple friction and contact were discretized into a discrete mixed nonlin-ear complementary model for application of computer simulation based on fixed time-stepping meth-ods.Thirdly,aiming at solution problem for mixed nonlinear complementary model,the mixed non-linear complementary model was changed into a linear complementary model to resolve by Coulomb friction approximation methods and simplification methods of equality constraints.Finally,the validi-ty of the dynamics model for multi-rigid-body with multiple friction and contact and its numerical solution method was verified through a numerical example.%针对含有多点摩擦和接触的多刚体系统，建立了以互补方程形式表示的系统动力学模型。基于固定时间步长离散化方法，将动力学模型进行离散化处理，得到了描述摩擦接触问题的离散混合非线性互补模型，以方便计算机仿真应用。利用多刚体系统约束简化方法及库仑摩擦近似方法对混合非线性互补互补模型进行了简化，将该模型转化为标准的线性互补模型进行求解，解决了混合非线性互补模型无法求解的问题。最后通过一个算例验证了多点摩擦接触离散动力学模型及数值求解方法的有效性。