动摩擦接触问题速率型变分形式及等价性

The Rate-version Variational Formulation of Dynamic Frictional Contact and Equivalence with Its Local Formulation

推导动态接触问题平衡方程与接触约束条件的一种速率型变分形式。通过定义实值赋范可测向量函数空间中的正则虚速度函数 ,应用系统能量平衡关系将局部状态方程转变为积分弱形式的变分方程。这种变分方程适用于不同材料的有限变形情况。引入非负松弛函数和切向接触应力函数空间 ,提出接触约束条件的互补变分关系。证明了积分弱形式的变分方程与逐点满足的平衡方程、接触条件是完全等价的。

By defining a virtual velocity on real-value measured vector normed-space and introduction of slack function and admitted stress space for tangential contact traction, the velocity rate-version variational counterparts of energy balance equation and contact constraints are formulated. It has been proved that the variational formulations of energy balance equation and contact constraints, brought forward in this paper are equivalent with their local formulations.