用有限元法分析接触问题的一种新的力学模型及计算方法

阐明了用有限元法计算物体接触问题的一种新的力学模型:主动接触体网格中一个节点与被动接触体单元中任意点相接触的模型,放弃了过去常用的节点对模型,为网格划分带来了便利。在这种模型下,给出了粘式、摩擦滑移、开式等接触边界条件。按照修正势能原理导出了对称的接触控制方程,可求解接触体具有非线性的静态/动态的接触问题。本文给出了在一次求解迭代后判断各节点新的接触状态的方法,可进一步决定是否和如何修改接触控制方程。

A NEW MECHANICAL MODEL AND ALGORITHM FOR FINITE ELEMENT ANALYSIS OF CONTACT PROBLEMS

A new mechanical model for FEM analysis of contact problems ispresented, in which a nodal point on the surface of contact body comes into contact with an arbitrary point on the surface of target body instead of the nodal point pair model. It is convenient to construct FE nets. The boundary conditions such as stick slid with friction and open contact were given in terms of this model. The contact boundary conditions as Lagrangian multipliers are substituted into the functional according to the principle of modified potential energy and therefrom the symmetrical nonlinear governing equations are deduced for the static and dynamic contact problems with material and/or geometric nonlinearities. Due to the symmetrization of equations, the general effective solution methods of nonlinear equations can also be used to the contact governing equations. In the paper the judgement criteria of contact conditions after each iteration are presented, which can decide whether and how the contact conditions of each contact nodal point to be modified.