电磁接触问题的变分原理与有限元求解

电磁接触耦合作用的力学分析的难点是必须考虑电磁场以及由此引起的电磁力与可移动接触边界间的耦合作用，属于强非线性问题。本文给出接触面区域电磁场分析的处理条件，并进一步建立了两类变分方程，一类是电磁分析的变分泛函，其考虑了接触区域对结构电磁场的影响；另一类是二维电磁力学接触分析的参数变分原理，可以方便地对接触问题进行求解。数值结果验证了本文的理论与算法。

Variational Principle and Finite Element Analysis of Electro-Magnetic Contact Problems

The important aspect in the analysis of coupled electromagnetic mechanical problems is the consideration of the coupled interaction between the electromagnetic field and the deformation/force on the contact boundaries, which leads strongly non linear behaviors. To solve the coupled problems, the conditions for electromagnetic field on the contact boundaries are given and two kinds of variational principles for the corresponding problems are respectively developed. Based on the proposed variational principles, the finite element discretized formulations are derived, and the numerical example demonstrates the validity of model and algorithm proposed.