大变形非线性弹性动力学的分区变分原理

该文提出了论证分区变分原理的“Ｎ＞２直接方法”，并且用这一方法把大变形非线性弹性静力学的分区变分原理￣［１］推广到弹性动力学问题。该方法提出并解决了在从Ｎ＝２情形推广到Ｎ＞２情形的过程中必然存在的问题。当非线性高阶项可忽略时，由该文结果可直接得到线性弹性动力学的分区变分原理及其广义变分原理￣［２］。该文结果可以作为大变形非线性弹性动力学问题有限元计算的基础。

Region-wise Variational Principles in Nonlinear Elastodynamics with Large Deformation.

In this paper,a method of demonstrating the region-wise variational principles called N>2 direct method is suggested.It is applied to extend the region-wise variational principles in nonlinear elastostatics with great deformation to the elastodynamic problems. The method reveals and solves the questions accompanied inevitably by the process of extending the region-wise variational principles from N=2 case to N>2.When the nonlinear high-order terms are neglected,the region-wise variational principles in linear elastody-namics and their generalized variational principles can be obtained di-rectly from the paper,The results can be used as a basis of finite ele-ment calculation of nonlinear elastodynamic problems with large de-formation.