ON THE VARIATIONAL PRINCIPLES IN LINEAR ELASTODYNAMICS

A new approach is proposed for the systematic derivation of various variational principles inlinear elastodynamics.Based on an important integral relation in terms of convolutions given by the authors,the new approach can be used to derive the complementary functionals for the five-field,four-field,three-field,two-field and one-field variational principles more simply and directly.Furthermore,with thisapproach,it is possible not only to derive the variational principles given by Herrera and Bielak,Oden andReddy,but also to develop new more general variational principles.And the intrinsic relationship amongvarious principles can be explained clearly.