UNCONVENTIONAL GURTIN-TYPE VARIATIONAL PRINCIPLES FOR FINITE DEFORMATION ELASTODYNAMICS

摘要

According to the basic idea of classical Yin-Yang complementarity and modern dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Gurtin-type variational prinicples for finite deformation elastodynamics can be established systematically. In this paper, an important integral relation in terms of convolution is given, which can be considered as the expression of the generalized principle of virtual work for finite deformation dynamics. Based on this relation, it is possible not only to obtain the principle of virtual work for finite deformation dynamics, but also to derive systematically the complementary functionals for five-field, three-field, two-field and one-field unconventional Gurtin-type variational principles by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationship among various principles can be clearly explained.