Some basic principles for the linear theory of piezoelectric micropolar elastodynamics
According to the basic idea of classical yin-yang complementarity and modern dual-complementarity, in a simple and unified way proposed by Luo, some basic principles in the linear theory of piezoelectric micropolar elastodynamics can be established systematically. In this paper, an important integral relation in terms of convolutions is given, which can be considered as the generalized principle of virtual work in mechanics. Based on this relation, it is not only possible to obtain the principle of virtual work and the reciprocal theorem, but also to systematically derive the complementary functionals for the eleven-field, nine-field and six-field simplified Gurtin-type variational principles and the potential energy-functional for the three-field one in the linear theory of piezoelectric micropolar elastodynamics by the generalized Legendre transformations given in this paper. Furthermore, with this approach, the intrinsic relationships among various principles can be explained clearly.