Various Reciprocal Theorems and Variational Principles in the Theories of Nonlocal Micropolar Linear Elastic Mediums

In the first part of our paper,we have extended the concepts of the classical convolution and the“convolution scalar product”given by I.Hlavácěk and presented the concepts of the“convolution vector”and the“convolution vector scalar product”,which enable us to extend the initial value as well as the initial-boundary value problems for the equation with the operator coefficients to those for the system of equations with the operator coefficients.In the second part of this paper,based on the concepts of the convolution vector and the con-volution vector scalar product,two fundamental types of reciprocal theorems of the non-local micro-polar linear elastodynamics for inhomogeneous and anisotropic solids are derived.In the third part of this paper,based on the concepts and results in the first and second parts as well as the Lagrange multiplies method which is presented by W.Z.Chien,four main types of variational principles are given for the nonlocal micropolar linear elastodynamics for inhomogeneous