Some Properties of the Set of Homogeneous Solutions of Elasticity Theory

摘要

We study the basic properties of the characteristic set of homogeneous solutions of elasticity theory. It is known that homogeneous solutions of elasticity theory do not form a basis in the classical sense, i.e., on segment. In particular, there are no sets of functions biorthogonal to homogeneous solutions in the classical sense. Here, we show that a set of functions biorthogonal to homogeneous solution can be uniquely constructed by generalizing classical concepts of a function basis. The biorthogonal relation constructed for homogeneous solutions is of fundamental importance for solving boundary-value problems of elasticity theory in a rectangle [1].