Elastic Boundary-Value Problems

Abstract

The basic elasticity theory is briefly described for two-dimensional solids. The displacement vector and strain tensor, the stress tensor and Airy’s stress function, and the relation between stress and strain tensors are first introduced for a homogeneous isotropic elastic body. Then, the elastic boundary-value problem is defined based on the displacement formulation and the stress formulation, which, respectively, use the displacement vector and the stress or the stress function as the primary unknown functions of the problem. The general solution of two-dimensional elasticity is obtained in the form of infinite series using the polar coordinate system.