Chapter 5 - Formulation and Solution Strategies

Abstract

This chapter discusses general formulation by first developing boundary conditions appropriate for use with the field equations. Using boundary conditions, it presents a list of basic field equations for linear isotropic elasticity. These conditions specify the physics that occur on the boundary of the body, and generally provide the loading inputs that physically create the interior stress, strain, and displacement fields. Although the field equations are the same for all problems, boundary conditions are different for each problem. Therefore, proper development of boundary conditions is essential for problem solution, and thus it is important to acquire a good understanding of such development procedures. Combining field equations with boundary conditions then establishes the fundamental boundary value problems of the theory. This eventually leads to two different formulations: one in terms of displacements and the other in terms of stresses. Because boundary value problems are difficult to solve, many different strategies have been developed to solve a problem.