Boundary Value Problems in Elasticity

Abstract

All problems in solid mechanics require three basic components: (a) equations of geometry of deformation relating the displacements (i.e., the map) to strains; (b) equations of equilibrium relating the applied tractions and body forces to the stresses; and (c) equations of constitution relating stresses to strains. All of these equations are necessary to the statement of mechanics problems like the torsion of a bar or the bending of a beam, but they are not sufficient to solve such problems. In addition to these equations, which describe what is happening inside the body, we must also describe what is happening on the surface, or boundary, of the body. These boundary conditions and generally comprise given data about the displacements and applied tractions on the surface of the body. The combination of domain equations and boundary conditions is called a boundary value problem.