Continuous Solid

Abstract

In this chapter, we will develop first how a continuous solid will deform under the application of a load. A general theory describing governing equations to understand the solid deformation, Theory of Elasticity, is presented. We will describe what tractions (loads) are in a continuous solid, a structure or a machine member. The stress and strain are defined arising out of the tractions applied. The equilibrium relations in general case are derived. The coordinate transformation for a special case of 2D stress and the resulting principal stresses, von Mises stress are explained. The familiar Mohr’s circle is illustrated. This is extended to 3D case using Cauchy’s stress tensor and Eigen values. The 2D and 3D cases of strain in the continuous solid are explained; strain-displacement relations and compatibility conditions are presented. The stress strain relations and simple tensile stress test are described. Lame’s parameters and the relations between them are derived. The relation between strain energy and work done in a continuous solid are explained.