ABSTRACT
This chapter covers the fundamentals of the linearized theory of elasticity. The material is essential for understanding the application of the finite element method to problems in the area of solid mechanics. It begins with the derivation of Cauchy's law, which is a very useful tool for assessing the accuracy of finite element solutions. The chapter also covers the important topics of the small strain tensor, Hooke's law, plane stress and plane strain, and axisymmetric problems. Axisymmetric problems are another important class of problems that are two-dimensional simplifications of fully three-dimensional problems. In order for a problem to be considered axisymmsetric, both the geometry and the loading must possess the same axial symmetry about a fixed axis. The geometry of an axisymmetric problem is obtained by revolving a two-dimensional domain about a fixed axis, creating a solid of revolution.
