ABSTRACT
This chapter analyzes linear elastic continua under the assumption that they undergo small strains. The linear theory of elasticity is based on the following two basic assumptions: The material is subject to an infinitesimal strain and the stress is expressed as a linear function of strain, and any variation in the orientation of this material due to displacements is negligible. These assumptions lead to small strain and equilibrium equations under an undeformed geometry. The linearity assumption is an attempt to simplify the mathematical aspect of the behavior of solids. Although the author assumes that the material properties are linear, the deformations in a body may not be completely linear. It may be noted that the equilibrium stress field as well as the virtual displacement field bears no resemblance to the actual stress and strain field encountered by any real or ideal material under the given circumstances.
