Abstract
This chapter provides a background for the formulation part of the study. Similar to other field theories, such as fluid mechanics, heat conduction, and electromagnetics, the study and application of elasticity theory requires the knowledge of several areas of applied mathematics. The theory is formulated in terms of a variety of variables including scalar, vector, and tensor fields, and this calls for the use of tensor notation along with tensor algebra and calculus. Through the use of principles from continuum mechanics, the theory is developed as a system of partial differential field equations, which are to be solved in a region of space coinciding with the body under study. Solution techniques used on these field equations commonly employ Fourier methods, variational techniques, integral transforms, complex variables, potential theory, finite differences, and finite and boundary elements. Therefore, to develop proper formulation methods and solution techniques for elasticity problems, it is necessary to have an appropriate mathematical background.
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