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The first step in finite element analysis of a given problem is the development of an appropriate model of the problem. As described in Chap. 1, the development of a model involves making approximations of the physics, geometry, boundary conditions and material behavior. Once a model is developed, (a) the mathematical equations governing the physics are developed, (b) the boundary value problem is formally defined, and (c) an appropriate technique is used to solve the problem. In this chapter, we focus on the derivation of the governing equations and the definition of the boundary/initial value problems for linear, single-physics, solid mechanics (load-deformation) problems.
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Boresi, A.P., Schmidt, R.J. and Sidebottom, O.M. (1993). Advanced Mechanics of Materials. Wiley, New York, 811 pages.
Zienkiewicz, O.C. and Taylor, R.L. (1991). The Finite Element Method. McGraw-Hill, Oxford, 807 pages.
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Anandarajah, A. (2010). Governing Equations in Solid Mechanics. In: Computational Methods in Elasticity and Plasticity. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6379-6_3
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DOI: https://doi.org/10.1007/978-1-4419-6379-6_3
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