Theory of Elasticity

ENG MS 580

An introduction to the general theory of solid deformation; small deformation emphasized. Topics include: Cartesian tensors, indicial notation. Introduction to continuum mechanics: deformation of continuous media, deformation gradient, strain definitions. Stress, Cauchy's postulate, Cauchy and Piola-Kirchhoff stress tensors. Balance laws. Constitutive equations, strain energy and Green's postulate. Linear Elasticity: Two dimensional problems, Airy stress function, in plane loading of strips, St. Venant's principle, complex variable methods, Goursat-Muskhelishvili representation, stress concentrations around holes and cracks. Three dimensional problems, Kelvin's solution, the Boussinesq problem, Hertzian contact, Eshelby's energy-momentum tensor. Meets with ENGME580. Students may not receive credit for both.

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