EMA 700/Math 707: Theory of Elasticity

Description/content: Gibbs/vector, index and linear algebra notations. Tensors. Strain tensor for finite and infinitesimal deformations. Compatibility equations. Cauchy stress tensor. General form of Hooke's law for a 3D body. Anisotropic, orthotropic and isotropic materials. Navier's equations. Elastodynamic waves, P-waves and S-Waves. Wave reflection. Solution of some classic problems in elasticity using Fourier and complex methods. Plane stress and plane strain. Bending. Torsion. Airy's stress function, Biharmonic equation, Michell solution. Thomson and Boussinesq solutions (tensor Green functions). Hertz solution (contact mechanics). Euler buckling, bifurcations.