Introduction to the mathematical theory of elasticity: Two-dimensional idealizations, plane stress and plane strain problems, equations of equilibrium, strain-displacement relations, constitutive relations, compatibility conditions, displacement and traction boundary conditions. Two-dimensional problems in rectangular coordinates: Stress function, solution by polynomials, Saint Vénant’s principle, bending of a cantilever. Two-dimensional problems in polar coordinates: General equations, problems of axisymmetric stress distribution, pure bending of curved bars, effect of circular hole, concentrated force on a straight boundary.
Stress and strain problems in three dimensions: Principal stresses, principal strains, three-dimensional problems. Energy Theorems and Variational Principles of Elasticity, uniqueness of elasticity solution. – Torsion of straight bars, membrane analogy, narrow rectangular cross-section, torsion of rectangular bars, rolled profile sections, hollow shafts and thin tubes. Introduction to plasticity: One-dimensional elastic-plastic relations, isotropic and kinematic hardening, yield function, flow rule, hardening rule, incremental stress-strain relationship, governing equations of elasto plasticity.