Course info

The displacement vector of a particle of a body. Components of strain of a particle of a body. Implications of the assumption of small deformation. Traction and components of stress acting on a plane of a particle of a body. Proof of the tensorial property of the components of stress. Properties of the strain and stress tensors. Components of displacements for a general rigid body motion of a particle. The compatibility equations. Equations of equilibrium. Stress-strain relations. Formulation and solution of boundary value problems using the linear theory of elasticity. The principle of Saint-Venant. Prismatic bodies subjected to pure tension. Prismatic bodies subjected to pure bending. Plane stain and plane stress problems in elasticity. Fundamental assumptions of the theories of mechanics of materials for line members. Internal actions on a cross-section of line members. The boundary value problems in the theories of mechanics of materials for line members. The boundary value problem for computing the axial component of translation and the internal force in a member made from an isotropic linearly elastic material subjected to axial centroidal forces and to a uniform change in temperature. The boundary value problem for computing the angle of twist and the internal torsional moment in members made from an isotropic linearly elastic material subjected to torsional moments. Primary and secondary warping functions. Warping normal stresses. The classical theory of beams. Solution of the boundary value problem for computing the transverse components of translation and the internal actions in prismatic beams made from isotropic linearly elastic material. The Timoshenko theory of beams. A displacement and a stress function solution to transverse shear loading of beams. Computation of the shearing components of stress in beams subjected to bending without twisting. Shear center. Theory of plates. Buckling of elastic structures. Nonlinear theory of elasticity.