Vectors and Tensors. Physical components of tensors.
Strain. Strain tensor, coordinate transformations for strains, principal
strains, determination of planes of principal strains, principal strain
invariants, maximum shear strains, Mohr circle representation, deviatoric
strain tensor.
Stress. Forces and stresses, coordinate transformations for stresses, principal
stresses, determination of planes of principal stresses, principal stress
invariants, maximum shear stresses, Mohr circle representation, deviatoric
stress tensor.
Elastic Solids. Constitutive equations for linear elastic solid, orthotropic
material, isotropic material, plane strain, plane stress, virtual work and
total potential energy, energy principles, complementary energy, boundary
conditions.
Linear Stress-Strain-Temperature Relations.
General Theories. Differential equations of equilibrium, condition of
compatibility, equations of equilibrium in terms of displacement, general
solution for the displacements.
Elementary Problems of Elasticity in three Dimensions. Twist of circular shafts
of constant cross section, pure bending of a prismatic bars, pure bending of
plates, torsion of a prismatic bars with non circle cross section, other
elementary solution, membrane analogy, bending of a prismatic bars, stress
function, shear centre, axially symmetrical stress distribution in a solid,
circular cylinder, twist of circular ring, pure bending of a circular plates,
thermal stresses.
Selected Advanced Topics. Stress concentrations, stress concentration factors -
theory of elasticity, stress concentration factor-combined loads, fracture
mechanics, failure criteria, contact stresses, geometry of the contact surface,
expressions for principal stresses, deflection of bodies in point of contact,
stress for two bodies in line contact.