1. Orthogonal transformation. Transformation of coordinate system. Transformation properties of vectors and tensors. Physical components of vectors and tensors.
2. Analysis of strain at a point in a deformable body. Strain-displacement relations. Geometric meaning of individual components of Cauchy strain tensor.
3. The state of stress at a point in a body. Stress tensor. Invariants of the stress tensor. Principal stresses, principal planes, principal directions of the stress tensor at a point.
4. Mohr´s representation of 3D stress state. Extreme shear stresses. Spherical and deviatoric stress tensor. Octahedral normal and shear strains.
5. Strain tensor invariants. Principal strains and directions. Maximum shear strains. Spherical and deviatoric strain tensor. Normal and shear stresses on the octahedral plane.
6. Compatibility and equilibrium equations.
7. Constitutive equations. Hook´s law for anisotropic, orthotropic, transversely isotropic and isotropic material. Pre-heating and initial deformation effect on constitutive equations.
8. Boundary conditions. Solution of the 2D elastic problem, formulation in terms of displacements - Lamé (Navier) equations, formulation in terms of stresses - Beltrami-Michell equations.
9. Two variants of the 2D elastic problem. Plane stress and plane strain problem. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates.
10. Expression of boundary conditions using Airy´s stress function. Biharmonic equation in polar coordinates.
11. 2D elastic problem with axially symmetric stress distribution. Pure bending of the circular curved bar.
12. Bending of the circular curved bar with the force acting at the free end. The effect of circular hole on the stress field in the plate.
13. The Flamant-Boussinesq problem.
14. Axially symmetric problem in cylindrical coordinates. Force acting in point of infinite isotropic elastic space (Kelvin problem).
15. Free torsion of arbitrary cross-section.
2. Analysis of strain at a point in a deformable body. Strain-displacement relations. Geometric meaning of individual components of Cauchy strain tensor.
3. The state of stress at a point in a body. Stress tensor. Invariants of the stress tensor. Principal stresses, principal planes, principal directions of the stress tensor at a point.
4. Mohr´s representation of 3D stress state. Extreme shear stresses. Spherical and deviatoric stress tensor. Octahedral normal and shear strains.
5. Strain tensor invariants. Principal strains and directions. Maximum shear strains. Spherical and deviatoric strain tensor. Normal and shear stresses on the octahedral plane.
6. Compatibility and equilibrium equations.
7. Constitutive equations. Hook´s law for anisotropic, orthotropic, transversely isotropic and isotropic material. Pre-heating and initial deformation effect on constitutive equations.
8. Boundary conditions. Solution of the 2D elastic problem, formulation in terms of displacements - Lamé (Navier) equations, formulation in terms of stresses - Beltrami-Michell equations.
9. Two variants of the 2D elastic problem. Plane stress and plane strain problem. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates.
10. Expression of boundary conditions using Airy´s stress function. Biharmonic equation in polar coordinates.
11. 2D elastic problem with axially symmetric stress distribution. Pure bending of the circular curved bar.
12. Bending of the circular curved bar with the force acting at the free end. The effect of circular hole on the stress field in the plate.
13. The Flamant-Boussinesq problem.
14. Axially symmetric problem in cylindrical coordinates. Force acting in point of infinite isotropic elastic space (Kelvin problem).
15. Free torsion of arbitrary cross-section.