330-3001/01 – Applied Mechanics (AM)

Educate students in basic procedures which are applied for a definition and solving of more exciting engineering technical problems in the sphere of mechanics of solid elastic deformable bodies. Ensure understanding of teaching problems. To learn the students apply gained theoretical peaces of knowledge in praxis.

Action of the forces on a body. Internal forces, method of sections, stress, deformation of the body. Normal stress, strain and deformation on terms of simple tension (compression). Hooke`s law for simple tension, Poisson`s ratio, Saint-Venant`s principle. Stress on an oblique plane under axial loading. Plane stress state. Stresses in an inclined plane. Mohr`s circle for stress. Principal stresses and principal planes. Application of Mohr`s circle to various types of stress analysis. Stresses and strains in pure shear. Extended Hooke`s law. Change in volume. Strain energy for a general state of stress. Volumetric and distortion strain energy density. Criteria of failure for ductile and brittle materials under three-dimensional state of stress, failure surface in Haigh-Westergard principal stress space. Maximum shear stress criterion (Guest`s or Tresca`s criterion), distortion energy criterion (von Mises or HMH criterion). Maximum normal stress fracture criterion (Rankine`s criterion), Coulomb-Mohr fracture criterion. Analysis of strain at a point in a deformable body. Strain-displacement relations. The Green-Lagrange strain tensor, Cauchy`s small (linear) strain tensor. Small strain tensor invariants. Principal strains. Principal axes of strain. Spherical tensor, strain deviator tensor. Octahedral normal and shear strains. Compatibility of strain conditions. 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. Spherical tensor and stress deviator. Normal and shear stresses on the octahedral plane. The method of Mohr`s circles. Cauchy`s differential equations of equilibrium. Physical equations for anisotropic, orthotropic, transversely isotropic and isotropic, linearly elastic homogeneous solid. Boundary conditions. Planar problems of the theory of elasticity, plane stress and plane strain. Airy`s stress function, biharmonic differential equation in orthogonal Cartesian coordinates. The planar problem in polar coordinates.

FRYDRÝŠEK, K., ADÁMKOVÁ, L.: Mechanics of Materials 1 (Introduction, Simple Stress and Strain, Basic of Bending), Faculty of Mechanical Engineering, VŠB-Technical University of Ostrava, Ostrava, ISBN 978-80-248-1550-3, Ostrava, 2007, Czech Republic, pp. 179.