Analysis of strain, deformation, affine deformation, infinitesimal affaine deformation, geometrical interpretation of the components of strain, principal directions, invariants, general infinitesimal deformation, Examples of strain, strain compatibility equations; Analysis of stress, body and surface forces, stress tensor, equations of equilibrium, stress quadric of Cauchy, examples of stress; The strain – energy function and its connection with hooks law, Saint Venant's principle. Boundary value problems in elasticity; Extension, bending and Torsion: statement of problem, extension of beams by longitudinal forces, Beam stretched by its own weight, Bending of beams by terminal couples of elliptic cylinder, Torsion of a circular shaft, Torsion of cylindrical bars, stress function, Torsion of elliptical cylinder; Two-dimensional elastostatic problems: plane deformation, plane stress, Generalized plane stress, plane elastostatic problems, Airy’s stress function, General solution of Biharmonic equation, formulas for stresses and displacements, the structure of the functions ø(z) and φ(Z); Vibration of elastics solids, wave propagation in infinite regions, Ryleigh and Love waves . |