339-0920/01 – Mechanics of Continuum (MK)

Teach a students derive benefit from the newest knowledge of subject with possibility the knowledge further evolve and apply for complicated problems.

Vectors and Tensors. Physical components of vectors and 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, stress tensor, coordinate trans-formations 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, wirtual work and total potential energy, complementary energy, energy principles, boundary conditions.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 two and three Dimensions. Twist of circular shafts of constant cross section, pure bending of prismatic bars, shear centre, pure bending of plates, torsion of prismatic bars with non circle cross section, membrane analogy, stress function, axially symmetrical stress distribution in a solid, circular cylinder, twist of circular ring, pure bending of a circular plates, thermal stresses. The Grounds of Mechanics of Composite Materials. Type of material, homogenity, heterogenity or inhomogenity, isotropy, anisotropy, orthotropy, material response, types and classification of composite materials,lamina, laminate, basic lamina properties, degree of anisotropy, elastic behaviour of unidirectional lamina, stress-strain relations, relations between mathematical and engineering constants, transformation of stress and strain, transformation of elastic parameters, transformations of stress-strain relations in terms of engineering constants, elastic behaviour of multidirectional laminates, strain displacements relations, stress-strain relations of layer, force and moment resultants, symmetrical laminates.

[1] TIMOSHENKO, S. P.-GOODIER, J. N.: Theory of elasticity. New York-Toronto- London: Mc Graw-Hill, 1951, 3.ed.1970. [2] LEIPHOLZ, H.:Theory of elasticity. Noordhoff International Publishing Leyden, 1974. ISBN 90 286 0193 7

Příprava zadané problematiky v písemné formě.