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.