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FSI-WAMAcad. year: 2025/2026
Introduction, basic terminology. Stress and strain tensors, principal stresses. Mathematical theory of elasticity, differential approach (equilibrium equations, Hooke´s law, geometrical equations, boundary conditions). Variational approach, principle of virtual work. Finite element method (FEM), displacement version. Fundamentals of linear fracture mechanics. Associated theory of plasticity. Kinematic and isotropic hardening rule, mixed hardening. Mechanics of composite materials, homogenization and elements of micromechanics. Stiffness and strength of the unidirectional fibre composite (lamina) in longitudinal and transversal direction. Stiffness and strength of the short fibre composites. Hooke's law of anisotropic, orthotropic and transversal orthotropic material in the principal material directions, strength conditions. Mechanisms of toughening of brittle matrix composites.
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1.Basic equations of mathematical theory of elasticity. Equilibrium equations. Geometrical equations General Hooke’s law 2. Stress state in a point of body, principal stresses, principal coordinate system.3.Differential formulation of problem of elasticity in displacements. Lame’s equations. Yield criterion.4. Virtual work principle. Lagrange’s principle. Ritz method.5.Deformational variant of finite element method (FEM). Basic FEM equations. Introduction into FEM program system ANSYS. Basic types of elements.6. FEM model creation in the FEM program system ANSYS. Solution of a simple two-dimensional beam structure7.2D modelling with utilization of plane stress, plane strain and rotational symmetry vs 3D models.8.Calculation of fracture mechanical parameters - stress intensity factor (SIF) K, J-integral.9.FEM determination of plastic zone ahead of a crack tip using various yield criteria.10.Homogenization of fibre composites using FEM -Material characteristics in longitudinal direction.11. Homogenization of fibre composites using FEM -Material characteristics in transversal direction. Effective temperature expansion of a composite in various directions.12.Final project. 13.Credit.
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