Course detail
Applied Mechanics
FSI-WAMAcad. year: 2019/2020
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Gross, D., Seeling T.: Fracture mechanics. Springer-Verlag, Berlin, Heidelberg, 2006
Hill,R.: The mathematical theory of plasticity. Oxford U. P., Oxford, 1950
Chawla, K.K.: Composite materials. Science and engineering. Springer-Verlag, New York, Berlin, Heidelberg, 1998
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2.Differential formulation of problem of elasticity in displacements. Possibilities of solution. Variational formulation, virtual work principle, Lagrangean variational principle.
3. Mises condition of plasticity. Kinematic and isotropic stiffening. Prager and Ziegler condition for plasticity surface displacement.
4. Associated theory of plastic creep with combined stiffening. Basic assumptions. Normality rule, strain superposition principle.
5.Deformational variant of finite element method (FEM) for a two-dimensional problem. Triangulation, approximate functions for displacements, problem discretization.
6.FEM equilibrium equation for an element and the whole body. Local and global stiffness matrix.
7. Fundamentals of linear fracture mechanics. Stress intensity factor (SIF) K, J-integral, crack tip opening CTOD. Stress and strain states for the three basic modes I, II and III.
8.Paris-Erdogan’s law. Residual lifetime of the body with a defined crack. Possibilities of SIF evaluation for a generally located crack using FEM.
9.Mechanics of composite materials. Definition and basic terms, classification of composites. Mechanical properties of fibres and of matrix materials
10. Introduction to micromechanics and homogenization of composite materials. Hooke’s law for isotropic, orthotropic and transversally isotropic materials in principal material directions and in general directions. Directional stiffness matrix. Strength conditions.
11. Unidirectional long-fibre composite loaded in longitudinal direction. Elasticity modulus and strength. Critical and minimal volume of fibres.
12.Short-fibre unidirectional composite. Theory of load bearing. Transmission and critical length. Elasticity modulus in tension and strength.
13. Mechanisms of toughening of brittle matrix composites.
Computer-assisted exercise
Teacher / Lecturer
Syllabus
2. Stress state in a point of body.
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 structure
7.Three-dimensional beam structure in the system ANSYS
8.Plane problems in linear elasticity theory. Calculation of fracture mechanical parameters - stress intensity factor (SIF) K, J-integral, crack tip opening CTOD
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.
E-learning texts
UMTMB-AplikovanaMechanika-120924.pdf 1.24 MB