Course detail
Elasticity and Plasticity
FAST-CD03Acad. year: 2012/2013
Basic equations of theory of elasticity, two-dimensional problems – plane stress and plane strain, axisymmetric problems, energy theorems, variational methods, computational models, theory of the finite element method, the finite elements for 2D problems, isoparametric elements, Gauss numerical integration, theory of thick and thin plates, introduction into shell theory, shell elements, tree-dimensional elements, static solution of foundation, models of soil, analysis of elastic-plastic and limit state of beam structures.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
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
2. Plane stress and plane strain state. Axisymetric problems.
3. Energy principles and variational methods in continuum mechanics.
4. Computational models.
5. Principle of finite elements method.
6. The finite elements for 2D problems.
7. Isoparametric elements. Gauss numerical integration.
8. Theory of thick plates.
9. Theory of thin plates. Boundary conditions. The special types of plates.
10. Introduction into shell theory. Membrane and bending state.
11. Shell elements. Tree-dimensional elements.
12. Static solution of foundation. Models of soil.
13. Analysis of elastic-plastic and limit state of beam structures.
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Servít, R., Drahoňovský, Z., Šejnoha, J., Kufner, V.: Teorie pružnosti a plasticity II. STNL/ALFA Praha, 1984. (CS)
Teplý, B., Šmiřák, S.: Pružnost a plasticita II.. VUT, 2000. (CS)
Zdeněk Bittnar, Jiří Šejnoha: Numerical Methods in Structural Mechanics. ASCE Press, Thomas Telford, 1996. (EN)
Recommended reading
Kolář, V., Němec, I, Kanický, V.: FEM – principy a praxe metody konečných prvků. Computer Press, 1997. (CS)
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Plane stress and plane strain state. Axisymmetric problem.
3. Energy principles and variational methods in continuum mechanics.
4. Computational models.
5. Principle of finite elements method.
6. The finite elements for 2D problems.
7. Isoparametric elements. Gauss numerical integration.
8. Theory of thick plates.
9. Theory of thin plates. Boundary conditions. The special types of plates.
10. Introduction into shell theory. Membrane and bending state.
11. Shell elements. Tree-dimensional elements.
12. Static solution of foundation. Models of soil.
13. Analysis of elastic-plastic and limit state of beam structures.
Exercise
Teacher / Lecturer
Syllabus
2. The principal stresses (stress invariants), the calculation for different cases of stress.
3. Strength and plasticity criteria - calculation of equivalent stress by different theories.
4. Determining the work of external forces. Application of Lagrange and Castigliano theorems. Calculation of the strain energy.
5. The principle of virtual work. Practical application of Castiglian’s theorem.
6. Approximation of the deflection curve of beam by Ritz method.
7. Derivation of flexibility matrix and stiffness matrix in problems of plane stress and strain.
8. The use of finite element method to solve truss structure.
9. Analysis of plane stress by FEM (triangular element, the effect of refinement mesh elements, compare with the calculation by beam theory).
10. Analysis of plane stress by FEM – continue.
11. A thin plate and implementation of boundary conditions. Principal and design moments.
12. Membrane and bending state of shells - the calculation of internal forces for the basic shapes of shell.
13. Analysis of plastic behavior of the bars and statically indeterminate structures.