Course detail

# Elasticity and Plasticity

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.

Department

Institute of Structural Mechanics (STM)

Learning outcomes of the course unit

By finishing the course, the student will know fundamental equation of elasticity describing the linear behavior of element. Student will be able to use virtual work principle for solving simple elasticity tasks. Student familiarize with Ritz method. Student is able to motel the structure as 2-D elasticity task (plane stress, deformation) and knows plate theory. Marginally have cognizance of shell theory. Student knows FEM principles and fundamentals of single type finite element derivation. Knowledge of Finite Element Method (FEM) is sufficient for understanding and usage programs based on FEM in practice.

Prerequisites

Diagrams of internal forces on a beam, the meaning of the quantities: stress, strain and displacement, Hook’s law, equilibrium conditions for a beam, physical and geometrical equations for a beam.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Servít, R., Doležalová, E., Crha, M.: Teorie pružnosti a plasticity I. STNL/ALFA Praha, 1981. (CS)
Servít, R., Drahoňovský, Z., Šejnoha, J., Kufner, V.: Teorie pružnosti a plasticity II. STNL/ALFA Praha, 1984. (CS)
Zdeněk Bittnar, Jiří Šejnoha: Numerical Methods in Structural Mechanics. ASCE Press, Thomas Telford, 1996. (EN)
Teplý, B., Šmiřák, S.: Pružnost a plasticita II.. VUT, 2000. (CS)
Bathe, K., J., Wilson, L.: Numerical Methods in Finite Element Analysis. Prentice-Hall, Inc., 1976. (EN)
Kolář, V., Němec, I, Kanický, V.: FEM – principy a praxe metody konečných prvků. Computer Press, 1997. (CS)

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech

Work placements

Not applicable.

Course curriculum

1. Tree-dimensional elasticity. Basic equations of theory of elasticity.
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.

Aims

During the course the student will obtain knowledge about basic quantities and relations of theory of elasticity for solid, beam, plane and plate structures. He will be skilled in the basic laws of mechanics - the principle of the virtual work and the principle of minimum of potential energy - and variational methods - Ritz method and finite elements method. After finishing the course he will be able to apply these methods on mentioned types of structures, to derive finite elements and to use computational programs based on finite elements methods in practise.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Exercise

26 hours, compulsory

Teacher / Lecturer