Course detail

Elasticity and Plasticity

FAST-CD03Acad. year: 2014/2015

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

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Vlastislav Salajka, CSc.

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.

Planned learning activities and teaching methods

During lectures, standard model of theory explanation using the projector and blackboard is used. In the training course, students themselves solve tasks on a paper.

Assesment methods and criteria linked to learning outcomes

Conditions to get credit are active presence in training course (two absences are allowed) and successful evaluated of two tests. Tests are consists of both theoretical questions and practical tasks.

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.

Work placements

Not applicable.

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.

Recommended optional programme components

Extended theoretical knowledge of nonlinear mechanics including its applications in analysis of structures should be gained on a voluntary specialized seminar.

Prerequisites and corequisites

Not applicable.

Basic literature

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)
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

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)

Classification of course in study plans

  • Programme N-K-C-SI Master's

    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory

  • Programme N-P-C-SI Master's

    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory

  • Programme N-P-E-SI Master's

    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory
    branch S , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Vlastislav Salajka, CSc.

Syllabus

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.

Exercise

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Vlastislav Salajka, CSc.

Syllabus

1. The calculation of stress and strain using equations of elasticity - the relationship between stress and strain.
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.