Czech

5

Institute of Structural Mechanics (STM)

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.

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.

Not applicable.

Not applicable.

Not applicable.

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.

Not applicable.

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.

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

Not applicable.

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)

26 hours, compulsory

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.