Elasticity and Plasticity
FAST-NDA015Acad. year: 2020/2021
Basic equations of theory of elasticity, stress and strain analysis in point, two-dimensional problems – plane stress and plane strain, axisymmetric problems, duality solution of the problem, energy theorems, variational methods, theory of thick and thin plates, theory of shells, static solution of foundation structures, models of soil, basics of elastic-plastic analysis, physical equations for elastic-plastic material with hardening, analysis of elastic-plastic state structures, the plastic limit of load carrying capacity.
Institute of Structural Mechanics (STM)
Offered to foreign students
Of all faculties
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.
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. Stress states of beam and combinations thereof. Statically indeterminate beams systems and force and displacement methods of solution. The matrix notation of solutions.
Recommended optional programme components
Recommended or required reading
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
1. A brief historical reference of the theory of elasticity. Fields in the theory of the continua and the definition of state variables.
2. Basic equations of elasticity. The derivation of geometric equations and physics equations. The properties of the strain and stress tensors. The equilibrium conditions and compatibility conditions.
3. Analysis of stress and strain in point. Plane stress and plane strain. Levy condition. Airy‘s stress function. Procedure for solving plane stress.
4. Axisymmetric problems - basic equations of plane problem in polar coordinates. Rheological models of material.
5. The deformation of non-force effects. Display of stress (Becker-Westergard, Mohr).
6. The potential energy of deformation and strain of work. Energy principles. The principle of virtual work and variational methods in continuum mechanics.
7. Theory of plates. Types of plates, boundary conditions. Special types of plates.
8. Analytical solution of plates in a rectangular coordinate system. Approximate solution of plates.
9. Introduction to the theory of shells. Membrane and bending state of stress. Internal forces with shells.
10. Cylindrical shells - basic equations of the bending theory of cylindrical shells. Flat shell.
11. Static solution of foundations. Models of soil.
12. Basics elastic-plastic analysis. The physical equations for elastic-plastic material with hardening.
13. Analysis of elastic-plastic state. The limit state plastic bearing capacity of beam structures.
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.