Course Details
Elasticity and Plasticity
Academic Year 2025/26
Course Guarantor
Institute
Language of instruction
Czech, English
Credits
5 credits
Semester
winter
Forms and criteria of assessment
course-unit credit and examination
Offered to foreign students
To offer to students of all faculties
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
Syllabus
- 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 A brief historical reference of the theory of elasticity.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.
Exercise
13 weeks, 2 hours/week, compulsory
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 various theories.
- 4. The graphical representation of stress. The Mohr’s method.
- 5. Determining the work of external forces. Application of Lagrange and Castigliano's theorem. Calculation the strain energy.
- 6. Analytical solutions of wall – Airy stress function.
- 7. Principle of virtual work. Practical use of Castigliano‘s method.
- 8. Approximations of the line deflection of the beam by Ritz's method.
- 9. Application of the Galerkin method for solving simple problems of elasticity
- 10. Classical solutions of plates - method of an infinite series.
- 11. Calculation graph of internal forces of a cylindrical shell.
- 12. Determination a limit plastic resistance of the beam and plate.
- 13. Analysis of the formation of plastic hinges on a simple frame structure.