Aims

The purpose of this course is to introduce the basic theories and knowledge and general solution techniques of elasticity and plasticity, covering the theory of tress and strain, the introduction of stress-strain constitutive relation, the solution techniques in two-dimensional and three-dimensional boundary value problems of elasticity and plasticity, the energy principles and energy method of solution of solid continuum mechanics, and the elementary theory of classical Kirchhoff plate. As a basic branch of solid mechanics, it is intended to give graduate students sound foundations on which to build advanced courses such as thermal elasticity and plasticity, fracture mechanics, the theory of plates and shells, mechanics of composite materials, and the computational mechanics.

Intended learning outcomes

By studying this course and reading relevant Chinese version books, the students will be able to:

1) Understand and apply the basic theories, knowledge and solution in boundary value problems of elasticity and plasticity;

2) Understand and apply the energy principle and approximate solution method of solid mechanics;

3) Apply the theories, knowledge and solution skills to the study of analysis of stress and strain, fracture and strength problems, numerical methods for solid mechanics and advanced theories of elasticity and plasticity, and the design of effective structures in engineering.

Brief description of content

1.Fundamental assumptions of elasticity theory and certain mathematic preliminaries

2.Theory of tress and strain

3.Stress-strain constitutive relations

4.Boundary value problems and its general solution techniques of elasticity

5.Two-dimensional problems and its solution methods

6.Energy principle and approximate solution method of solid mechanics

7.Kirchhoff plate theory

8.Basic concepts in plasticity

9.Yield criteria and deformation theory of plasticity

10.Two-dimensional problems and its solution method of plasticity

Timetable

Semester 1 (autumn)

Course material

Introduction to elasticity and plasticity, Ed by Yang Guitong, Tsinghua University Press, 2007

Indicative reading

Timoshenko S P and Goodier J N, Theory of Elasticity, Tsinghua University Press, 2004

Barber J R, Elasticity, Springer Press, 2009

Roberts M J, Deformation theory of plasticity, Bull Bridge Publishing, 2008