**Recommended reading:**

T.
Mura, T. Koya, Variational methods in mechanics, OUP 1992.

H.M. Westergaard, Theory of elasticity and plasticity, Dover, 1964.

S. Wolfram, The Mathematica Book, 4th ed., CUP 1999.

and

Lecture notes and Mathematica example files

To open PDF versions of lecture notes, click on 'Lecture #'

To download example Mathematica notebooks, right-mouse-click on one of the .nb files listed below, and 'Save link as...' in a local directory.

The
Department currently holds a license for 14 simultaneous copies of
Mathematica.

You
can use the program to study the examples in the ECS lab (the Solarium)
on any of the machines booth36.ecs to booth50.ecs (inclusive).

To
run Mathematica, type start_mathematica. This will start a window titled "Mathematica4.0 Execution Window".

Run
Mathematica in this window by typing mathematica.

Fundamentals of elasticity: strain energy density, generalised Hooke's law, elastic coefficients. Equilibrium and compatibility equations. Plane strain and generalised plane stress. Point loading of a wedge and fundamental singular solutions. Connection with the Boundary Element Method.

**Lecture
2.**

Introduction
to further stress analysis. Mimimum energy principles in the Theory of
Elasticity. Finding solutions by energy minimisation. Elements of
variational calculus: formulation and solution of the Euler equation.
Example problem: bent beam. Rayleigh-Ritz method. Galerkin method.
Using Mathematica.

intro.nb

eulerbeam.nb

ritzbeam.nb

ritzbeamn.nb

Further examples on the Rayleigh-Ritz method: cantilever problem. Piecewise R-R. The connection between the R-R method and matrix methods. The connection between piecewise R-R method and the FEM. R-R in two dimensions: plate problems.

ritzlever.nb

ritzlevern.nb

ritzpiece.nb

shapefun.nb

tie.nb

ritzplate.nb

**Lecture
4.**

Williams
asymptotic analysis of stresses in the vicinity of a wedge. Complex
variable approach to plane elasticity. The Westergaard solution. Crack
tip stress fields. Stress intensity factor.

This page was last modified on 15 January 2008.

Professor AM Korsunsky's home page.