C1B Stress Analysis

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

A. Constantinescu, A.M. Korsunsky, Elasticity with Mathematica - An Introduction to Continuum Mechanics and Linear Elasticity, CUP 2007.  

 Lecture notes and Mathematica example files

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.
 

wedge.nb
punch.nb
intro1.nb

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

Lecture 3.
 

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.

williams.nb

Tutorial sheet and solution