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Variational methods and stress analysis
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| Organization: | University of Oxford |
| Department: | Engineering Science |
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College
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A four lecture undergraduate engineering course on variational methods and stress analysis.
Lecture 1: 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)
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)
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Variations, Rayleigh-Ritz, Galerkin, Euler, series
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http://users.ox.ac.uk/~engs0161/4me6.html
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