ME 552: Energy Methods in Mechanics

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ME 552 - Energy Methods in Mechanics

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Catalog Description

552 Energy Methods in Mechanics. (Crosslisted with EMA 552.) Irr; 3 cr (P-A). Variational principles of mechanics, virtual displacements, minimum potential energy; Hamilton's principle and Lagrange equations. Applications include stress analysis, elastic stability, dynamics and vibrations of rigid and elastic systems. P: Sr st or cons inst.

Course Prerequisite(s)

See catalog description above.

Prerequisite knowledge and/or skills

First course in stress/strain analysis
First course in dynamics
Calculus and differential equations

Textbook(s) and/or other required material

I. H. Shames, C. L. Dym, Energy and Finite Element Methods in Structural Mechanics, Hemisphere Publishing, 1985.

Course objectives

The purpose of the course is to develop skills and experience in mechanical analysis and design using the energy methods of applied mechanics. Such training is intended to enhance the problem solving ability of practicing engineers and also serve as background for more advanced courses in dynamics, vibration, structural mechanics and finite element methods.

Topics covered

Generalized coordinates, Fourier's inequality, virtual work (3 classes)
Generalized force, potential energy, stability (4 classes)
Energy in beams, columns, rings, shafts (3 classes)
Trusses - pin jointed/flexural members (4 classes)
Introductory variational calculus (3 classes)
Applications to structural components (2 classes)
Isoperimetric problems (2 classes)
Rayleigh Ritz, Galerkin, Kantorovich methods (3 classes)
Strain energy for elastic bodies (2 classes)
Complementary energy (1 class)
Castigliano's Theorem (2 classes)
Reissner's Theorem (1 class)
Unit dummy load method (2 classes)
Statically indeterminate systems (2 classes)
Classical plate theory (5 classes)
Hamilton's principle/Lagrange equations (5 classes)

Person(s) who prepared this description

Edward G. Lovell

Copyright 2007 The Board of Regents of the University of Wisconsin System
Date last modified: 04-Aug-2007
Content by: deptinfo@me.engr.wisc.edu
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