ME 6202 Energy & Variational Methods in Elasticity & Plasticity

ME 6770: Energy and Variational Methods in Elasticity and Plasticity
Offered Every Fall

Credit Hours:	3-0-3
Prerequisites:	MATH 2403 and (AE3120 or ME 3201)
Catalog Description:	Applications in energy and variational methods in engineering mechanics to elastic, plastic and dynamical behavior of deformable media. Crosslisted with AE 6770.
Text Book:	J. N. Reddy, Energy and Variational Methods in Applied Mechanics, 1st Edition, John Wiley, 1984.
Instructors:	Iwona Jasiuk (ME), Chris Lynch (ME), David McDowell (ME), Richard Neu (ME), Jianmin Qu (ME - Fall 2003), Min Zhou (ME), Olivier A. Bauchau (AE - Fall 2004) Mechanics of Materials Research Group

Goal:

This class will emphasize the applications of energy and variational methods in engineering mechanics. Several energy and numerical methods that are derived from the variational principles will be introduced and their use will be illustrated through various examples including elasticity, plasticity, dynamics, etc.

Audience:

Review of Fundamental Equations: - Stresses, strains and their relationships; - Equations of equilibrium; - Compatibility conditions; - Boundary conditions
Review of variational calculus: - Functional and its first variation; - Euler equations; - Natural and essential boundary conditions; - Constraint conditions and Lagrange multiplier
Virtual work: - Principle of virtual work; - Principle of complimentary virtual work
Variational Principles: - Principle of minimum potential energy; - Principle of minimum complimentary potential energy; - Hellinger-Reissner principle; - Hu-Washizu principle
Energy theorems in mechanics: - Castigliano's theorems; - Rayleigh-Betti reciprocity theorem
Approximate methods: - RayleighRitz method; - Galerkin method; - Weighted residual methods; - Finite element method; - Boundary element method
Applications: - Elasticity; * bending of beams and plates; * torsion of prismatic bars (St. Venant problem); * buckling and natural frequencies (eigenvalue problems); - Elastoplasticity; * deformation theory; * flow theory; * limit analysis; - Composite materials; * upper and lower bounds of effective properties

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Revised June 2004