Stress as a constraint reaction in rigid bodies
by
R.L. Fosdick and G. Royer
in
J. Elasticity, 74, 265-276, 2004.
Category: Journal Article
Keywords: rigid body mechanics, constraint minimization, Riesz representation, Lagrange multipliers.
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Abstract:
The unique construction of stress as a constraint reaction in a rigid body loaded on its boundary in a state of equilibrium is described through the use of the elementary variational problem of minimum potential energy. We suppose that the body is naturally constrained to be strain free and this leads to a non-trivial constrained minimization problem. Our construction is based on an application of a Riesz-like representation theorem within the context of the classical Lagrange multiplier theorem of variational calculus.
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