Variational Principles for EIastoplastic Continua∗

Eggers, H.

doi:10.1080/03601217408907272

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1978

1985

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Cited by 7 publications

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Yielding of plates with hardening and large deformations

Eggers

Kröplin

1978

Numerical Meth Engineering

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A mixed finite element technique is used to study the influence of yielding on buckled plates. Orthogonal anisotropic hardening is determined solely by a yield condition, which is introduced into a mixed functional for the elastic plate by Lagrange Multipliers. The Euler equations of the constrained functional include Prager's normality rule.Numerical results are given for rectangular plates of different size calculated for various material properties. DUALISM IN THE PLASTICITY THEORYGeneralized stresses u will be called dual to generalized strains E, if the product yields the energy U = U ' . E . (1)If the stresses u are fixed for the parts of an arbitrary loaded body, the dual strains E, in general, cannot be zero and vice versa.Using the dualism between the generalized stresses and strains a clear explanation of Prager's normality rule can be given. It is illustrated in Figure 1 for a simple beam with plastic hinges. The generalized stresses u are the internal forces and moments, and the generalized plastic strains E' are the deformations of the plastic hinge.

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