Elastostatics of Structures with Unilateral Conditions on Stress and Displacement Fields
A general analysis of the elastostatic problem for structures with unilateral conditions on the stress distributions and on the displacement fields is developed.
The unilateral external constraints are assumed to define a convex conical manifold of admissible displacement fields.
Linear elastic materials with a convex constitutive condition on the stress are considered.
Anelastic strain are assumed to develop according to a convex coniugacy rule which generalizes the standard normality rule of perfect plasticity.
A complete theoretical scheme of the constitutive properties of the material is developed on this basis.
The existence of a convex and differentiable elastic strain energy is proved and the expression of the complementary elastic energy is given.
Two general results yielding the equilibrium and the geometric compatibility conditions under external and internal convex constraints are invoked to formulate the basic variational principles governing the elastostatic problem.
The minimum principles for the potential and the complementary energy functionals and the related error bounding techniques, extending the classical results in linear elasticity, are established.
It is shown that, under suitable regularity assumptions, namely the additivity of the involved subdifferentials, the stress formulation yields the existence of the solution for the elastostatic problem.
KeywordsDisplacement Field Linear Elastic Material Closed Convex Cone Unilateral Constraint Complementary Energy
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