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Keywords:
plane elastostatics; stress equilibrium finite element; slab analogy; choice of the degrees of freedom; normal trace; stress tensor; complementary energy functional; existence; convergence
plane elastostatics; stress equilibrium finite element; slab analogy; choice of the degrees of freedom; normal trace; stress tensor; complementary energy functional; existence; convergence
Summary:
The fundamental problem in the application of the principle of complementary energy is the construction of suitable subsets that approximate the set of all statically admissible fields satisfying both the conditions of equilibrium inside the body and the static boundary conditions.
The notion "slab analogy" is motivated and the interface conditions for the Airy stress function are established at the contact of two domains. Some spaces of types of conforming equilibrium stress elements, which can be obtained by slab analogy, are investigated. A weak version of the Castigliano principle is established and the approximate variational problem is defined by using equilibrium stress fields. Some subspaces of equilibrium stress elements are introduced and a priori error estimates in the $L^2$-norm (provided the solutions are smooth enough) and convergence results are obtainded from the well-known results for compatible finite elements.
References:
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