Reasonable Selection of the Stress Modes in a Hybrid Stress Element
A reasonable condition is suggested to match the displacements and stresses in a hybrid stress element. Based on Hellinger-Reissner principle the displacement and stress modes are assumed to include the complete polynomials in the natural coordinates of an element. The work done by the assumed stresses on the nonconforming strains in an element should vanish. Taking this as a matching condition the dependent stress parameters can be eliminated and a rank sufficient hybrid stress element can be formulated. it contains the minimum number of stress parameters and is invariant for coordinates. Without perturbation a new 4-node (5 stress parameters) plane hybrid stress element has been developed. It can be arranged to satisfy the patch test. To demonstrate the properties of the element the solutions to some example problems are included
KeywordsPatch Test Stress Parameter ACTA MECHANICA SINICA Stress Mode Element Stiffness Matrix
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