Three-dimensional hybrid-Trefftz stress elements

The stress model of the hybrid-Tre!tz "nite element formulation is applied to the linear elastostatic analysis of solids. The stresses are approximated in the domain of the element and displacements on its boundary. Complete, linearly independent, hierarchical polynomial approximation functions are used in both domain and boundary approximations. The displacement basis is de"ned independently on each inter-element surface. Continuity at the edges and on the corners of the elements is not enforced a priori. The stress basis is constrained to solve locally the Beltrami governing di!erential equation. It is derived from the associated Papkovitch}Neuber elastic displacement solution. Generalized variables are used to ensure that the approximations are independent of the geometric description of the elements. The solving system is derived directly from the fundamental relations of elastostatics. The solving system is symmetric, when the same property applies to the local elasticity condition, sparse, described by boundary integral arrays and well suited to p-re"nement and parallel processing. The numerical implementation of these equations is discussed and numerical tests are presented to illustrate the performance of the "nite element formulation