Hybrid trefftz plane elasticity elements with p ‐method capabilities

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Abstract
A family of p‐method plane elasticity elements is derived based on the hybrid Trefftz formulation.1 Exact solutions of the Lamé‐Navier equations are used for the intra‐element displacement field together with an independent displacement frame function field along the element boundary. The final unknowns are the parameters of the frame function field consisting of the usual degrees of freedom at corner nodes and an optional number of hierarchic degrees of freedom associated with the mid‐side nodes. Since the element matrices do not involve integration over the element area, the elements have a polygonal contour with an optional number of curved sides. The quadrilateral element has the same external appearance as the conventional p‐method plane elasticity element.2,3 But unlike in the conventional p‐method approach, suitable special‐purpose Trefftz functions are generally used to handle the singularity and/or stress concentration problems rather than a local mesh refinement. The practical efficiency of the new elements is assessed through a series of examples.

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