SUMMARYA family of p-method plane elasticity elements is derived based on the hybrid Trefftz formulation.' Exact solutions of the LambNavier 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.', 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.

This paper presents a finite-element analysis of vibration control in planar mechanisms consisting of flexible links provided with nearly collocated piezoceramic sensors and actuators. Euler-Bemoulli-theoty-based beam finite elements with p-convergence capabilities have been cast into a total Lagrangian formulation in order to represent large rotations of the links. A simple control strategy based on the placement of closed-loop poles has been applied. Numerical predictions of active vibration control in links undergoing geometrically non-linear deflections of the von Karman class are presented.

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