Shape optimization with hybrid-Trefftz displacement elements

The displacement model of the hybrid-Tre1tz 9nite element formulation is applied to the shape optimizationof linear elastostatic problems. The model is based onthe direct approximationof the displacements in the domain of the element and of the tractions on its boundary. The independent description of the geometry is based onthe parametric descriptionof the shape of the element sides. The 9nite element solving system is symmetric and sparse. As the displacement approximation is extracted from the solution set of the governing di1erential equations, all structural matrices are de9ned by boundary integral expressions. The approximation bases are compact and naturally p-hierarchical. High-order approximations are implemented to obtain accurate solutions using coarse meshes of macro-elements. The sensitivities are determined analytically and remeshing is not implemented during the optimization procedure because the elements are weakly sensitive to gross shape distortion. Numerical testing is based on a standard set of two-dimensional linear elastostatic problems