Abstract
The displacement model of the hybrid‐Trefftz finite element formulation is applied to the shape optimization of linear elastostatic problems. The model is based on the direct approximation of the displacements in the domain of the element and of the tractions on its boundary. The independent description of the geometry is based on the parametric description of the shape of the element sides. The finite element solving system is symmetric and sparse. As the displacement approximation is extracted from the solution set of the governing differential equations, all structural matrices are defined 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. Copyright © 2001 John Wiley & Sons, Ltd.