The displacement model of the hybrid-{T}refftz finite element formulation is applied to the solution of geometrically and physically linear static and dynamic problems. As the approximation bases solve locally the governing system of differential equations, the errors in the approximation affect only the implementation of the boundary conditions. Potential and elastostatic problems are used to illustrate the enforcement of the boundary conditions and the convergence of the solutions in energy, stresses and displacements, under both p- and h-refinement sequences and their insensitivity to mesh distortion, incompressibility and positioning of the coordinate system of the approximation basis. Also illustrated is the use of elements with arbitrary geometry and the efficiency that can be reached by including in the bases the solutions associated with dominant local effects, in particular those associated with singular stress fields. An adaptive p-refinement algorithm that exploits the naturally hierarchical nature of the approximation bases is presented and assessed. The formulation is generalised for elastodynamic analysis in the frequency domain of both bounded and unbounded domains, which are modelled either with absorbing boundary conditions or with semi-infinite elements that satisfy the Sommerfeld condition. The performance of the formulation is illustrated with tests on the convergence of the solutions in energy, stresses and displacements and on their insensitivity to mesh distortion, wave length and position of the absorbing boundary, for a wide spectrum of forcing frequencies and under both p- and h-refinement sequences.

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