A displacement model of the hybrid-Trefftz finite element formulation based on the independent approximation of the displacements and tractions is presented. The finite element equilibrium and compatibility equations represent dual transformations and are described by boundary integral arrays, independent from the structural constitutive relations. Reciprocity is preserved in the finite element elasticity equations, which are also found to be described by boundary integral arrays when the displacement approximation functions are constrained to solve the Navier equations. As a consequence of this duality and reciprocity, the resulting boundary integral governing system is symmetric. The formulation is derived from first-principles of Mechanics and the associated energy theorems are recovered through mathematical programming equivalence theory. Conditions for static and kinematic admissibility of the finite element solutions are also presented.

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