Convergence of the TRUNC plate element

Abstract The paper establishes a detailed mathematical analysis of the TRUNC element proposed by Bergan et al. [3] and developed further by Argyris et al. [1, 2]. It is shown that the new element uses the same finite element space as Zienkiewicz's incompatible cubic element [4], but its variational formulation is different through the application of numerical integrations to a certain part of the stiffness matrix. The convergence of the TRUNC element for an arbitrary mesh geometry is proved here and the error bounds for both moments and displacements are derived.