Abstract In this paper we develop a modification of the recently proposed Taylor series expansion-based formulation for computational solids to satisfy a generalized patch test. To achieve this property, the parametric derivatives of the strain rate-velocity matrix accounting for non-affine isoparametric element mappings and Taylor series expansion based on element averaging of the leading term are proposed within the computational framework. Besides passing the patch test the new reduced-quadrature formulation is demonstrated to have increased accuracy and robustness for unstructured and distorted meshes as compared with its predecessors.
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