Superconvergence and the superconvergent patch recovery
Finite Elements in Analysis and Design - Special issue: Robert J. Melosh Medal Competition
Finite Elements in Analysis and Design
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A 24-DOF quadrilateral hybrid stress element for couple stress theory is proposed in this study. In order to satisfy the equilibrium equation in the domain of the element, the $$21\beta $$ 21 β Airy stress functions are chosen a assumed stress interpolation functions, and beam functions are adopted as the displacement interpolation functions on the boundary. This element can satisfy weak C $$^{0}$$ 0 continuity with second-order accuracy and weak $$\hbox {C}^1$$ C 1 continuity simultaneously. So the element can pass the enhanced patch test of a convergence condition. Moreover, the reduced integration and a stresses smooth technique are introduced to improve the element accuracy. Numerical examples presented show that the proposed model can pass the $$\hbox {C}^{0-1}$$ C 0 - 1 enhanced patch test and indeed possesses higher accuracy. Besides, it does not exhibit extra zero energy modes and can capture the scale effects of microstructure.