A novel four-node quadrilateral smoothing element for stress enhancement and error estimation

A four-node, quadrilateral smoothing element is developed based upon a penalized-discrete-least-squares variational formulation. The smoothing methodology recovers C1-continuous stresses, thus enabling e¤ective a posteriori error estimation and automatic adaptive mesh reÞnement. The element formulation is originated with a Þve-node macro-element conÞguration consisting of four triangular anisoparametric smoothing elements in a cross-diagonal pattern. This element pattern enables a convenient closed-form solution for the degrees of freedom of the interior node, resulting from enforcing explicitly a set of natural edge-wise penalty constraints. The degree-of-freedom reduction scheme leads to a very e¦cient formulation of a four-node quadrilateral smoothing element without any compromise in robustness and accuracy of the smoothing analysis. The application examples include stress recovery and error estimation in adaptive mesh reÞnement solutions for an elasticity problem and an aerospace structural component. Copyright