Stress Field Gradient Analysis Technique Using Lower-Order Elements

For evaluating the stress gradient, a mathematical technique based on the stress field of lower-order elements is developed in this paper. With nodal stress results and location information, an overdetermined and inconsistent equation of stress gradient is established and the minimum norm least squares solution is obtained by the Moore-Penrose pseudoinverse. This technique can be applied to any element type in comparison with the superconvergent patch (SCP) recovery for the stress gradient, which requires the quadratic elements at least and has to invert the Jacobi and Hessian matrices. The accuracy and validity of the presented method are demonstrated by two examples, especially its merit of achieving high accuracy with lower-order linear elements. This method can be conveniently introduced into the general finite element analysis programs as a postprocessing module.