Development of point-wise error measures and an improved stress computation technique for shell structures

The analysis of shell structures remains a challenge. This is evidenced by the fact that there is continuous effort to develop successful high performance finite elements to improve solutions of shell structures. The objective of this work is to improve shell analysis by developing error analysis techniques for finite element models of these problems. These error measures can be used to drive the adaptive refinement techniques to produce improved results. Moreover, these error measures compare the stresses developed in the finite element model to those developed using local finite difference representation. This approach is successful because: (1) The error measures quantify the interelement stress jumps in the finite element solution by comparing the one-sided derivative of the finite element model to the smooth tresses computed across a patch of elements. (2) The finite difference representation contains the actual shell kinematics, while many finite element models only approximate the curved geometry, e.g. many finite element is represent the curved surface with flat shell elements. (3) Finite difference templates used in computing stresses have an order dictated by the order of the governing differential equation; this is not true for all finite element models.; The stresses computed using finite difference template are seen to be of better accuracy than the finite element results. This raises the possibility of using the local finite difference representation as a way to recover stresses from finite element models.