Error Criterion for Solution of Torsional Problems

Abstract

An error criterion for the optimization of finite element meshes based on the smoothness of the shear‐stress flow in torsional problems of prismatic bars is presented. Extensions are made to handle composite sections. In this method, nodes are added in regions of high error, i.e., regions where the interelement angular deviation in the shear‐stress vector exceeds a prescribed value, until the desired accuracy is achieved. This technique is implemented in a general purpose, finite element software called KANTHAM. A test problem, whose closed‐form solution is known, is executed to show the accuracy of the technique. The same problem is solved by the same program, modified to incorporate second‐order elements, using residuals as the error indicator for adaptive refinement, for comparative purposes. The proposed method is found to be computationally efficient and simple to implement.