Solving crack problems by an adaptive refinement procedure

Abstract

The effect of using collapsed quarter-point elements (CQPE) in conjunction with the adaptive refinement procedure in solving crack problems is investigated. It is found that by using the collapsed quarter-point elements around the tip of the crack, the efficiency of the adaptive procedure can be increased considerably. The number of times of remeshing, and hence the computation time, required for achieving a solution with the same prescribed accuracy is much reduced. In addition, it is demonstrated that by using a simple swapping procedure to control the mesh layout surrounding the crack tip, it is possible to obtain highly accurate estimates of stress intensity factors by the adaptive refinement procedure. From the results of the uniform and adaptive finite element analysis on a set of problems, we conclude that in general there is no strong correlation between the relative error in energy norm of the solution and the relative percentage error of the stress intensity factors. The latter is much more dependent on the mesh geometry around the crack tip. © 1992.