Self-adaptive finite elements in fracture mechanics

Abstract

A new finite element capability which permits the analyst to vary the order of polynomial approximation over each finite element is discussed with reference to its potential for application to stress intensity factor computations in linear elastic fracture mechanics. Computational experiments, in which polynomial orders ranging from 1 to 8 were used, indicated strong and monotonie convergence of the strain energy release rate even for very coarse finite element meshes as the order p of the approximating polynomial was increased. Pointwise convergence of stresses was achieved by averaging approximations of different polynomial orders. The strong and monotonie convergence of K I factors with respect to increasing p provides a new method for computing stress intensity factors. The main advantage of this method is that the accuracy of approximation can be established without mesh refinement or the use of special procedures.