Finite Element Analysis of Axisymmetric Cracked Solids

Abstract

This investigation was concerned with the development of a finite element facility for the determination of fracture mechanics and general stress analysis data in axisymmetric solids. The work was carried out in two stages. In the first stage a finite element program for solving axisymmetric problems subjected to axisymmetric loading was developed. The element used was a six node isoparametric triangularring element. An automatic mesh generation scheme was developed which reduced the effort of preparing the required input data. A complete program incorporating this scheme is described and examples of its application are presented which show very good agreement with theoretical and other finite element solutions. In the second stage the general finite element program was augmented to provide a fracture mechanics facility. In order to cater for singularities in the crack tip region, a singular core, over which an analytic solution is used, was embedded into the finite element mesh surrounding the crack tip. The modifications to the standard finite element program are described and several mode I and mixed mode I and II examples were solved to check the influence of mesh design and core parameters. The results obtained demonstrate the usefulness and accuracy of the technique and compare very well with solutions available in the published literature. A complete listing of all the computer programs is presented together with their input data instructions.