RELATIVE PERFORMANCE OF THREE MESH-REDUCTION METHODS IN PREDICTING MODE III CRACK-TIP SINGULARITY

Abstract

DUE TO THEIR ROBUSTNESS IN HANDLING THE INHERENT SINGULARITY DIFFICULTIES ASSOCIATED WITH CRACK ANALYSIS, MESH-REDUCTION METHODS PRESENT AN AVALANCHE OF FORMULATIONS IN THE LITERATURE WHICH, SOMETIMES, ENTAILS MODIFICATIONS TO THEIR CONVENTIONAL/STANDARD FORMS FOR BETTER RESULTS. ALTHOUGH SUCH FORMULATIONS PROVIDE A POOL OF ALTERNATIVE CHOICES TO THE ANALYST, INCREASE IN THEIR NUMBER REQUIRES SOME RELATIVE ASSESS-MENT BETWEEN THEM IN ORDER TO GUARANTEE OPTIMUM CHOICE OF ANALYSIS TOOL. THE PRESENT STUDY ASSESSES THE APPLICABILITY AND RELATIVE PERFOR-MANCE OF THREE SUCH MESH-REDUCTION METHODS, NAMELY THE RADIAL BASIS FUNCTION (RBF) METHOD, THE BOUNDARY ELEMENT METHOD (BEM), AND THE METHOD OF FUNDAMENTAL SOLUTION (MFS) FOR MODE III CRACK ANALYSIS. IN ORDER TO HAVE A COMMON GROUND FOR PERFORMANCE COMPARISON THESE METHODS ARE, FIRST, TESTED IN THEIR MOST BASIC FORMS AND SIMPLEST CON-VENTIONAL FORMULATIONS POSSIBLE. FAILURE OF SOME OF THEM TO PROVIDE RELIABLE RESULTS CALLS FOR SOME ENRICHMENTS. YET, UNLESS WHERE NECES-SARY, EFFORTS ARE MADE TO ENSURE THAT UNNECESSARY COMPUTATIONALLY EXPENSIVE FORMULATIONS ARE AVOIDED. CONSEQUENTLY, THE BEM FORMULA-TION IS NOT ALTERED IN ANY WAY, AND MODIFICATIONS TO BOTH THE RBF AND MFS ARE LIMITED TO ENRICHMENT BY THE ADDITION OF, AT MOST, ONE SINGULAR TERM AND/OR THE DOMAIN-DECOMPOSITION TECHNIQUE. VERIFICATION IS ACHIEVED USING THE LITERATURE RESULTS AND/OR THOSE OBTAINED BY FEM IN THIS STUDY. SUMMARY OF THE RELATIVE ADVANTAGES AND LIMITATIONS OF THE METHODS FOR MODE III CRACK ANALYSIS IS GIVEN TO SERVE AS A YARD-STICK BASED ON WHICH THE CHOICE OF ONE OVER THE OTHERS MAY BE INFLUENCED.