THE SIMULATION OF MULTIPLE CRACKS IN WELDED STRUCTURE USING ELEMENT FREE GALERKIN METHOD

Abstract

Welded joints are generally used in manufacturing various mechanical structures. Unfortunately, welds are often the weakest portions of these structures. Cracks are developed in weldment which may cause catastrophic failure of these components. Therefore, it becomes necessary to analyze these cracked welded joints. Over the last decade or so, meshfree methods have been developed as a promising alternative to the finite element methods. The goal of meshfree methods is to facilitate the simulation of increasingly demanding problems, which may be used to handle large deformations, advanced materials, complex geometry, nonlinear material behavior, discontinuities and singularities. Though, the finite element method is used rigorously in various applications due to its accuracy, simplicity and flexibility; but it has got some deficiencies such as element locking, discontinuous derivatives of the primary variable at element boundaries and re-meshing. In this dissertation work, welding joints having multiple cracks is analyzed using Element Free Galerkin Method (EFGM) in linear elastic fracture mechanics. In EFGM, elements are not required for the interpolation of field variables; only nodal data is required for its implementation. The essential feature of this method is the use of moving least square approximations, where the dependent variable at any point is obtained by minimizing a weighted discrete L2 -error norm involving the nodal variable within a small domain surrounding the point. Intrinsic enrichment EFGM criterion is used for the simulation of the crack problems. In this enrichment approach, the asymptotic displacement is added to basis function which enables the EFGM to accurately capture singular stress field in the crack tip region. This technique is then used for the analysis of a multiple crack welded joint problems under mixed mode loading. Stress intensity factors are calculated for various model problems. The results obtained by EFGM are compared with standard finite element simulations, and are found to be quite accurate.