دانلود رایگان مقاله روش انتگرال دامنه معادل مش مستقل برای ارزیابی انتگرال-J

Abstract

The equivalent domain integral method is a reliable tool for J-integral computation in two- and threedimensional elastic and elastic-plastic fracture mechanics problems. A variant of this method that is independent of finite element mesh is presented. Finite element solution of a boundary value problem is performed on a mesh composed of arbitrary elements. Nodal results are approximated by the moving least squares method that does not require knowledge of mesh topology. Domain integrals are evaluated on a background mesh of hexahedral elements. The mesh has the polar structure with the refinement towards the crack front. Elements of the background mesh are generated in the coordinate system associated with the crack front and then transformed to the global system. Domain integration for each background element is performed once during computations. Evaluation of J-integral for multiple domains is achieved by multiplication of an element domain integral with multiple domain weight functions. Performance of the proposed algorithm is demonstrated by the examples of three-dimensional cracks using meshes of both hexahedral and tetrahedral elements.

5. Conclusion

A mesh-independent variant of the equivalent domain integral method for estimating components of the J-integral and stress intensity factors KI, KII and KIII is presented. Calculations of domain integrals are performed in the global coordinate system based on the displacements and other data at nodes of the finite element mesh or any other points in space. Regular background mesh of hexahedral elements is introduced around the crack front for domain integration. Vector weight function q is used to obtain components of the J-integral in the local crack front coordinate system. Integration of the strain energy density over the crack surface in the J2 component is performed with a special algorithm that removes singularity using the double coordinate change. The energy release rate of the third type JIII can be computed if it is necessary to separate the stress intensity factors. Performance of the mesh-independent domain integral method is demonstrated on several numerical examples for threedimensional cracks. Two types of meshes were generated for each of the crack problems. The first mesh is composed of hexahedral 20-node elements and regular polar mesh around the crack front. Singular quarter-point elements were placed at the crack front. Tetrahedral 10-node elements were used in the second mesh that was irregular except for the specified element size at the crack front. Calculated J-integral values and values of the stress intensity factors are in agreement with reference solutions.