Extended finite element method for calculating crack tip singularity field of fracture mechanics

Abstract

The invention relates to an extended finite element method for calculating a crack tip singularity field in fracture mechanics. The extended finite element method comprises the following steps: S1, establishing a geometric model containing cracks, obtaining a bezier unit, inputting material parameters, Young modulus and Poisson's ratio, and applying boundary conditions; S2, obtaining projection points, corresponding to the control points of the bezier unit, on the geometric model; S3, based on the projection points, using a least square meshless method with a selective interpolation characteristic as an approximate primary function, and obtaining a displacement field; S4, carrying out re-approximation on the interpolation coefficient in the meshless method by utilizing the approximate primary function; S5, mapping the interpolation coefficient in the meshless method subjected to the re-approximation to enable the interpolation coefficient to correspond to the control point of the bezier unit; and S6, approximating the displacement field by using the mapped interpolation coefficient, and solving to obtain a final displacement field. According to the method, the crack tip singularity field can be efficiently captured without adding the degree of freedom, a good system equation condition number can be obtained, and the geometric accuracy of the model can be kept.

Description

technical field [0001] The invention relates to the field of computer-aided engineering, in particular to an extended finite element method for calculating the singular field of a crack tip in fracture mechanics. Background technique [0002] The finite element numerical simulation based on linear elastic fracture mechanics is one of the effective means to evaluate the fatigue life of the service structure and to trace the cause of structural fracture and damage. [0003] However, the standard finite element technique requires the crack surface to be consistent with the cell boundary, which brings difficulties in dynamic mesh division for crack propagation simulation. And because the crack tip has the characteristic of stress singularity, that is, the stress is infinite at the crack tip, it is difficult for the elements constructed based on polynomials to approximate the physical field with singular characteristics, resulting in a great loss of numerical accuracy. The propo...

AI Technical Summary

Problems solved by technology

However, due to the loss of geometric accuracy and the low accuracy of linear elements, discrete meshes often cannot give reliable surface stress results.

Images