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Improved two-dimensional cracked finite element for crack fault diagnosis

Kaland A., Rao B. N.

Computer Assisted Methods in Engineering and Science

2012

Vol. 19, no. 3

213-239

In this paper the two-dimensional finite element with an embedded edge crack proposed by Potirniche et al. (2008) is improved further for crack depth ratios ranging up to 0.9 and for predicting the natural frequency of a cracked beam more accurately. The element is implemented in the commercial finite element code ABAQUS as user element subroutine. The accuracy of the proposed improved cracked element is verified by comparing the predicted, first natural frequency with available experimental data. Subsequently, a methodology to detect the crack’s location and size in conjunction with the proposed improved cracked element is also presented.

Mode I crack problems by coupled fractal finite element and meshfree method

Rao B. N., Rajesh K. N.

Computer Assisted Mechanics and Engineering Sciences

2010

Vol. 17, no. 2-3-4

113-135

This paper presents a coupling technique for integrating the fractal finite element method (FFEM) with element-free Galerkin method (EFGM) for analyzing homogeneous, isotropic, and two-dimensional linear-elastic cracked structures subjected to Mode I loading condition. FFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprise both the element-free Galerkin and the finite element shape functions, satisfy the consistency condition thus ensuring convergence of the proposed coupled FFEM-EFGM. The proposed method combines the best features of FFEM and EFGM, in the sense that no structured mesh or special enriched basis functions are necessary and no post-processing (employing any path-independent integrals) is needed to determine fracture parameters such as stress-intensity factors (SIFs) and T-stress. The numerical results show that SIFs and T-stress obtained using the proposed method, are in excellent agreement with the reference solutions for the structural and crack geometries considered in the present study. Also a parametric study is carried out to examine the effects of the integration order, the similarity ratio, the number of transformation terms, and the crack-length to width ratio, on the quality of the numerical solutions.