Continuum Shape Sensitivity Analysis of Cracks in Functionally Graded Materials

2004 ◽  
Author(s):  
B. N. Rao ◽  
S. Rahman
Keyword(s):  
Sensitivity Analysis ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Functionally Graded ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Intensity Factors ◽  
Material Derivative ◽  
First Order ◽  
Element Method

This paper presents two new methods for conducting a continuum shape sensitivity analysis of a crack in an isotropic, linear-elastic functionally graded material. These methods involve the material derivative concept from continuum mechanics, domain integral representation of interaction integrals, known as the M-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of approximate numerical techniques, such as the meshless method, finite element method, boundary element method, or others. Three numerical examples are presented to calculate the first-order derivative of the stress-intensity factors. The results show that first-order sensitivities of stress intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.

Continuum Shape Sensitivity Analysis of Mode-I Fracture in Functionally Graded Materials

2003 ◽  
Author(s):  
B. N. Rao ◽  
S. Rahman
Keyword(s):  
Sensitivity Analysis ◽  
Variational Equation ◽  
Finite Difference Methods ◽  
Functionally Graded ◽  
J Integral ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Material Derivative ◽  
First Order ◽  
Element Method

This paper presents a new method for continuum shape sensitivity analysis of a crack in an isotropic, linear-elastic functionally graded material. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of approximate numerical techniques, such as the meshless method, finite element method, boundary element method, or others. In addition, since the J-integral is represented by domain integration, only the first-order sensitivity of the displacement field is needed. Numerical results show that first-order sensitivities of J-integral obtained by using the proposed method are in excellent agreement with the reference solutions obtained from finite-difference methods for the structural and crack geometries considered in this study.

Sensitivity of Stress Intensity Factors with Respect to the Crack Geometry by the Scaled Boundary Finite Element Method

2014 ◽  
Vol 553 ◽  
pp. 737-742
Author(s):  
Morsaleen Shehzad Chowdhury ◽  
Chong Ming Song ◽  
Wei Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Shape Sensitivity ◽  
Intensity Factors ◽  
Element Discretization ◽  
Crack Geometry ◽  
Scaled Boundary Finite Element ◽  
Element Method

The sensitivity of the stress intensity factors (SIFs) with respect to the crack geometry, shape sensitivity, plays an important role in the reliability analysis of cracked structures and many other fracture mechanics applications. This paper presents a numerical technique to evaluate the shape sensitivity using the scaled boundary finite element method. It combines the finite element formulations with the boundary element discretization. The crack surface remains meshless. The variation in crack geometry is modelled by applying direct differentiation with respect to the crack geometry, without remeshing. The sensitivity of the stress modes are not required for the calculation of the sensitivity of the SIFs. A numerical example demonstrates the efficiency, accuracy and simplicity of the technique.

Shape Sensitivity Analysis of Linear-Elastic Cracked Structures Under Mode-I Loading

2002 ◽  
Vol 124 (4) ◽  
pp. 476-482 ◽  
Author(s):  
Guofeng Chen ◽  
Sharif Rahman ◽  
Young Ho Park
Keyword(s):  
Sensitivity Analysis ◽  
Finite Difference Methods ◽  
Mode I ◽  
J Integral ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Material Derivative ◽  
Linear Elastic ◽  
Mode I Loading ◽  
Element Method

A new method is presented for shape sensitivity analysis of a crack in a homogeneous, isotropic, and linear-elastic body subject to mode-I loading conditions. The method involves the material derivative concept of continuum mechanics, domain integral representation of the J-integral, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations are independent of any approximate numerical techniques, such as the finite element method, boundary element method, or others. Since the J-integral is represented by domain integration, only the first-order sensitivity of displacement field is needed. Two numerical examples are presented to illustrate the proposed method. The results show that the maximum difference in calculating the sensitivity of J-integral by the proposed method and reference solutions by analytical or finite-difference methods is less than three percent.

A Coupled SBFEM-FEM Approach for Evaluating Stress Intensity Factors

2013 ◽  
Vol 353-356 ◽  
pp. 3369-3377 ◽  
Author(s):  
Ming Guang Shi ◽  
Chong Ming Song ◽  
Hong Zhong ◽  
Yan Jie Xu ◽  
Chu Han Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Complex Geometry ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Finite Element Software ◽  
Scaled Boundary Finite Element ◽  
Element Method

A coupled method between the Scaled Boundary Finite Element Method (SBFEM) and Finite Element Method (FEM) for evaluating the Stress Intensity Factors (SIFs) is presented and achieved on the platform of the commercial finite element software ABAQUS by using Python as the programming language. Automatic transformation of the finite elements around a singular point to a scaled boundary finite element subdomain is realized. This method combines the high accuracy of the SBFEM in computing the SIFs with the ability to handle material nonlinearity as well as powerful mesh generation and post processing ability of commercial FEM software. The validity and accuracy of the method is verified by analysis of several benchmark problems. The coupled algorithm shows a good converging performance, and with minimum additional treatment can be able to handle more problems that cannot be solved by either SBFEM or FEM itself. For fracture problems, it proposes an efficient way to represent stress singularity for problems with complex geometry, loading condition or certain nonlinearity.

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