Continuum Shape Sensitivity analysis of a mode-I fracture in functionally graded materials

2004 ◽  
Vol 36 (1) ◽  
pp. 62-75 ◽  
Author(s):  
S. Rahman ◽  
B. N. Rao
Keyword(s):  
Sensitivity Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded ◽  
Mode I ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Graded Materials ◽  
Mode I Fracture

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.

Sensitivity analysis in design of constructions made of functionally graded materials

2012 ◽  
Vol 227 (1) ◽  
pp. 19-28 ◽  
Author(s):  
Igor V Andrianov ◽  
Jan Awrejcewicz ◽  
Alexander A Diskovsky
Keyword(s):  
Sensitivity Analysis ◽  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Asymptotic Method ◽  
Functionally Graded ◽  
Asymptotic Solutions ◽  
Graded Materials ◽  
Material Parameters ◽  
Graded Material

This article is focused on analysis of influence of functionally graded material parameters in the problem of longitudinal rod deformations. This analysis is based on exact and asymptotic solutions. Accuracy rating of the proposed asymptotic method of calculating deformations in constructions made of functionally graded material is also given.

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.

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