Structural shape sensitivity analysis - Relationship between material derivative and control volume approaches

AIAA Journal ◽  
1992 ◽  
Vol 30 (6) ◽  
pp. 1638-1648 ◽  
Author(s):  
Jasbir S. Arora ◽  
Tae Hee Lee ◽  
J. B. Cardoso
Keyword(s):  
Sensitivity Analysis ◽  
Control Volume ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Structural Shape ◽  
Material Derivative ◽  
And Control

scholarly journals Structural shape sensitivity analysis for nonlinear material models with strain softening

1999 ◽  
Vol 17 (2-3) ◽  
pp. 162-171 ◽  
Author(s):  
G. Bugeda ◽  
L. Gil ◽  
E. O�ate
Keyword(s):  
Sensitivity Analysis ◽  
Strain Softening ◽  
Nonlinear Material ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Structural Shape ◽  
Material Models

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.

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.

Level Set Method for Topological Optimization of the Naiver-Stokes Fluid Flow

2012 ◽  
Vol 182-183 ◽  
pp. 1668-1672
Author(s):  
Xian Bao Duan ◽  
Fu Cai Qian ◽  
Xin Qiang Qin
Keyword(s):  
Sensitivity Analysis ◽  
Fluid Flow ◽  
Level Set Method ◽  
Level Set ◽  
Topological Optimization ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis ◽  
Material Derivative ◽  
Level Set Function ◽  
Stokes Fluid

This paper presents a general algorithm for topological optimization of the incompressible Navier-Stokes fluid flow based on a level set method. This is a direct extension of our previous work on Stokes flow of such problems. First we obtain the shape sensitivity analysis using the material derivative concept and adjoint variable technique, and then we couple the shape sensitivity analysis result into the level set function as the advection velocity. Since the level set method is implemented in an Euleran framework, the computational cost of the proposed algorithm is moderate. A Benchmark example is provided to illustrate the efficiency and validity of this method.

Continuum-based Shape Sensitivity Analysis for Steady-state Metal Forming Processes

2007 ◽  
Vol 10 (2) ◽  
pp. 195-218 ◽  
Author(s):  
Jalaja Repalle ◽  
Ramana V Grandhi ◽  
Joo Hoo Choi
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Metal Forming ◽  
Shape Sensitivity ◽  
Shape Sensitivity Analysis
Sign in / Sign up

Export Citation Format

Share Document