Adjoint Design Sensitivity Analysis of Fracture Mechanics Using Molecular-Continuum Multiscale Approach

2011 ◽  
Author(s):  
Hyun-Seok Kim ◽  
Hong-Lae Jang ◽  
Min-Geun Kim ◽  
Seonho Cho
Keyword(s):  
Sensitivity Analysis ◽  
Projection Operator ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Generalized Langevin Equation ◽  
Multiscale Approach ◽  
Scale Analysis ◽  
Analysis Method ◽  
Sensitivity Analysis Method ◽  
Bridging Scale Method

We have developed a multiscale design sensitivity analysis method for transient dynamics using a bridging scale method by a projection operator for scale decomposition. Employing a mass-weighted projection operator, we can fully decouple the equations of motion into fine and coarse scales using the orthogonal property of complimentary projector to the mass matrix. Thus, independent solvers in response analyses can be utilized for the fine scale analysis of molecular dynamic (MD) and the coarse scale analysis of finite element analysis. To reduce the size of problems and to improve the computational efficiency, a generalized Langevin equation is used for a localized MD analysis. Through demonstrative numerical examples, it turns out that the derived sensitivity analysis method is accurate and efficient compared with finite difference sensitivity.

Design Sensitivity Analysis for the Meshfree Shell Structure

2001 ◽  
Author(s):  
Kyung K. Choi ◽  
Nam H. Kim ◽  
Mark E. Botkin
Keyword(s):  
Sensitivity Analysis ◽  
Shell Structure ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Analysis Method ◽  
Sensitivity Equation ◽  
Material Derivative ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Shell Formulation

Abstract A unified design sensitivity analysis method for a meshfree shell structure with respect to sizing, shape, and configuration design variables is presented in this paper. A shear deformable shell formulation is characterized by a CAD connection, thickness degeneration, meshfree discretization, and nodal integration. The design variable is selected from the CAD parameters, and a consistent design velocity field is then computed by perturbing the surface geometric matrix. The material derivative concept is used to obtain a design sensitivity equation in the parametric domain. Numerical examples show the accuracy and efficiency of the proposed design sensitivity analysis method compared to the analytical solution and the finite difference solution.

scholarly journals Structural Optimization of Variable Section Slender Manipulator Based on Sensitivity Analysis Method

2011 ◽  
Vol 2-3 ◽  
pp. 291-295
Author(s):  
Zhong Luo ◽  
Le Liang ◽  
Yan Yan Chen ◽  
Fei Wang
Keyword(s):  
Sensitivity Analysis ◽  
Structural Optimization ◽  
Optimization Method ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Analysis Method ◽  
Design Variables ◽  
Variable Section ◽  
Sensitivity Analysis Method ◽  
In The Beginning

A parameter optimization method based on sensitivity analysis is presented for the structural optimization of variable section slender manipulator. Structure mechanism of a polishing robot is introduced firstly, and its stiffness model is established. Then, a design sensitivity analysis method and a sequential liner programming (SLP) strategy are proposed. In the beginning of the optimization, the design sensitivity analysis method can be used to select the sensitive design variables which can make the optimized results more efficient and accurate. And then, it can be used to improve the convergence during the process of the optimization. The design sensitivities are calculated using the finite difference method. The search for the final optimal structure is performed using the SLP method. Simulation results show that the structure optimization method is effective to enhance the stiffness of the manipulator, no matter when the manipulator suffers constant force or variable force. This work lays a theoretical foundation for the structural optimization for such manipulators.

scholarly journals Structural Optimization of Slender Robot Arm Based on Sensitivity Analysis

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Zhong Luo ◽  
Xueyan Zhao ◽  
Le Liang ◽  
Fei Wang
Keyword(s):  
Sensitivity Analysis ◽  
Structural Optimization ◽  
Optimization Method ◽  
Design Sensitivity ◽  
Robot Arm ◽  
Analysis Method ◽  
Design Variables ◽  
Stiffness Model ◽  
Variable Section ◽  
Sensitivity Analysis Method

An effective structural optimization method based on a sensitivity analysis is proposed to optimize the variable section of a slender robot arm. The structure mechanism and the operating principle of a polishing robot are introduced firstly, and its stiffness model is established. Then, a design of sensitivity analysis method and a sequential linear programming (SLP) strategy are developed. At the beginning of the optimization, the design sensitivity analysis method is applied to select the sensitive design variables which can make the optimized results more efficient and accurate. In addition, it can also be used to determine the scale of moving step which will improve the convergency during the optimization process. The design sensitivities are calculated using the finite difference method. The search for the final optimal structure is performed using the SLP method. Simulation results show that the proposed structure optimization method is effective in enhancing the stiffness of the robot arm regardless of the robot arm suffering either a constant force or variable forces.

Continuum-Based Design Sensitivity Analysis and Optimization of Springback in Stamping Process

2005 ◽  
Author(s):  
Kyung K. Choi ◽  
Kiyoung Yi ◽  
Nam H. Kim ◽  
Mark E. Botkin
Keyword(s):  
Sensitivity Analysis ◽  
Process Development ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Forming Process ◽  
Sensitivity Equation ◽  
Material Derivative ◽  
Stamping Process ◽  
Sensitivity Analysis Method ◽  
Blank Holding Force

The springback is a significant manufacturing defect in the stamping process. A serious impediment to the use of lighter-weight, higher-strength materials in manufacturing is the relative lack of understanding about how these materials respond to the complex forming process. The springback problem can be reduced by using appropriate designs of die, punch, and blank holder shape together with friction and blank holding force. That is, an optimum stamping process can be determined using a gradient-based optimization to minimize the springback. However, for an effective optimization of the stamping process, development of an efficient analytical design sensitivity analysis method is crucial. In this paper, a continuum-based shape and configuration design sensitivity analysis (DSA) method for the stamping process has been developed. The material derivative concept is used to develop the continuum-based design sensitivity. The design sensitivity equation is solved without iteration at each converged load step in the finite deformation elastoplastic nonlinear analysis with frictional contact, which makes the design sensitivity calculation very efficient. The accuracy and efficiency of the proposed method is illustrated by minimizing springback in an S-rail part, which is often used as an industrial benchmark to verify the numerical procedures employed for stamping processes.

Sizing Design Sensitivity Analysis of Dynamic Frequency Response of Vibrating Structures

1992 ◽  
Vol 114 (1) ◽  
pp. 166-173 ◽  
Author(s):  
Kyung K. Choi ◽  
Jae Hwan Lee
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Analysis Data ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Frame Structure ◽  
Cross Sectional ◽  
Design Variables ◽  
Sensitivity Analysis Method ◽  
Dynamic Frequency

A continuum design sensitivity analysis method of dynamic frequency response of structural systems is developed using the adjoint variable and direct differentiation methods. A variational approach with a non-selfadjoint operator for complex variable is used to retain the continuum elasticity formulation throughout derivation of design sensitivity results. Sizing design variables such as thickness and cross-sectional area of structural components are considered for the design sensitivity analysis. A numerical implementation method of continuum design sensitivity analysis results is developed using postprocessing analysis data of COSMIC/NASTRAN finite element code to get the design sensitivity information of displacement and stress performance measures of the structures. The numerical method is tested using basic structural component such as a plate supported by shock absorbers and a vehicle chassis frame structure for sizing design variables. Accurate design sensitivity results are obtained even in the vicinity of resonance.

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