Boundary Formulations for Three-Dimensional Continuum Structural Shape Sensitivity Analysis

1992 ◽  
Vol 59 (4) ◽  
pp. 827-834 ◽  
Author(s):  
J. H. Kane ◽  
G. Zhao ◽  
H. Wang ◽  
K. Guru Prasad
Keyword(s):  
Sensitivity Analysis ◽  
Three Dimensional ◽  
Structural Response ◽  
Surface Displacement ◽  
Design Sensitivity ◽  
Singular Boundary ◽  
Shape Sensitivity ◽  
Element Analysis ◽  
Theoretical Formulation ◽  
Structural Shape

The direct, singular, boundary element analysis formulation is shown to provide a basis for a computationally efficient and accurate shape design sensitivity analysis approach for the structural response of three-dimensional solid objects. The theoretical formulation for surface displacement and traction component sensitivities, and all components of the stress tensor is presented along with a formulation for the recovery of displacement and stress components in the interior of the object under consideration. Discussion of computational issues related to the overall efficiency of these formulations is given, along with numerical results to demonstrate the accuracy and efficiency of this approach.

Isogeometric Shape Design Sensitivity Analysis Using Mixed Transformation Method for Kronecker Delta Property

2011 ◽  
Author(s):  
Seonho Cho ◽  
Bon-yong Koo ◽  
Minho Yoon ◽  
Seung-Wook Lee ◽  
Youn Doh Ha
Keyword(s):  
Sensitivity Analysis ◽  
Boundary Conditions ◽  
Transformation Method ◽  
Design Sensitivity ◽  
Basis Functions ◽  
Meshfree Methods ◽  
Design Sensitivity Analysis ◽  
Shape Design ◽  
Shape Sensitivity ◽  
Element Analysis

The isogeometric method is very effective in shape design optimization due to its effectiveness through the easy design parameterization and accurate sensitivities considering the higher order geometric terms. Due to non-interpolatory property of the NUBRS basis functions, however, the treatment of essential boundary condition is not as straightforward in the isogeometric analysis as in the finite element analysis. Taking advantages of the transformation method developed in meshfree methods, we investigate the isogeometric shape sensitivity analysis with the treatment of essential boundary conditions. Using the property that isogeometric basis functions do not depend on design changes, the transformed shape sensitivity equation is developed and verified for the problem having the essential boundary conditions. Numerical costs to construct the transformed basis function are not as much as the meshfree methods due to the NURBS property that only boundary nodes have their supports on the boundary. Through demonstrative numerical examples having the essential boundary conditions, the effectiveness of proposed design sensitivity analysis is verified.

Shape Sensitivity Formulation for Axisymmetric Thermal Conducting Solids

1993 ◽  
Vol 207 (3) ◽  
pp. 209-216 ◽  
Author(s):  
Boo Youn Lee
Keyword(s):  
Shape Change ◽  
Direct Method ◽  
Design Sensitivity ◽  
Boundary Integral ◽  
Singular Boundary ◽  
Concept Design ◽  
Shape Sensitivity ◽  
Material Derivative ◽  
Thermal Conducting ◽  
Thermal Diffuser

A direct differentiation method is presented for the shape design sensitivity analysis of axisymmetric thermal conducting solids. Based purely on the standard boundary integral equation (BIE) formulation, a new BIE is derived using the material derivative concept. Design derivatives in terms of shape change are directly calculated by solving the derived BIE. The present direct method has a computational advantage over the adjoint variable method, in the sense that it avoids the problem of solving for the adjoint system with the singular boundary condition. Numerical accuracy of the method is studied through three examples. The sensitivities by the present method are compared with analytic sensitivities for two problems of a hollow cylinder and a hollow sphere, and are then compared with those by finite differences for a thermal diffuser problem. As a practical application to numerical optimization, an optimal shape of the thermal diffuser to minimize the weight under a prescribed constraint is found by use of an optimization routine.

Development of a Design Sensitivity Analysis Technique for Explicit Finite Element Software With Applications in Crashworthiness

2000 ◽  
Author(s):  
Douglas W. Stillman
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Time Integration ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Element Analysis ◽  
Automotive Safety ◽  
Explicit Finite Element ◽  
Finite Element Software ◽  
Analysis Technique

Abstract Design Sensitivity Analysis (DSA) is a widely used technique in many areas of finite element analysis, but one that hasn’t yet become available for industrial problems in crashworthiness and automotive safety. In the following effort, an implementation of DSA in the automotive safety simulation program, Radioss, is described. Radioss is a non-linear structures program using an explicit time integration method. A full set of DSA equations are developed and integrated into Radioss so that the design sensitivities can be computed directly and accurately as a result of a single crashworthiness simulation. Some validation results are included. The resulting methodology promises to be an extremely useful tool for engineers involved in the design of safety and crashworthiness of automobiles.

Design Sensitivity Analysis of Structure-Induced Noise and Vibration

1997 ◽  
Vol 119 (2) ◽  
pp. 173-179 ◽  
Author(s):  
K. K. Choi ◽  
I. Shim ◽  
S. Wang
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Method ◽  
Variational Equation ◽  
Adjoint Operator ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Adjoint Variable ◽  
Element Analysis ◽  
Modal Frequency ◽  
Noise And Vibration

A continuum design sensitivity analysis (DSA) method for dynamic frequency responses of structural-acoustic systems is developed using the adjoint variable and direct differentiation methods. A variational approach with a non-self-adjoint operator for complex variables is used to retain the continuum elasticity formulation throughout derivation of design sensitivity results. It is shown that the adjoint variable method is applicable to the variational equation with the non-self-adjoint operator. Sizing design variables such as the thickness and cross-sectional area of structural components are considered for the design sensitivity analysis. A numerical implementation method of continuum DSA results is developed by postprocessing analysis results from established finite element analysis (FEA) codes to obtain the design sensitivity of noise and vibration performance measures of the structural-acoustic systems. The numerical DSA method presented in this paper is limited to FEA and boundary element analysis (BEA) is not considered. A numerical method is developed to compute design sensitivity of direct and modal frequency FEA results. For the modal frequency FEA method, the numerical DSA method provides design sensitivity very efficiently without requiring design sensitivities of eigenvectors. The numerical method has been tested using passenger vehicle problems. Accurate design sensitivity results are obtained for analysis results obtained from established FEA codes.

Three-dimensional optimum design of the cooling lines of injection moulds based on boundary element design sensitivity analysis

2002 ◽  
Vol 216 (7) ◽  
pp. 1067-1071 ◽  
Author(s):  
H Zhou ◽  
D Li ◽  
S Cui
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Boundary Element ◽  
Optimum Design ◽  
Three Dimensional ◽  
Design Sensitivity ◽  
Boundary Integral ◽  
Optimization Techniques ◽  
Design Sensitivity Analysis ◽  
Design Variables

A three-dimensional numerical simulation using the boundary element method is proposed, which can predict the cavity temperature distributions in the cooling stage of injection moulding. Then, choosing the radii and positions of cooling lines as design variables, the boundary integral sensitivity formulations are deduced. For the optimum design of cooling lines, the squared difference between the objective temperature and the temperature of the cavity is taken as the objective function. Based on the optimization techniques with design sensitivity analysis, an iterative algorithm to reach the minimum value of the objective function is introduced, which leads to the optimum design of cooling lines at the same time.

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