Design Sensitivity Analysis and Optimization of Nonlinear Anisotropic Structures

2004 ◽  
Vol 261-263 ◽  
pp. 809-814
Author(s):  
Tae Hee Lee ◽  
J.J. Jung
Keyword(s):  
Sensitivity Analysis ◽  
Nonlinear Analysis ◽  
Yield Criterion ◽  
Design Sensitivity ◽  
Euler Method ◽  
Design Sensitivity Analysis ◽  
Design Variables ◽  
Nonlinear Constitutive Equation ◽  
Anisotropic Structures ◽  
Hill's Yield Criterion

Nonlinear analysis of anisotropic structures is described by using Hill's yield criterion that anisotropic yield contour is assumed to be retained its shape during the hardening process. Nonlinear constitutive equation of anisotropic material is derived using plastic potential concept. Linear strain hardening model is utilized and forward Euler method is employed as a stress integration method. Newton-Raphson method is implemented for numerical nonlinear analysis. Direct differentiation method differentiating directly the equilibrium equation with respect to design variables is applied to design sensitivity analysis of nonlinear anisotropic plate. The results of design sensitivity analysis are compared with those of finite difference method to verify the accuracy. Optimization is accomplished for a rectangular plate using evaluated sensitivity coefficients.

Design Sensitivity Analysis of Nonlinear Multidisciplinary Multibody Systems in the MIXEDMODELS Platform

2007 ◽  
Author(s):  
Shilpa A. Vaze ◽  
Prakash Krishnaswami ◽  
James DeVault
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
The State ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
State Variables ◽  
Sensitivity Coefficients ◽  
Design Variables

Most state-of-the-art multibody systems are multidisciplinary and encompass a wide range of components from various domains such as electrical, mechanical, hydraulic, pneumatic, etc. The design considerations and design parameters of the system can come from any of these domains or from a combination of these domains. In order to perform analytical design sensitivity analysis on a multidisciplinary system (MDS), we first need a uniform modeling approach for this class of systems to obtain a unified mathematical model of the system. Based on this model, we can derive a unified formulation for design sensitivity analysis. In this paper, we present a modeling and design sensitivity formulation for MDS that has been successfully implemented in the MIXEDMODELS (Multidisciplinary Integrated eXtensible Engine for Driving Metamodeling, Optimization and DEsign of Large-scale Systems) platform. MIXEDMODELS is a unified analysis and design tool for MDS that is based on a procedural, symbolic-numeric architecture. This architecture allows any engineer to add components in his/her domain of expertise to the platform in a modular fashion. The symbolic engine in the MIXEDMODELS platform synthesizes the system governing equations as a unified set of non-linear differential-algebraic equations (DAE’s). These equations can then be differentiated with respect to design to obtain an additional set of DAE’s in the sensitivity coefficients of the system state variables with respect to the system’s design variables. This combined set of DAE’s can be solved numerically to obtain the solution for the state variables and state sensitivity coefficients of the system. Finally, knowing the system performance functions, we can calculate the design sensitivity coefficients of these performance functions by using the values of the state variables and state sensitivity coefficients obtained from the DAE’s. In this work we use the direct differentiation approach for sensitivity analysis, as opposed to the adjoint variable approach, for ease in error control and software implementation. The capabilities and performance of the proposed design sensitivity analysis formulation are demonstrated through a numerical example consisting of an AC rectified DC power supply driving a slider crank mechanism. In this case, the performance functions and design variables come from both electrical and mechanical domains. The results obtained were verified by perturbation analysis, and the method was shown to be very accurate and computationally viable.

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.

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.

Implementation of Design Sensitivity Analysis with Existing Finite Element Codes

1987 ◽  
Vol 109 (3) ◽  
pp. 385-391 ◽  
Author(s):  
K. K. Choi ◽  
J. L. T. Santos ◽  
M. C. Frederick
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Cross Sectional ◽  
Design Variables ◽  
Accurate Design ◽  
Analysis Theory ◽  
Problem Design ◽  
Selection Of

A numerical method is presented to implement structural design sensitivity analysis theory, using the versatility and convenience of existing finite element structural analysis programs. Design variables such as thickness and cross-sectional areas of components of individual members and built-up structures are considered. Structural performance functionals considered include displacement and stress. The method is also applicable for eigenvalue problem design sensitivity analysis. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. Thus design sensitivity analysis software does not have to be imbedded in an existing finite element code. Feasibility of the method is shown through analysis of several problems, including a built-up structure. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of finite difference perturbations.

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.

Design Sensitivity Analysis Applied to Injection Molding Process: Injection Pressure and Multi-Gate Location Optimization

2000 ◽  
Author(s):  
Kalonji K. Kabanemi ◽  
Jean-François Hétu ◽  
Abdessalem Derdouri
Keyword(s):  
Sensitivity Analysis ◽  
Injection Molding ◽  
Injection Pressure ◽  
Pressure Profile ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Injection Molding Process ◽  
Molding Process ◽  
Filling Fraction ◽  
Design Variables

Abstract In this work, we develop a numerical simulation method to optimize the injection molding process using the design sensitivity analysis (DSA). The optimization concerns the filling stage and focuses on the number and location of gates in a mold cavity as well as the injection pressure, considered as one of the key processing parameters, in order to minimize the fill time. Since the problem to be solved involves transient flow with free surfaces, the direct differentiation method is used to evaluate the sensitivities of the Hele-Shaw, filling fraction and the energy equations with respect to the design variables used in the analysis. The mesh domain parameterization is coped with using B-spline functions. Sensitivity equations are solved by means of finite element method. The proposed numerical approach is combined with the sequential linear and quadratic programming method of the DOT optimization tools to find the new design variables at each iteration. Starting with any initial gate locations and injection pressure profile, the method enables us to find the optimal gate locations together with the optimal injection pressure profile. Finally, numerical results involving complex mold geometries are presented and discussed to assess the validity and robustness of the proposed method.

Design Sensitivity Analysis and Topology Optimization Method Applied to Stiffener Layout in Hull Structures

2006 ◽  
Vol 50 (03) ◽  
pp. 222-230
Author(s):  
Yoondo Ha ◽  
Woojong Kim ◽  
Seonho Cho
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Numerical Models ◽  
Optimization Method ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Von Mises Stress ◽  
Mindlin Plate ◽  
Design Variables ◽  
Topology Optimization Method

A continuum-based design sensitivity analysis (DSA) method is developed for threedimensional Mindlin plate structures. The first-order variations of energy form, load form, and structural responses with respect to nonshape design variables are derived. An adjoint variable method is employed because of its computational efficiency, especially with respect to problems where there are many design variables but only a few performance measures. The developed DSA method is utilized with the topology optimization method by using a density approach, which yields an optimal structural layout for the required structural performances. For the numerical implementation, a finite element method, the developed DSA method, and a gradient-based topology optimization method are integrated into a unified and automated framework. The developed topology optimization method is applied to the numerical models of stringer and cargo hold to find the optimal layout of stiffeners. Comparing the existing and optimal designs, significant improvements in the displacement and Von Mises stress distributions are observed. The results show that the topology optimization method can be used as a useful tool for determining a suitable layout of stiffeners in the early stage of hull structural design.

Design Sensitivity Analysis and Optimization of Nonlinear Structural Systems With Critical Loads

1990 ◽  
Author(s):  
Jong Sang Park ◽  
Kyung K. Choi
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Design ◽  
Critical Load ◽  
Critical Loads ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Shape Design ◽  
Structural Systems ◽  
Nonlinear Structural ◽  
Design Variables

Abstract A continuum formulation for design sensitivity analysis of critical loads is developed for nonlinear structural systems that are subjected to conservative loading. Both geometric and material nonlinear effects are considered. Sizing design variables such as cross-sectional areas of beam or truss design components and thicknesses of plate or membrane design components, together with their shape design variables, are treated. A continuum approach is used to obtain design sensitivity expressions in integral form. For shape design sensitivity analysis, the material derivative concept and domain method are used to find variations of the critical load due to variations in shape of the physical domain. The total Lagrangian formulation for incremental equilibrium equation and one-point linearized eigenvalue problems are utilized. A numerical method is presented to evaluate continuum design sensitivity expressions using analysis results of established finite element codes. It is found that no adjoint system is necessary for design sensitivity analysis of the critical load. Numerical results show the proposed method for design sensitivity of critical loads is accurate for both sizing and shape design variables. A numerical procedure for optimal design of nonlinear structural systems is presented, using the proposed continuum design sensitivity analysis method. An optimal design problem with a stability constraint is solved.

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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