First- and Second-Order Design Sensitivity Analysis Scheme Based on Trefftz Method

1999 ◽  
Vol 121 (1) ◽  
pp. 84-91 ◽  
Author(s):  
E. Kita ◽  
Y. Kataoka ◽  
N. Kamiya
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Second Order ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
Trefftz Method ◽  
Analysis Scheme ◽  
Complete Functions ◽  
Approximate Expressions ◽  
Physical Quantities

This paper presents a new scheme for the first- and second-order design sensitivity analysis of the two-dimensional elastic problem by using Trefftz method. In the Trefftz method, the physical quantities are approximated by superposition of regular T-complete functions. Therefore, direct differentiation of the approximate expressions with respect to design parameters leads to the regular expressions of the sensitivities. The present schemes are applied to some examples in order to confirm the validity.

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.

Probabilistic Optimal Design Using Second Moment Criteria

1988 ◽  
Vol 110 (3) ◽  
pp. 324-329 ◽  
Author(s):  
A. D. Belegundu
Keyword(s):  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Optimal Design ◽  
Design Sensitivity ◽  
Design Criterion ◽  
Second Order ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Programming Technique ◽  
Second Moment

Probability-based optimal design of structures is presented. The emphasis here is to develop a practical approach to optimal design given random design parameters. The method is applicable to structures which are modeled using the finite element method. The Hasofer-Lind (H-L) second-moment design criterion is used to formulate the general design problem. A method for calculating the sensitivity coefficients is presented, which involves second-order design sensitivity analysis. The importance of second order derivatives is established. A nonlinear programming technique is used to solve the problem. Numerical results are presented, where stiffness parameters are treated as random variables.

Second Order Design Sensitivity Analysis of Kinematically-Driven Mechanical Systems

1992 ◽  
Author(s):  
Qiushu Cao ◽  
Prakash Krishnaswami
Keyword(s):  
Sensitivity Analysis ◽  
Mechanical Systems ◽  
Design Sensitivity ◽  
Second Order ◽  
Design Sensitivity Analysis ◽  
System Response ◽  
Reliability Design ◽  
Constrained Mechanical Systems ◽  
Minimum Sensitivity ◽  
Element Technique

Abstract Second order design sensitivity information is required for several design applications, including second order optimization, minimum sensitivity design and reliability design. The problem of computing this information in a generalized manner becomes difficult when the dependence of system response on design is not explicitly known, as in the case of kinematic systems. This paper presents a general method for second order design sensitivity analysis of constrained mechanical systems. This method uses the constrained multi-element technique for kinematic analysis combined with a direct differentiation approach for obtaining first and second order design sensitivities of the system response. The method was implemented in a computer program on which several examples were solved. Three of the examples are presented in this papers. For each example, the second order sensitivities are checked against values obtained by finite differencing. In all cases, the agreement is seen to be very close, indicating that the proposed method is accurate and reliable.

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