Second‐order design sensitivity analysis using diagonal hyper‐dual numbers

2021 ◽  
Author(s):  
Vitor Takashi Endo ◽  
Eduardo Alberto Fancello ◽  
Pablo Andrés Muñoz‐Rojas
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Second Order ◽  
Design Sensitivity Analysis ◽  
Dual Numbers

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.

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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