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An Accurate Method for First and Second Derivatives of Dynamic Responses

Published online by Cambridge University Press:  31 August 2011

Q. Liu ,
J. Zhang ,
L. Gu  and
L. Yan
Q. Liu*
Affiliation:
Department of Civil Engineering, Guangxi University of Technology, Liuzhou 545006, PR ChinaDepartment of Mechanical Engineering, University of Nebraska Lincoln, NE 68588, U.S.A.College of Civil and Architecture Engineering, Guangxi University, Nanning 530004, PR China
J. Zhang
Affiliation:
Department of Mechanical Engineering, Indiana University – Purdue UniversityIndianapolis (IUPUI), Indianapolis, IN 46202, U.S.A.
L. Gu
Affiliation:
Department of Mechanical Engineering, University of Nebraska Lincoln, NE 68588, U.S.A.
L. Yan
Affiliation:
College of Civil and Architecture Engineering, Guangxi University, Nanning 530004, PR China
*
*Associate Professor, corresponding author
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Abstract

This paper has developed an accurate method for calculating the first and second derivatives of dynamic responses with respect to the design variables of structures subjected to dynamic loads. An efficient algorithm to calculate the dynamic responses, their first and second derivatives with respect to the design variables is formulated based on the Newmark-β method. The algorithm is achieved by direct differentiation and only a single dynamics analysis is required. An example is demonstrated with the new method proposed in this paper and the analytical method. The comparative numerical results show the new method is highly accurate compared to the analytical method.

Keywords

First derivative of dynamic responseSensitivity analysisSecond derivative of dynamic responseHessian matrix
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 3 , September 2011 , pp. 389 - 398
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

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References

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