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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 40
ADVANCES IN OPTIMIZATION FOR STRUCTURAL ENGINEERING
Edited by: B.H.V. Topping
Paper V.1

Efficient Optimum Design of Structures with Frequency Response Constraints using High Quality Approximation

E. Salajegheh

Civil Engineering Department, University of Kerman, Kerman, Iran

Full Bibliographic Reference for this paper
E. Salajegheh, "Efficient Optimum Design of Structures with Frequency Response Constraints using High Quality Approximation", in B.H.V. Topping, (Editor), "Advances in Optimization for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 107-113, 1996. doi:10.4203/ccp.40.5.1
Abstract
An efficient technique is presented for optimum design of structures with both natural frequency and complex frequency response constraints. The main idea is to reduce the number of dynamic analysis by introducing high quality approximations. Eigenvalues are approximated using the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvalues and frequency responses. A two point approximation is used to approximate the functions under consideration. After the substitution of the approximate functions into the original optimization problem, the dynamic analysis of the structure is not necessary in the specified move limits. The sensitivities of the eigenvalues and eigenvectors are calculated analytically. In the problems under consideration repeated eigenvalues occur. Thus the sensitivities are evaluated for repeated eigenvalues.

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