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Optimization of support positions to maximize the fundamental frequency of structures
Author(s) -
Wang D.,
Jiang J. S.,
Zhang W. H.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1124
Subject(s) - sensitivity (control systems) , convergence (economics) , interpolation (computer graphics) , simple (philosophy) , heuristic , finite element method , interval (graph theory) , mathematical optimization , position (finance) , grid , process (computing) , mathematics , computer science , optimization problem , algorithm , geometry , engineering , structural engineering , motion (physics) , artificial intelligence , philosophy , epistemology , finance , combinatorics , electronic engineering , economics , economic growth , operating system
In this paper, the position optimization of simple supports is implemented to maximize the fundamental frequency of a beam or plate structure. Both elastic and rigid supports are taken into account. First, the frequency sensitivity with respect to the movement of a simple support is derived using the discrete method. By means of the shape functions of the finite element method, closed‐form sensitivity formulations are developed straightforwardly. Then, a heuristic approach, called evolutionary shift method, is presented for optimizing support positions with a fixed grid mesh scheme. Based on the design sensitivity analysis, the support with the highest efficiency is shifted in priority along the elementary edges with the interval (step) of the elementary size. To facilitate the convergence of the process, the interpolation technique is employed to evaluate the solution more accurately. Finally, three numerical examples are presented to demonstrate the validity of the sensitivity analysis and the effectiveness of the optimization method. Copyright © 2004 John Wiley & Sons, Ltd.