A seminalytical approach to large deflections in compliant beams under point load
type: Item
instance of: scholarly article
title: A seminalytical approach to large deflections in compliant beams under point load
zbMATH Open document ID: 1207.74077
DOI: 10.1155/2009/910896
author: N. Tolou
author: Just L. Herder
published in: Mathematical Problems in Engineering
publication date: 2009-11-13T00:00:00Z
full work available at URL: https://eudml.org/doc/45916
review text: Summary: The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H15
zbMATH DE Number: 5632558
MaRDI profile type: Publication
OpenAlex ID: W2131697821
Wikidata QID: Q58649543
cites work: Q5608690
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description: scientific article; zbMATH DE number 5632558