Optimum design of structures subjected to follower forces

Katsikadelis, JT; Tsiatas, GC

dc.contributor.author	Katsikadelis, JT	en
dc.contributor.author	Tsiatas, GC	en
dc.date.accessioned	2014-03-01T01:26:50Z
dc.date.available	2014-03-01T01:26:50Z
dc.date.issued	2007	en
dc.identifier.issn	0020-7403	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18249
dc.subject	Analog equation method	en
dc.subject	Beams	en
dc.subject	Dynamic stability	en
dc.subject	Nonconservative load	en
dc.subject	Shape optimization	en
dc.subject	Variable cross-section	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Cantilever beams	en
dc.subject.other	Compressive stress	en
dc.subject.other	Shape optimization	en
dc.subject.other	Stability	en
dc.subject.other	Stiffness	en
dc.subject.other	Analog equation method	en
dc.subject.other	Eigenvalue sensitivity	en
dc.subject.other	Euler-Bernoulli theory	en
dc.subject.other	Hyperbolic differential equation	en
dc.subject.other	Nonconservative load	en
dc.subject.other	Variable cross-section	en
dc.subject.other	Structural design	en
dc.title	Optimum design of structures subjected to follower forces	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijmecsci.2007.03.011	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijmecsci.2007.03.011	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	In this paper, shape optimization is used to optimize the critical load of an Euler-Bernoulli cantilever beam with constant volume subjected to a tangential compressive tip load and/or a tangential compressive load arbitrarily distributed along the beam. This is achieved by varying appropriately the beam cross-section, thus its stiffness and mass properties, along its length, so that the critical load reaches its maximum or a prescribed value. The problem is reduced to a nonlinear optimization problem under equality and inequality constraints as well as specified lower and upper bounds, which, together with large slenderness ratios, ensure the validity of the Euler-Bernoulli theory and the serviceability of the beam. The evaluation of the objective function requires the solution of the dynamic stability problem of a cantilever beam with variable cross-section. This problem is solved using the analog equation method (AEM) of Katsikadelis for the fourth-order hyperbolic differential equation with variable coefficients, together with a simple and direct iterative method for the evaluation of the critical load based on the eigenvalue sensitivity. Besides its accuracy, this method overcomes the shortcoming of a possible FEM solution, which would require resizing of the elements and re-computation of their stiffness properties during the optimization process. Example problems of various types of follower forces are presented, which illustrate the method and demonstrate its applicability and efficiency. (C) 2007 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Mechanical Sciences	en
dc.identifier.doi	10.1016/j.ijmecsci.2007.03.011	en
dc.identifier.isi	ISI:000251070400002	en
dc.identifier.volume	49	en
dc.identifier.issue	11	en
dc.identifier.spage	1204	en
dc.identifier.epage	1212	en