Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

Sapountzakis, EJ; Dourakopoulos, JA

dc.contributor.author	Sapountzakis, EJ	en
dc.contributor.author	Dourakopoulos, JA	en
dc.date.accessioned	2014-03-01T01:31:20Z
dc.date.available	2014-03-01T01:31:20Z
dc.date.issued	2009	en
dc.identifier.issn	0924-090X	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19784
dc.subject	Boundary element method	en
dc.subject	Moderate large displacements	en
dc.subject	Nonlinear dynamic analysis	en
dc.subject	Shear center	en
dc.subject	Shear deformation coefficients	en
dc.subject	Timoshenko beam	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Moderate large displacements	en
dc.subject.other	Nonlinear dynamic analysis	en
dc.subject.other	Shear center	en
dc.subject.other	Shear deformation coefficients	en
dc.subject.other	Timoshenko beam	en
dc.subject.other	Axial loads	en
dc.subject.other	Beams and girders	en
dc.subject.other	Bending (deformation)	en
dc.subject.other	Dynamic analysis	en
dc.subject.other	Equations of motion	en
dc.subject.other	Newton-Raphson method	en
dc.subject.other	Nonlinear analysis	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Number theory	en
dc.subject.other	Particle beams	en
dc.subject.other	Shear deformation	en
dc.subject.other	Boundary element method	en
dc.title	Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11071-009-9481-4	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11071-009-9481-4	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical developments and their numerical implementation and Part II discusses analytical and numerical results obtained from both analytical or numerical research efforts from the literature and the proposed method. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton-Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member, as well as the shear forces along the span induced by the applied axial loading. © 2009 Springer Science+Business Media B.V.	en
heal.publisher	SPRINGER	en
heal.journalName	Nonlinear Dynamics	en
dc.identifier.doi	10.1007/s11071-009-9481-4	en
dc.identifier.isi	ISI:000269885100021	en
dc.identifier.volume	58	en
dc.identifier.issue	1-2	en
dc.identifier.spage	295	en
dc.identifier.epage	306	en