Dynamic analysis of 3-D beam elements including warping and shear deformation effects

Sapountzakis, EJ; Mokos, VG

dc.contributor.author	Sapountzakis, EJ	en
dc.contributor.author	Mokos, VG	en
dc.date.accessioned	2014-03-01T01:24:01Z
dc.date.available	2014-03-01T01:24:01Z
dc.date.issued	2006	en
dc.identifier.issn	0020-7683	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17171
dc.subject	Bar	en
dc.subject	Beam	en
dc.subject	Boundary element method	en
dc.subject	Damping	en
dc.subject	Dynamic analysis	en
dc.subject	Mass	en
dc.subject	Nonuniform torsion	en
dc.subject	Shear deformation	en
dc.subject	Stiffness matrix	en
dc.subject	Warping	en
dc.subject.classification	Mechanics	en
dc.subject.other	Bars (metal)	en
dc.subject.other	Boundary element method	en
dc.subject.other	Damping	en
dc.subject.other	Shear deformation	en
dc.subject.other	Stiffness matrix	en
dc.subject.other	Torsional stress	en
dc.subject.other	Dynamic analysis	en
dc.subject.other	Mass	en
dc.subject.other	Nonuniform torsion	en
dc.subject.other	Warping	en
dc.subject.other	Beams and girders	en
dc.title	Dynamic analysis of 3-D beam elements including warping and shear deformation effects	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.ijsolstr.2006.02.004	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.ijsolstr.2006.02.004	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	In this paper the dynamic analysis of 3-D beam elements restrained at their edges by the most general linear torsional, transverse or longitudinal boundary conditions and subjected in arbitrarily distributed dynamic twisting, bending, transverse or longitudinal loading is presented. For the solution of the problem at hand, a boundary element method is developed for the construction of the 14 x 14 stiffness matrix and the corresponding nodal load vector of a member of an arbitrarily shaped simply or multiply connected cross section, taking into account both warping and shear deformation effects, which together with the respective mass and damping matrices lead to the formulation of the equation of motion. To account for shear deformations, the concept of shear deformation coefficients is used, defining these factors using a strain energy approach. Eight boundary value problems with respect to the variable along the bar angle of twist, to the primary warping function, to a fictitious function, to the beam transverse and longitudinal displacements and to two stress functions are formulated and solved employing a pure BEM approach that is only boundary discretization is used. Both free and forced transverse, longitudinal or torsional vibrations are considered, taking also into account effects of transverse, longitudinal, rotatory, torsional and warping inertia and damping resistance. Numerical examples are presented to illustrate the method and demonstrate its efficiency and accuracy. The influence of the warping effect especially in members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the dynamic analysis of a space frame. Moreover, the discrepancy in the dynamic analysis of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect, especially in thick walled cross section members. (c) 2006 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	International Journal of Solids and Structures	en
dc.identifier.doi	10.1016/j.ijsolstr.2006.02.004	en
dc.identifier.isi	ISI:000241432900003	en
dc.identifier.volume	43	en
dc.identifier.issue	22-23	en
dc.identifier.spage	6707	en
dc.identifier.epage	6726	en