On the application of a mixed finite-element approach to beam-soil interaction

Vedran Jagodnik (Author), Gordan Jelenić (Author), Željko Arbanas (Author)

Abstract

In this paper the deformation of a Bernoulli beam resting on Winkler's soil is reviewed in terms of the mixed finite-element methodology. While the stiffness matrix of the Bernoulli beam problem utilizing the standard displacement-based approach, in which only the displacement field is interpolated, may be alternatively obtained using a mixed-type approach to the absolutely shear-stiff second-order Timoshenko beam (in which the rotation and shear-stress resultant fields are additionally interpolated), the two approaches lead to different Winkler-type soil-stiffness contributions. Furthermore, extending the mixed-type formalism to both of these elements by additionally interpolating the distributed soil-reaction field, the soil-stiffness contributions also differ. In this way four different elements are obtained, with one, two, three or four independently interpolated fields, in which the beam-stifness matrix is equal, but the soil-stiffness matrices are different. It is demonstrated that the displacement-based one-field element is the least convergent, while the mixed-type element with four interpolated fields is the most convergent.

Keywords

Bernoulli beam;Winkler soil;mixed finite-element method;

Data

Language:	English
Year of publishing:	2013
Typology:	1.01 - Original Scientific Article
Organization:	UM FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
UDC:	624.131.53
COBISS:	277754112
ISSN:	1854-0171
Parent publication:	Acta geotechnica Slovenica
Views:	818
Downloads:	46
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	Uporabne mešane metode končnih elementov pri interakciji nosilec-tla
Secondary abstract:	Članek daje pregled deformacij Bernoullijevega nosilca na Winklerjevi zemljini z uporabo mešane metode končnih elementov. Togostno matriko Bernoullijevega nosilca lahko dobimo z uporabo standardnega pristopa, ki temelji na pomikih in pri katerem je interpolirano zgolj polje pomikov, pa tudi z mešanim pristopom, ki se uporablja pri Timoshenkovem nosilcu drugega reda s popolno strižno togostjo (pri katerem sta dodatno interpolirana rotacijsko polje in iz tega izhajajoče polje strižnih napetosti), vendar pa oba pristopa privedeta do različnih rezultatov togosti zemljine Winklerjevega tipa. Poleg tega se togost zemljine razlikuje tudi v primeru, ko mešano metodo razširimo na oba elementa z dodatnim interpoliranjem porazdeljenega polja reakcije zemljine. Na ta način dobimo štiri različne elemente z enim, dvema, tremi ali štirimi neodvisno interpoliranimi polji, v katerih je togostna matrika nosilca enaka, togostne matrike zemljine pa so različne. Članek pokaže, da je najmanj konvergenten element z enim poljem, ki temelji na pomikih, medtem ko je element mešanega tipa s štirimi interpoliranimi polji najbolj konvergenten.
Secondary keywords:	geomehanika;Bernoullijev nosilec;Winklerjeva zemljina;metoda končnih elementov;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 14-27
Volume:	ǂVol. ǂ10
Issue:	ǂ[no.] ǂ2
Chronology:	2013
ID:	10941241