20.500.12556/DKUM-70804 On the application of a mixed finite-element approach to beam-soil interaction Uporabne mešane metode končnih elementov pri interakciji nosilec-tla 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. 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. Bernoulli beam Winkler soil mixed finite-element method geomehanika Bernoullijev nosilec Winklerjeva zemljina metoda končnih elementov mešana metoda končnih elementov true false true Angleški jezik Slovenski jezik Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo Univerze v Mariboru Znanstveno delo 2018-06-14 09:59:32 2018-06-14 10:00:19 2022-08-01 19:50:41 2019-07-11 18:20:21 2013 0 0 str. 15-27 št. 2 Letn. 10 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1854-0171 624.131.53 215987712 277754112 1854-0171 URN:SI:UM:DK:I8UTYTWZ Acta_geotechnica_Slovenica_2013_Jagodnik,_Jelenic,_Arbanas_On_the_application_of_a_mixed_finite-element_approach_to_beam-soil_interactio.pdf Acta_geotechnica_Slovenica_2013_Jagodnik,_Jelenic,_Arbanas_On_the_application_of_a_mixed_finite-element_approach_to_beam-soil_interactio.pdf 1 4A700C5A654C5D525BD193F9F211327E d7b4e030c2202dd26eb112819978c55b954f1a88cd4243a7af66d1ad9628577e 07dabe26-7c10-11eb-bb7a-00155d0001ca 20.500.12556/dkum/242f3ac9-7dde-4249-a2a5-0266eada778a https://dk.um.si/Dokument.php?lang=slv&id=125647 http://fgserver3.fg.um.si/journal-ags/2013-2/article-2.asp 1 https://dk.um.si/Dokument.php?lang=slv&id=125648 Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo Acta geotechnica Slovenica 0 0 0