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1
Content available remote Analytical modeling of I-beam as a sandwich structure
Magnucki K., Lewinski J.
Engineering Transactions
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2018
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Vol. 66, iss. 4
357--373
EN
The paper is devoted to an analytical model of I-beam, with consideration of the shear effect. The model is based on the sandwich beam theory. The field displacements and strains are formulated with consideration of a nonlinear hypothesis of flat cross-section deformation of the beam. The governing differential equations for the I-beam are obtained based on the principle of stationary total potential energy. The shear effect of the beam is illustrated for the threepoint bending case. The analytical solution is compared to FEM numerical calculation. The results of the analysis are presented in Tables and Figures.
2
Content available remote Finite element stress analysis of laminated composite plates
Singh P., Singh R.
International Journal of Applied Mechanics and Engineering
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2011
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Vol. 16, no 3
851-867
EN
In the present work, a finite element program based on the classical lamination theory improved by Vinson's weighting function to include transverse shear effects is developed for the analysis of laminated composite plates. The finite element analysis of a clamped three layered square symmetric laminate under uniform loading is carried out using 8-noded isoparametric elements having five degrees of freedom at each node. The effect of plate side-to-thickness ratio (a/h) 4, 10, 50 and 100 100 is studied on the maximum values of the non-dimensionalized central deflection (w), non-dimensionalized stress resultants [...] and non-dimensionalized stresses [...]. The variation of non-dimensionalized normal stresses [...] and shear stresses [...] through the thickness (z/h) of the laminate at plate side-to-thickness ratio (a/h) 10 is also studied.
3
Content available remote Elastic bending of an isotropic porous beam
Magnucki K., Stasiewicz P.
International Journal of Applied Mechanics and Engineering
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2004
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Vol. 9, no 2
351-360
EN
The subject of this paper is an isotropic porous beam with a rectangular cross section. Mechanical properties of the isotropic porous material vary across the depth of the beam. A nonlinear hypothesis of deformation of a plane cross section of this beam is described. The system of differential equations and boundary conditions of the problem is derived on the basis of the principle of minimum potential energy. A numerical analysis for simply supported beams under uniformly distributed load is made. A comparative analysis with the use of FEM and the COSMOS/M system is presented.
4
Wpływ cyklicznego ścinania na przebieg lokalizacji odkształceń w gruntach piaszczystych
Tejchman J.
Zeszyty Naukowe. Budownictwo / Politechnika Śląska
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2003
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z. 97
185-192
PL
W artykule przedstawiono wyniki wpływu cyklicznego ścinania na przebieg lokalizacji odkształceń stycznych w zagęszczonych gruntach piaszczystych. Proces ścinania wąskiej i nieskończenie długiej warstwy piasku pomiędzy dwoma bardzo szorstkimi brzegami pod obciążeniem stałym w warunkach nieskrępowanej dylatacji modelowany był przy zastosowaniu metody elementów skończonych i mikropolarnego hipoplastycznego prawa konstytutywnego. Obliczenia wykonano dla dużej amplitudy cyklicznego ścinania.
EN
Paper presents results of the effect of cyclic shearing on the evolution of localization of shear deformations in dense sandy soils. The process of shearing of an infinite narrow layer of sand between two very rough boundaries under constant vertical pressure in conditions of free dilatation is modelled with a finite element method and a polar hypoplastic constitutive law. Numerical calculations were performed with large cyclic shear amplitude.
5
Content available remote Static analysis of isotropic thick/thin skew plates by finite element method
Haldar S., Manna M. C., Sheikih A. H.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no 2
245-254
EN
A general first order shear deformation theory has been developed to analyze the bending behavior of isotropic skew plates. The plates having different skew angles ('alpha'), aspect ratios (a/b), boundary conditions and transverse loading conditions (concentrated load, uniformly distributed load, hydrostatic varying load and sinusoidal varying load) have been analyzed by the nine node isoparametric element. The analysis has also been performed considering plate thickness ratio varying from a/b=0.001 to a/b=0.02. The deflections and principal bending moments in non-dimensional forms have been presented at different locations of the plates. The present solutions have been compared with the published results wherever available and have got good agreement. Some numerical solutions have been given which may be treated as new results.
6
Content available remote A generalized FE formulation for buckling analysis of solid or built-up columns with nonprismatic section
Li G.-Q., Li J.-J.
International Journal of Applied Mechanics and Engineering
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2003
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Vol. 8, no 4
651-663
EN
In this paper, a generalized FE formulation for buckling analysis of nonprismatic columns with various cross-sections is established by using the Chebyshev polynomial approach to the governing differential equation. The proposed formulation includes the effects of shear deformation and is therefore applicable to solid or built-up columns. The change of the sectional properties along the length direction, such as the area and inertia moment, need not be fitted with approximate expressions and can be defined exactly and freely with user-defined functions in programming. Buckling of the three structures, respectively for a tapered mast column with a circular hollow section, a web-tapered I-sectional column and a tapered lattice column, is studied numerically and compared with the results of previous studies. The effects of shear deformation on the buckling loads of those tapered columns are specified.
7
Content available remote Nonlinear oscillations pliable to shear transversal deformations and compression of composite plates
Marchuk M., Pakosh V., Maksymuk O.
Vibrations in Physical Systems
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2002
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Vol. 20
222--222
8
Rozwiązania belki Timoshenki wyrażone w terminach rozwiązań Eulera-Bernoulliego dla zginanych włóknokompozytowych belek prostych
Gołaś J.
Zeszyty Naukowe. Mechanika / Akademia Techniczno-Rolnicza w Bydgoszczy
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2000
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Z. 47 (228)
111--120
PL
W pracy omówiono zginanie poprzeczne kompozytowych belek prostych o warstwowym układzie włókien wzmacniających. Uwzględniono podatność belek na poprzeczne odkształcenia postaciowe (teoria Timoshenki) oraz przyjęto, że matryca (osnowa) włóknokompozytu jest materiałem poprzecznie izotropowym o własnościach liniowo-lepkosprężystych. Uzyskane rozwiązania na siły przekrojowe (M, T) i przemieszczenia (w, psi) dla kompozytowych belek prostych (tj. swobodnie podpartej, wspornikowej, obustronnie utwierdzonej oraz na jednym końcu utwierdzonej, a na drugim swobodnie podpartej) wyrażono w terminach rozwiązań korespondujących z teorią belek Eulera-Bernoulliego. Podane w pracy rozwiązania i zależności pozwalają na łatwe uzyskiwanie rozwiązań dla belek Timoshenki, korzystając z rozwiązań prostszych Eulera-Bernoulliego, bez potrzeby wykonywania skomplikowanej analizy uwzględniającej giętno-postaciowe deformacje. Dla uzyskanych w pracy rozwiązań istnieją przejścia graniczne do rozwiązań podanych przez Wanga [10], dotyczących sprężystych belek jednorodnych.
EN
The present paper discusses transverse bending of straight composite beams of reinforcing fibre layer structure and considers beam flexibility under transverse shear strains (Timoshenko's theory). It is assumed that the matrix of fibre-reinforced composite is a transversally isotropic material with linear viscoelastic properties. Solutions obtained for cross-sectional forces (M; T) and displacements (w, psi) of straight beams (simply supported, cantilevered, fixed at both ends and fixed at one end with other end simply supported) are expressed in terms corresponding to the solutions of Euler-Bernoulli theory for beams. Solutions and relationships presented in the paper allow for obtaining solutions for Timoshenko beams via simpler solutions of Euler-Bemoulli easily, without performing a very complicated analysis of flexural shear deformations. For the solutions developed in the paper a suitable limit transition exists to the solutions given by WANG [10] for homogeneous elastic beams.
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