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1
Content available Three-point bending of a beam with non-homogeneous structure in the depth direction
Magnucki Krzysztof, Magnucka-Blandzi Ewa, Witkowski Dawid, Wittenbeck Leszek
Engineering Transactions
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2023
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Vol. 71, iss. 4
645--665
EN
This paper is devoted to the behavior of a non-homogeneous simply supported beam under three-point bending. The individual shear deformation function of a planar cross-section is adopted, and longitudinal displacements, strains, and stresses for two parts of the beam are explained. By applying the principle of stationary potential energy, a system of two differential equations of equilibrium is derived and solved analytically. The positions of the neutral axis, shear coefficients, and deflections are then calculated for three different beam families. Additionally, the bending problem of these beams is studied numerically using the finite element method (FEM). The results of both analytical and numerical calculations are presented in tables and figures. The main contribution of this paper lies in the development of an analytical model incorporating the individual shear deformation function and a numerical FEM model for this beam.
2
Content available Elastic buckling of a generalized cylindrical sandwich panel under axial compression
Magnucki Krzysztof, Magnucka Ewa, Wittenbeck Leszek
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2023
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Vol. 71, nr 2
art. no. e144623
EN
The paper is devoted to buckling problem of an axially compressed generalized cylindrical sandwich panel and rectangular sandwich plate. The continuous variation of mechanical properties in thickness direction of the structures is assumed. The generalized theory of deformation of the straight line normal to the neutral surface is applied. The analytical model of this sandwich panel is elaborated. Three differential equations of equilibrium of this panel based on the principle of stationary potential energy are obtained. This system of equations is analytically solved and the critical load is derived. Moreover, the limit transformation of the sandwich panel to a sandwich rectangular plate is presented. The critical loads of the example cylindrical panels and rectangular plates are derived.
3
Content available Three models of a sandwich beam: bending, buckling, and free vibrations
Magnucki Krzysztof, Magnucka-Blandzi Ewa, Wittenbeck Leszek
Engineering Transactions
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2022
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Vol. 70, iss. 2
97--122
EN
This paper is devoted to the analytical modelling of a sandwich beam. Three models of this beam are elaborated. Two nonlinear individual shear theories of deformation of a plane cross-sections are proposed. Based on Hamilton’s principle, two differential equations of motion for each model are obtained. The bending, buckling and free flexural vibration problems of the simply-supported sandwich beam considering these three models are studied. The results of these analytical investigations are presented in tables.
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