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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 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.
3
Content available Bending of a generalized circular sandwich plate under a concentrated force with consideration of an improved shear deformation theory
Magnucki K., Magnucka-Blandzi E., Wittenbeck L.
Archives of Mechanics
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2022
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Vol. 74, nr 4
267--282
EN
The paper is devoted to an axisymmetric bending problem of a generalized circular sandwich plate with continuous variation of mechanical properties in the thickness direction of the core. The plate is clamped and carries a concentrated force in its center. The improved shear deformation theory of the normal straight line to the neutral surface is elaborated. The deformation of this normal straight line is graphically presented for the exemplary sandwich structures of the plate. Two differential equation of equilibrium of the plate are obtained based on the principle of stationary potential energy. This system of equations is analytically solved and the maximum deflection of the example plates are derived. Moreover, the deformation of the normal strain line and the maximum deflection of the plate are calculated numerically (FEM). Results of these calculations are compared.
4
Content available Static bending of isotropic circular cylindrical shells based on the higher order shear deformation theory of Reddy and Liu
Nwoji C. U., Ani D. G., Oguaghamba O. A., Ibeabuchi V. T.
International Journal of Applied Mechanics and Engineering
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2021
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Vol. 26, no. 3
141--162
EN
In this paper, a displacement based shear deformation theory formulated on the cubic in-plane displacement field equation of Reddy and Liu is presented for the static bending analysis of isotropic circular cylindrical shells. The adopted displacement field accounts for a quadratic (parabolic) distribution of the transverse shear through the shell thickness as well as satisfies the need for a stress free upper and lower boundary surfaces of the shell. The equations of static equilibrium are obtained on application of the principle of virtual work. Numerical results of the bending analysis for the displacements and stresses are presented for the simply supported shell. A comparison made to those of the Kirchhoff-Love theory for varying shell length to mean – radius of curvature ratios, shows good agreement for thin shells irrespective of the shell length to radius of curvature ratio [...]. The transverse sharing effect is found to be noticeable in the deformation of thick shells, however, this effect diminishes with a continuous increase in [...] ratios.
5
Content available Free Vibration Analysis of A357 Alloy Reinforced with Dual Particle Size Silicon Carbide Metal Matrix Composite Plates Using Finite Element Method
Lakshmikanthan A., Mahesh V., Prabhu R. T., Patel M. G. C., Bontha S.
Archives of Foundry Engineering
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2021
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Vol. 21, iss. 1
101--112
EN
In this work, the free vibration behaviour of A357 composite plate reinforced with dual particle size (DPS) (3 wt.% coarse + 3 wt.% fine, 4 wt.% coarse + 2 wt.% fine, and 2 wt.% coarse + 4 wt.% fine) SiC is evaluated using the finite element method. To this end, first-order shear deformation theory (FSDT) has been used. The equations of motion have been derived using Hamilton’s principle and the solution has been obtained through condensation technique. A thorough parametric study was conducted to understand the effect of reinforcement size and weight fraction, boundary conditions, aspect ratio and length-to-width ratio of plate geometry on natural frequencies of A357/DPS-SiC composite plates. Results reveal significant influence of all the above variables on natural frequency of the composite plates. In all the cases, A357 composite plate reinforced with 4 wt.% coarse and 2 wt.% fine SiC particles displayed the highest natural frequency owing to its higher elastic and rigidity modulus. Further, the natural frequencies increase with decrease in aspect ratio of the plate geometry. Natural frequency also decreases with increase in the number of free edges. Lastly, increasing the length-to-width ratio drastically improves the natural frequency of the plates.
6
Content available Hybrid sandwich panels: a review
Sandeep S. H., Srinivasa C. V.
International Journal of Applied Mechanics and Engineering
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2020
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Vol. 25, no. 3
64--85
EN
A high specific stiffness, high specific strength, and tailoring the properties for specific application hale attracted the attention of the researchers to work in the field of laminated composites and Sandwich structures. Rapid use of these laminated composites and Sandwich structures necessitated the development of new theories that suitable for the bending, buckling and vibration analysis. Many articles were published on free vibration of beams, plates, shells laminated composites and sandwich structures. In this article, a review on free vibration analysis of shear deformable isotropic beams, plates, shells, laminated composites and sandwich structures based on various theories and the exact solution is presented. In addition to this, the literature on finite element modeling of beams, plates, shells laminated composites and sandwich structures based on classical and refined theories is also reviewed. The present article is an attempt to review the available literature, made in the past few decades on free flexural vibration response of Fiber Metal laminated Composites and Sandwich panels using different analytical models, numerical techniques, and experimental methods.
7
Content available remote Bending of beams with consideration of a seventh-order shear deformation theory
Magnucki Krzysztof, Stawecki Włodzimierz, Magnucka-Blandzi Ewa
Engineering Transactions
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2020
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Vol. 68, iss. 2
119--135
EN
The subject of the paper is a simply-supported prismatic beam with bisymmetrical crosssections under non-uniformly distributed load. The shapes of the cross-sections and the nonuniformly distributed load are described analytically. The individual seventh-order shear deformation theory-hypothesis of the planar beam cross-sections is assumed. Based on the principle of stationary potential energy two differential equations of equilibrium are obtained. The system of the equations is analytically solved, and the shear and deflection coefficients of the beam are derived. Moreover, the shear stress patterns for selected cross-sections are determined and compared with stresses determined by Zhuravsky’s formula. The results of example calculations are presented in tables and figures.
8
Content available remote A shear deformation theory of beams with bisymmetrical Cross-sections based on the Zhuravsky shear stress formula
Magnucki Krzysztof, Lewinski Jerzy, Magnucka-Blandzi Ewa
Engineering Transactions
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2020
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Vol. 68, iss. 4
353--370
EN
This paper is devoted to simply supported beams with bisymmetrical cross-sections under a generalized load. Based on the Zhuravsky shear stress formula, the shear deformation theory of a planar beam cross-section is formulated. The deflections and the shear stresses of exemplary beams are determined. Moreover, the numerical-FEM computations of these beams are carried out. The results of the research are shown in figures and tables.
9
Content available Hygrothermoelastic buckling response of composite laminates by using modified shear deformation theory
Kazemi M.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 1
3--14
EN
In this study, a finite element based formulation is developed for analyzing the buckling and post-buckling of composite laminates subjected to mechanical and hygrothermal loads using Modified Hyperbolic Shear Deformation Theory (MHSDT). The changes in the critical buckling load are presented for different lamination schemes, thicknesses, material properties and plate aspect ratios. In addition, post buckling analysis is performed for a composite plate subjected to uniform in-plane thermal and moisture induced loadings by using MHSDT. Matlab software has been used for programming the analysis. The results obtained by Matlab codes are in a satisfactory consistence compared to the references. Thus, the developed MHSDT has been validated for buckling and post buckling analysis of laminated plates in hygrothermal environment.
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