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1
Content available Free flexural axisymmetric vibration of a clamped circular sandwich plate with a functionally graded core
Magnucka-Blandzi Ewa, Magnucki Krzysztof
Archive of Mechanical Engineering
|
2025
|
LXXII, nr 3
545--561
EN
This study presents an analytical model of a clamped circular sandwich plate with a functionally graded core, developed within the framework of an individual nonlinear shear deformation theory. The mathematical formulation is an original contribution, providing a unified representation of various structural configurations – including three-layer-like, five-layer-like, homogeneous single-layer, and intermediate forms – through a single continuous function. The variation of Young’s modulus across the core is controlled by three parameters, enabling flexible modeling of material gradation. The governing equations are derived using Hamilton’s principle and are solved analytically through an approximate solution method. The proposed model allows investigation of the effects of material property variation and the core-to-plate thickness ratio on the fundamental natural frequency, as well as on the shear effect coefficient and plate mass, yielding general conclusions supported by a coherent theoretical framework.
2
Content available Free flexural vibrations of standard wide-flange H-beams with consideration of the shear effect
Magnucki Krzysztof
Pojazdy Szynowe
|
2024
|
Nr 1-2
46--50
EN
The subject of the paper is a simply supported standard wide-flange H-beam. Cross sections of this beam is analytically described as a three-layer structure. The shear effect in its successive layers is taking into account with consideration of the classical shear stress formula called Zhuravsky shear stress. Based on Hamilton’s principle, two differential equations of motion are obtained. These equations are analytically solved and the fundamental natural frequency of flexural vibration for this beam is derived. Exemplary calculations are carried out for selected five I-beams.
3
Content available A shear effect in a bending non-standard I-beam under uniformly distributed load
Magnucka-Blandzi Ewa, Magnucki Krzysztof
Pojazdy Szynowe
|
2024
|
Nr 3-4
28--35
EN
The paper is devoted to the analytical study of the bending problem of a simply supported or clamped non-standard I-beam under a uniformly distributed load. The cross-sectional shape of this beam, as a three-part structure, is analytically described. The purpose of this research is to present a detailed analytical model of this beam, considering the shear effect and its influence on the beam's deflection. This model is formulated according to linear elastic theory, and the deformation of a planar cross-section after the bending of this beam due to the shear effect is determined. Based on the principle of stationary potential energy, two differential equations of equilibrium are obtained. These equations are analytically solved, and the dimensionless shear effect function and the relative deflection of this beam are derived. Consequently, the maximum dimensionless relative deflection and the dimensionless coefficient of the shear effect are determined. Exemplary calculations are carried out for three selected non-standard I-beams of different lengths, demonstrating a significant influence of the shear effect on the deflections of short beams, especially clamped beams.
4
Content available Elastic buckling of a rectangular sandwich plate with an individual functionally graded core
Magnucki Krzysztof, Magnucka-Blandzi Ewa, Sowiński Krzysztof
Journal of Theoretical and Applied Mechanics
|
2024
|
Vol. 62 nr 1
171--185
EN
This paper is devoted to a thin-walled sandwich plate with an individual functionally graded core. The nonlinear shear deformation theory of a straight normal line is applied. A system of three differential equations of equilibrium of this plate is obtained, based on the principle of stationary potential energy, which is reduced to two differential equations and solved analytically. The critical load of the rectangular sandwich plate is determined. A detailed analytical study is carried out for selected exemplary plates. Moreover, a numerical FEM model of this plate is developed. The results of these calculations are compared with each other.
5
Content available Buckling and free flexural vibration of an asymmetric sandwich beam with a functionally graded core
Magnucki K., Magnucka-Blandzi E., Sowiński K.
Archives of Mechanics
|
2024
|
Vol. 76, nr 4
335--355
EN
This paper is devoted to an asymmetrical sandwich beam with a functionally graded core with three different variants of boundary conditions. An analytical model of this beam, considering individual nonlinear shear deformation theory, is developed. Based on Hamilton’s principle, two differential equations of motion for this beam are obtained. These equations are solved analytically, and as a consequence, the critical forces and basic natural frequencies for each beam support variant are determined. Detailed calculations are carried out for selected exemplary beam structures, and their results are compared with numerical FEM analysis.
6
Content available remote Thermoelastic bending analysis of thick functionally graded sandwich plates with arbitrary graded material properties using a novel quasi-3D HSDT
Houari Mohammed Sid Ahmed, Bessaim Aicha, Bezzina Smain, Tounsi Abdelouahed, Daikh Ahmed Amine, Garg Aman, Belarbi Mohamed-Ouejdi
Archives of Civil and Mechanical Engineering
|
2024
|
Vol. 24, no. 2
art. no. e80, 2024
EN
In this paper, a novel integral higher shear deformation theory including the stretching effect is developed for the thermoelastic bending analysis of symmetric and non-symmetric functionally graded materials (FGM) sandwich plates with an arbitrary gradient. This integral theory has only five unknowns, which is even less than the other shear and normal deformation theories. The proposed model has a reduced number of equations and satisfies automatically the free surface conditions without using the shear correction factor. The present model has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the virtual work principle and solved via Navier’s procedure. The convergence of the proposed theoretical numerical model is performed to demonstrate the efficacy of the model. Moreover, several parametric examples are presented to show the thermoelastic bending response of the various symmetric P-FG sandwich plates with arbitrarily varying material properties.
7
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
|
2023
|
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.
8
Content available remote Extension of a novel higher order modeling to the vibration responses of sandwich graphene origami cylindrical panel
Vali Hossein, Arefi Mohammad
Archives of Civil and Mechanical Engineering
|
2023
|
Vol. 23, no. 4
art. e268, 1--27
EN
This paper presents dynamic formulation for a sandwich cylindrical panel based on higher order shear-deformation theory and Hamilton’s principle. The sandwich cylindrical panel is composed of a porous core sandwiched by two graphene origami reinforced copper matrix layers. The material properties of porous core and graphene origami-reinforced copper matrix layers are estimated using the Halpin–Tsai and rule of mixture for various distributions of porosity and graphene origami dispersion in terms of material and geometric characteristics of constituent materials. Through calculation of strain energy, kinetic energy and external work, the governing equations of motion are derived using Hamilton’s principle. The analytical solu tion is applied for parametric analysis of the problem. The natural frequencies are analytically obtained in terms of material and geometric parameters of graphene origami such as volume fraction and folding degree, various distributions, porosity coefcient, porosity distribution, and temperature. The numerical results indicate that the maximum natural frequency is obtained for X distribution of graphene origami.
9
Content available Three models of a sandwich beam: bending, buckling, and free vibrations
Magnucki Krzysztof, Magnucka-Blandzi Ewa, Wittenbeck Leszek
Engineering Transactions
|
2022
|
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.
10
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
|
2022
|
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.
11
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
|
2021
|
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.
12
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
|
2021
|
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.
13
Content available Hybrid sandwich panels: a review
Sandeep S. H., Srinivasa C. V.
International Journal of Applied Mechanics and Engineering
|
2020
|
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.
14
Content available Bending of beams with consideration of a seventh-order shear deformation theory
Magnucki Krzysztof, Stawecki Włodzimierz, Magnucka-Blandzi Ewa
Engineering Transactions
|
2020
|
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.
15
Content available 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
|
2020
|
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.
16
Content available Hygrothermoelastic buckling response of composite laminates by using modified shear deformation theory
Kazemi M.
Journal of Theoretical and Applied Mechanics
|
2018
|
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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