Articoli di riviste: "Plate theory"

1

Shiau, Le-Chung, and Yuan-Shih Chen. "Effects of In-plane Load on Flutter of Homogeneous Laminated Beam Plates with Delamination." Journal of Vibration and Acoustics 123, no. 1 (July 1, 2000): 61–66. http://dx.doi.org/10.1115/1.1315593.

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The effects of in-plane load on flutter characteristics of delaminated two-dimensional homogeneous beam plates at high supersonic Mach number are investigated theoretically. Linear plate theory and quasi-steady supersonic aerodynamic theory are employed. A simple beam-plate model is developed to predict the effects of in-plane load on flutter boundaries for the delaminated beam plates with simply supported ends. Results reveal that the presence of an in-plane compressive load degrades the stiffness and natural frequencies of the plate and thereby decreases the flutter boundary for the plate. However, for certain geometry, the flutter boundaries were raised due to flutter coalescence modes of the plate altered by the presence of the in-plane load on the plate.

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Rogacheva, Nelly, and Yulia Zheglova. "PROBLEM OF PLATE BENDING IN THE MOMENT ASYMMETRIC THEORY OF ELASTICITY." International Journal for Computational Civil and Structural Engineering 19, no. 2 (June 27, 2023): 71–80. http://dx.doi.org/10.22337/2587-9618-2023-19-2-71-80.

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For a number of materials used in modern practice, calculations according to the classical theory of elasticity give incorrect results. To ensure the reliable operation of structures, there is a need for new theories. At present, of particular interest for practical applications is the asymmetric moment theory of elasticity. In the work, by the method of hypotheses, the three-dimensional equations of the moment asymmetric theory of elasticity are reduced to the equations of the theory of plates. The hypotheses of the theory of plates in the moment theory of elasticity are formulated on the basis of previously obtained our results of the reduction of three-dimensional equations to two-dimensional theories by a mathematical method. Just as in the classical theory of elasticity, the complete problem of the moment theory of plates is divided into two problems - a plane problem and a problem of plate bending. The equations of the plane problem have been obtained in many papers. The situation is different with the construction of the theory of plate bending in the moment theory of elasticity. In this work, for the first time, substantiated hypotheses are formulated and a consistent theory of plate bending is presented. A numerical calculation of the bending of a rectangular hinged plate is carried out according to the obtained applied theory. The calculation results are presented in the form of graphs.

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3

Deepak, S. A., Rajesh A. Shetty, K. Sudheer Kini, and G. L. Dushyanthkumar. "Buckling analysis of thick plates using a single variable simple plate theory." Journal of Mines, Metals and Fuels 69, no. 12A (April 28, 2022): 67. http://dx.doi.org/10.18311/jmmf/2021/30097.

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Buckling analysis of thick plates has been carried out herein by using a single variable simple plate theory. Theory used herein is a third order shear deformation plate theory which uses a single displacement function for the complete formulation of plates. Plate formulation is governed by only one governing differential equation. Governing equation of the theory has close resemblance to that of Classical Plate Theory. Thus, plate problems can be solved in the similar lines as in case of classical plate theory. Plate theory used herein does not require a shear correction coefficient. To check the efficacy of the theory buckling analysis of simply supported thick rectangular plates is carried out. Critical buckling loads for simply supported plates are evaluated and the results obtained are compared to other shear deformation plate theories. Buckling load results are found to be in good agreement with other plate theory results.

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4

Kim, Jun-Sik, and Maenghyo Cho. "Enhanced First-Order Shear Deformation Theory for Laminated and Sandwich Plates." Journal of Applied Mechanics 72, no. 6 (May 22, 2005): 809–17. http://dx.doi.org/10.1115/1.2041657.

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A new first-order shear deformation theory (FSDT) has been developed and verified for laminated plates and sandwich plates. Based on the definition of Reissener–Mindlin’s plate theory, the average transverse shear strains, which are constant through the thickness, are improved to vary through the thickness. It is assumed that the displacement and in-plane strain fields of FSDT can approximate, in an average sense, those of three-dimensional theory. Relationship between FSDT and three-dimensional theory has been systematically established in the averaged least-square sense. This relationship provides the closed-form recovering relations for three-dimensional variables expressed in terms of FSDT variables as well as the improved transverse shear strains. This paper makes two main contributions. First an enhanced first-order shear deformation theory (EFSDT) has been developed using an available higher-order plate theory. Second, it is shown that the displacement fields of any higher-order plate theories can be recovered by EFSDT variables. The present approach is applied to an efficient higher-order plate theory. Comparisons of deflection and stresses of the laminated plates and sandwich plates using present theory are made with the original FSDT and three-dimensional exact solutions.

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5

Ji, Ming, Yi-Chuang Wu, and Chien-Ching Ma. "In-plane-dominated vibration characteristics of piezoelectric thick circular plates based on higher-order plate theories." Journal of Mechanics 38 (2022): 410–32. http://dx.doi.org/10.1093/jom/ufac034.

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ABSTRACT Numerous engineering applications exist for the piezoelectric effect, which results from the electromechanical coupling between electrical and mechanical fields. In-plane vibrations of piezoelectric plates’ resonance frequencies and associated mode shapes have been thoroughly investigated. However, analytical solutions for in-plane-dominated vibrations of thick piezoelectric circular plates are limited. In this paper, higher-order plate theories for the in-plane-dominated vibration characteristics of piezoelectric circular thick plates under fully clamped and completely free boundary conditions are presented. The resonant frequencies and associated mode shapes were investigated based on two higher-order plate theories: second-order shear deformation plate theory and third-order shear deformation plate theory, as well as simplified third-order linear piezoelectric theory. Hamilton's principle was applied to derive equations of motion and boundary conditions. In the theoretical analysis, the resonant frequencies, associated mode shapes and distribution of electric displacements for various radius-to-thickness ratios were calculated. The numerical results obtained by the finite element method were compared with those obtained from theoretical analysis. Excellent agreement was found between the theoretical and numerical results for the thick piezoelectric circular plates.

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6

Toledano, A., and H. Murakami. "A Composite Plate Theory for Arbitrary Laminate Configurations." Journal of Applied Mechanics 54, no. 1 (March 1, 1987): 181–89. http://dx.doi.org/10.1115/1.3172955.

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In order to improve the accuracy of in-plane responses of shear deformable composite plate theories, a new laminated plate theory was developed for arbitrary laminate configurations based upon Reissner’s (1984) new mixed variational principle. To this end, across each individual layer, piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano (1969). A comparison with the exact solutions obtained for symmetric, antisymmetric, and arbitrary laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.

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7

CHALLAMEL, NOËL, GJERMUND KOLVIK, and JOSTEIN HELLESLAND. "PLATE BUCKLING ANALYSIS USING A GENERAL HIGHER-ORDER SHEAR DEFORMATION THEORY." International Journal of Structural Stability and Dynamics 13, no. 05 (May 28, 2013): 1350028. http://dx.doi.org/10.1142/s0219455413500284.

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The buckling of higher-order shear plates is studied in this paper with a unified formalism. It is shown that usual higher-order shear plate models can be classified as gradient elasticity Mindlin plate models, by augmenting the constitutive law with the shear strain gradient. These equivalences are useful for a hierarchical classification of usual plate theories comprising Kirchhoff plate theory, Mindlin plate theory and third-order shear plate theories. The same conclusions were derived by Challamel [Mech. Res. Commun.38 (2011) 388] for higher-order shear beam models. A consistent variational presentation is derived for all generic plate theories, leading to meaningful buckling solutions. In particular, the variationally-based boundary conditions are obtained for general loading configurations. The buckling of the isotropic or orthotropic composite plates is then investigated analytically for simply supported plates under uniaxial or hydrostatic in-plane loading. An analytical buckling formula is derived that is common to all higher-order shear plate models. It is shown that cubic-based interpolation models for the displacement field are kinematically equivalent, and lead to the same buckling load results. This conclusion concerns for instance the plate models of Reddy [J. Appl. Mech.51 (1984) 745] or the one of Shi [Int. J. Solids Struct.44 (2007) 4299] even though these models are statically distinct (leading to different stress calculations along the cross-section). Finally, a numerical sensitivity study is made.

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8

Thai, Huu-Tai, Thuc P. Vo, Trung-Kien Nguyen, and Jaehong Lee. "A nonlocal sinusoidal plate model for micro/nanoscale plates." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 14 (February 7, 2014): 2652–60. http://dx.doi.org/10.1177/0954406214521391.

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A nonlocal sinusoidal plate model for micro/nanoscale plates is developed based on Eringen’s nonlocal elasticity theory and sinusoidal shear deformation plate theory. The small-scale effect is considered in the former theory while the transverse shear deformation effect is included in the latter theory. The proposed model accounts for sinusoidal variations of transverse shear strains through the thickness of the plate, and satisfies the stress-free boundary conditions on the plate surfaces, thus a shear correction factor is not required. Equations of motion and boundary conditions are derived from Hamilton’s principle. Analytical solutions for bending, buckling, and vibration of simply supported plates are presented, and the obtained results are compared with the existing solutions. The effects of small scale and shear deformation on the responses of the micro/nanoscale plates are investigated.

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9

Murakami, H. "Laminated Composite Plate Theory With Improved In-Plane Responses." Journal of Applied Mechanics 53, no. 3 (September 1, 1986): 661–66. http://dx.doi.org/10.1115/1.3171828.

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In order to improve the accuracy of the in-plane response of the shear, deformable laminated composite plate theory, a new laminated plate theory has been developed based upon a new variational principle proposed by Reissner (1984). The improvement is achieved by including a zigzag-shaped C0 function to approximate the thickness variation of in-plane displacements. The accuracy of this theory is examined by applying it to a problem of cylindrical bending of laminated plates which has been solved exactly by Pagano (1969). The comparison of the in-plane response with the exact solutions for symmetric three-ply and five-ply layers has demonstrated that the new theory predicts the in-plane response very accurately even for small span-to-depth ratios.

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10

Elmardi Suleiman, Osama Mohammed, Mahmoud Yassin Osman, and Tagelsir Hassan. "B EFFECT OF BOUNDARY CONDITIONS ON BUCKLING LOAD FOR LAMINATED COMPOSITE DECKS PLATES." IRAQI JOURNAL FOR MECHANICAL AND MATERIALS ENGINEERING 20, no. 2 (June 28, 2020): 97–110. http://dx.doi.org/10.32852/iqjfmme.v20i2.491.

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Finite element (FE) method is presented for the analysis of thin rectangular laminatedcomposite decks plates under the biaxial action of in – plane compressive loading. Theanalysis uses the classical laminated plate theory (CLPT) which does not account for sheardeformations. In this theory it is assumed that the laminate is in a state of plane stress, theindividual lamina is linearly elastic, and there is perfect bonding between layers. The classicallaminated plate theory (CLPT), which is an extension of the classical plate theory (CPT)assumes that normal to the mid – surface before deformation remains straight and normal tothe mid – surface after deformation. Therefore, this theory is only adequate for bucklinganalysis of thin laminates. A Fortran program has been developed. New numerical results aregenerated for in – plane compressive biaxial buckling which serve to quantify the effect ofboundary conditions on buckling loading. It is observed that, for all cases the buckling loadincreases with the mode number but at different rates depending on whether the plate is simplysupported, clamped or clamped – simply supported. The buckling load is a minimum whenthe plate is simply supported and a maximum when the plate is clamped. Because of therigidity of clamped boundary condition, the buckling load is higher than in simply supportedboundary condition. It is also observed that as the mode number increases, the plate needsadditional supp

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11

Gilat, R., T. O. Williams, and J. Aboudi. "Buckling of composite plates by global–local plate theory." Composites Part B: Engineering 32, no. 3 (April 2001): 229–36. http://dx.doi.org/10.1016/s1359-8368(00)00059-7.

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12

Enayati, Seyed Ghasem, Morteza Dardel, and Mohammad Hadi Pashaei. "The effect of bi-axial in-plane loads on the natural frequency of nano-plates." Journal of Vibration and Control 24, no. 19 (August 30, 2017): 4513–28. http://dx.doi.org/10.1177/1077546317728154.

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In this paper, natural frequencies of nano-plates subjected to two-sided in-plane tension or compressive loads, based on Eringen nonlocal elasticity theory and displacement field of first-order shear deformation plate theory (FSDT), are investigated. By considering total rotational variables as the two rotations due to bending and shear, another formulation form of FSDT nano-plate is achieved, that can simultaneously consider classical plate theory (CLPT) and FSDT. In a comprehensive study, the effects of different parameters such as a nonlocal parameter, aspect ratio, thickness to length ratio, mode number, boundary conditions and also length of nano-plate are examined on the dimensionless natural frequency. The results show that simultaneously applying two-sided tension and compressive in-plane loads changes frequency in a manner which is different to one-directional loading.

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13

Chitnis, M. R., Y. M. Desai, and T. Kant. "Wave Propagation in Laminated Composite Plates Using Higher Order Theory." Journal of Applied Mechanics 68, no. 3 (October 6, 2000): 503–5. http://dx.doi.org/10.1115/1.1352062.

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A higher order displacement based formulation has been developed to investigate wave propagation in fiber-reinforced polymer composite laminated (FRPCL) plates. The formulation has been applied, as an illustration, to a plate made up of transversely isotropic laminae with the axes of symmetry lying in the plane of the lamina. Results for the plane as well as the antiplane strain cases are shown to be in excellent agreement with the exact solutions for isotropic and transversely isotropic single layered plates. Also, numerical results have been obtained for crossply (0 deg/90 deg/0 deg/90 deg) laminated composite plates, which agree very well with the previously published numerical results. The formulation can be employed to expeditiously investigate the dispersion characteristics of waves propagating in a plate with an arbitrary number of anisotropic laminae.

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14

Berg, L. J. "Boundary Layer Phenomena in Large Deflection, Small Strain Plate Theory." Journal of Applied Mechanics 60, no. 1 (March 1, 1993): 229–32. http://dx.doi.org/10.1115/1.2900759.

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Boundary layers exist at the edges of thin plates undergoing large deformations because the interior of the plate must assume a developable shape. The developable shape is sometimes incompatible with the force and moment resultants prescribed at the plate’s boundary, in particular when the edge of the plate is stress free. A boundary layer solution is presented which describes the shape of a boundary layer in a plate undergoing large deflections. The boundary layer is a slight perturbation of the interior shape which allows the appropriate boundary conditions to be satisfied. Since developable shells are applicable to a plane, the boundary layer is also appropriate for arbitrary developable shells.

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15

Bhimaraddi, Alavandi. "Nonlinear Dynamics of In-Plane Loaded Imperfect Rectangular Plates." Journal of Applied Mechanics 59, no. 4 (December 1, 1992): 893–901. http://dx.doi.org/10.1115/1.2894058.

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This paper deals with the nonlinear vibrations of composite laminated plates using the generalized formulation of which the von Karman-type formulation is a special case. The two-dimensional plate theory used is that of a parabolic shear theory in which the transverse shear strain distribution is parabolic across the plate thickness. The resulting governing equations of this formulation are nonlinear is all the plate displacement parameters unlike the von Karman model in which they are nonlinear in the lateral displacement only. Because of this complex nature of the equations the usual approach for nonlinear plate analysis cannot be used, and hence a regular perturbation technique has been adopted to obtain the solution of these equations. All the complexities like the initial imperfections and in-plane applied edge loads have also been included in the analysis. Numerical examples for simply-supported plates indicate that for in-plane loaded imperfect plates, the von Karman formulation differs slightly when compared with the present more general formulation.

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16

Lebée, Arthur, and Karam Sab. "On the Generalization of Reissner Plate Theory to Laminated Plates, Part I: Theory." Journal of Elasticity 126, no. 1 (May 27, 2016): 39–66. http://dx.doi.org/10.1007/s10659-016-9581-6.

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17

Sayyad, A. S., and Y. M. Ghugal. "Effect of Stress Concentration on Laminated Plates." Journal of Mechanics 29, no. 2 (December 19, 2012): 241–52. http://dx.doi.org/10.1017/jmech.2012.131.

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AbstractThis paper deals with the problem of stress distribution in orthotropic and laminated plates subjected to central concentrated load. An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is used to obtain in-plane normal and transverse shear stresses through the thickness of plate. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. A simply supported plate with central concentrated load is considered for the numerical analysis. Anomalous behavior of inplane normal and transverse shear stresses is observed due to effect of stress concentration compared to classical plate theory and first order shear deformation theory.

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18

Wang, C. M., S. Kitipornchai, and J. N. Reddy. "Relationship Between Vibration Frequencies of Reddy and Kirchhoff Polygonal Plates With Simply Supported Edges." Journal of Vibration and Acoustics 122, no. 1 (October 1, 1997): 77–81. http://dx.doi.org/10.1115/1.568438.

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This paper presents an exact relationship between the natural frequencies of Reddy third-order plate theory and those of classical Kirchhoff plate theory for simply supported, polygonal isotropic plates, including rectangular plates. The relationship for the natural frequencies enables one to obtain the solutions of the third-order plate theory from the known Kirchhoff plate theory for the same problem. As examples, some vibration frequencies for rectangular and regular polygonal plates are determined using this relationship. [S0739-3717(00)01601-9]

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Trubitsyn, A. P., and V. P. Trubitsyn. "Corrections to the Theory of Elastic Bending of Thin Plates for 2D Models in the Reissner Approximation." Физика земли 2023, no. 4 (July 1, 2023): 3–15. http://dx.doi.org/10.31857/s0002333723040129.

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Elastic bending stresses and strains in the lithosphere are typically calculated based on the Kirchhoff–Love (thin) plate theory. The criterion for its applicability is the smallness of plate thickness to length ratio. In oceanic plates, due to the buoyant force of the mantle, the main deformations are not uniformly distributed along the plate but are concentrated in the vicinity of the subduction zone. Therefore, the effective length of the bending part of the plate is a few fractions of the actual length, and the criterion of a thin plate is partially violated. In this paper, we analyze the possibility of applying thick plate bending equations. The existing variational theories of 3D bending of thick plates are much more complicated than the Kirchhoff–Love theory, as they involve solving three differential equations instead of one, and have limited application due to their complexity. Since geophysical applications frequently use 2D models, in this paper we analyze in detail the potential and accuracy of the thick plate bending theory for 2D models. After the conversion to the 2D plane strain and plane stress approximation, the original 3D Reissner thick plate bending equations are written out in the form similar to the Kirchhoff equations with additive corrections and are supplemented with the explicit formulas for longitudinal displacement. The comparison of the analytical solutions of the 2D Reissner equations with the exact solutions shows that the 2D approximation only provides a correction for the plate bending function. However, this correction refines the Kirchhoff–Love theory by almost an order of magnitude. At the same time, the solution of the equations in this case turns out to be almost as simple as the solution of the thin plate equations.

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Reddy, J. N. "A Small Strain and Moderate Rotation Theory of Elastic Anisotropic Plates." Journal of Applied Mechanics 54, no. 3 (September 1, 1987): 623–26. http://dx.doi.org/10.1115/1.3173079.

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A general nonlinear theory for the dynamics of elastic anisotropic plates that accounts for transverse shear strains and moderate rotations is presented. The theory contains, as special cases, the von Ka´rma´n classical plate theory, the first-order shear deformation theory (i.e., the Reissner-Mindlin plate theory) and the third-order shear deformation plate theory. The theory is characterized, even for isotropic plates, by strong coupling between various equations of motion.

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Thinh, Tran Ich, and Tran Huu Quoc. "Analysis of stiffened laminated composite plates by finite element based on higher-order displacement theory." Vietnam Journal of Mechanics 30, no. 2 (July 1, 2008): 112–21. http://dx.doi.org/10.15625/0866-7136/30/2/5623.

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In this paper, authors use a finite element model based on higher-order displacement plate theory for analysis of stiffened laminated composite plates. Transverse shear deformation is included in the formulation making the model applicable for both moderately thick and thin composite plates. The plate element used is a nine-noded isoparametric one with nine degrees of freedom at each node. The stiffness of stiffener is reflected at all nine nodes of plate element in which it is placed. Accordingly, the stiffeners can be positioned anywhere within the place element. Free vibration and deflection of stiffened laminated composite plates are carried out, and results are compared with existing analytical and other solutions.

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Dung, Dao Van, and Nguyen Thi Nga. "Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 2: Numerical results and discussions." Vietnam Journal of Mechanics 37, no. 4 (November 26, 2015): 251–62. http://dx.doi.org/10.15625/0866-7136/37/4/5885.

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Based on the first-order shear deformation plate theory (FSDT), the smeared stiffeners technique and Galerkin method, the analytical expressions to determine the static critical buckling load and analyze the post-buckling load-deflection curves of FGM plates reinforced by FGM stiffeners resting on elastic foundations and subjected to in-plane compressive loads or thermal loads are established in part 1. In this part, we will use them to study the effects of temperature, stiffener, volume fraction index, geometrical parameters, elastic foundations on the buckling and post-buckling behavior of plates. In addition, the results in comparisons between the classical plate theory (CPT) and the first order shear deformation theory (FSDT) also are carried out and shown that the buckling and post-buckling behavior of more thick plate should be studied by FSDT.

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Chung, Nguyen Thai, and Duong Thi Ngoc Thu. "Static stability study of stiffened functionally graded composite plates reinforced by carbon nanotubes using finite element method." Vietnam Journal of Mechanics 45, no. 3 (September 30, 2023): 216–34. http://dx.doi.org/10.15625/0866-7136/18862.

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This paper presents some results on the linear stability research of Stiffened Functionally Graded Carbon NanoTube-Reinforced Composite (SFG-CNTRC) plates under static in-plane loads by the Finite Element Method (FEM) and a new four-variable refined plate theory. The governing equations for the static buckling of the system are obtained by the new four-variable refined plate theory and FEM. The eigenvalue problem method was used to solve the equation to determine the critical force of the plates. A numerical example is compared with the results in another research to check the validity of the present algorithm. The influences of some factors such as plate theory, CNT distribution along the layer thickness, stiffener height ratio, and fiber orientation angle on the critical buckling loads and unstable regions are discussed.

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Asadi, Hamed, Mohammad M. Aghdam, and Mahmoud Shakeri. "Vibration analysis of axially moving line supported functionally graded plates with temperature-dependent properties." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 6 (July 26, 2013): 953–69. http://dx.doi.org/10.1177/0954406213498033.

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Vibration analysis of axially moving functionally graded plates with internal line supports and temperature-dependent properties is investigated using harmonic differential quadrature method. The plate is subjected to static in-plane forces while out-of-plane loading is dynamic. Stability of an axially moving plate, traveling at a constant velocity between different supports and experiencing small transverse vibrations are considered. The series of internal rigid line supports parallel to the plate edges are considered together with various arbitrary combinations of boundary conditions. Material properties of the plate are assumed temperature-dependent which is a non-linear function of temperature and differ continuously through thickness according to a power-law distribution of the volume fractions of the plate constituents. Two types of micromechanical models, namely, the Voigt and Mori–Tanaka models are considered. Based on the classical plate theory, the governing equations are obtained for functionally graded plate using the Hamilton’s principle. In the frame of a general dynamic analysis, it is shown that the onset of instability takes place in the form of divergence. The plate may experience divergence or flutter instability at a super critical velocity. Results for dynamic analysis of isotropic and laminated plates are validated with available data in the existing literature, which show excellent agreement. Furthermore, some new results are presented for vibration analysis of functionally graded material plates to study effects of the location of line supports, material properties, volume fraction, temperature, loading, aspect ratio and speed.

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Khalfi, Y., B. Sallai, and Y. Bellebna. "Buckling analysis of plates using an efficient sinusoidal shear deformation theory." Journal of Fundamental and Applied Sciences 14, no. 1 (June 5, 2023): 210–28. http://dx.doi.org/10.4314/jfas.v14i1.11.

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Mechanical buckling response of isotropic and orthotropic plates using the two variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate; hence it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The nonlinear strain-displacement of Von Karman relations are also taken into consideration. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

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Sadiq, Ebtihal Abbas, and Widad Ibraheem Majeed. "Transient Response Investigation of Cross-Ply Plates Using Refined Theory." Journal of Engineering 31, no. 5 (May 1, 2025): 113–28. https://doi.org/10.31026/j.eng.2025.05.07.

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Response of cross-ply plates subjected to transient load is obtained using five variables refined plate theory, and four variables plate theory. Equations of motion are derived through the principleof virtual work. Navier series used for simply supported laminated plates. The results of this work are presented for different parameters, such as the ply number, thickness, and modulus ratio with mechanical load (sinusoidal and step pulses), which are compared with those obtained using high-order shear plate theory. Five variables of refined plate theory give results that are considerably different from the four variables of refined plate theory and higher-order theory. The obtained results from the four variables theory have the same behavior as those given by higher order theory, but are under-predicted with small time shifting.

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Revenko, Viktor P. "Analytical Solution of the Problem of Symmetric Thermally Stressed State of Thick Plates Based on the 3D Elasticity Theory." Journal of Mechanical Engineering 24, no. 1 (March 30, 2021): 36–41. http://dx.doi.org/10.15407/pmach2021.01.036.

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An important place among thermoelasticity problems is occupied by the plane elasticity problem obtained from the general three-dimensional problem after using plane stress state hypotheses for thin plates. In the two-dimensional formulation, this problem has become widespread in the study of the effect of temperature loads on the stress state of thin thermosensitive plates. The article proposes a general three-dimensional solution of the static problem of thermoelasticity in a form convenient for practical application. To construct it, a particular solution of the inhomogeneous equation, the thermoelastic displacement potential, was added by us to the general solution of Lamé's equations, the latter solution having been previously found by us in terms of three harmonic functions. It is shown that the use of the proposed solution allows one to satisfy the relation between the static three-dimensional theory of thermoelasticity and boundary conditions, and also to construct a closed system of partial differential equations for the introduced two-dimensional functions without using hypotheses about the plane stress state of a plate. The thermoelastic stress state of a thick or thin plate is divided into two parts. The first part takes into account the thermal effects caused by external heating and internal heat sources, while the second one is determined by a symmetrical force load. The thermoelastic stresses are expressed in terms of deformations and known temperature. A three-dimensional thermoelastic stress-strain state representation is used and the zero boundary conditions on the outer flat surfaces of the plate are precisely satisfied. This allows us to show that the introduced two-dimensional functions will be harmonic. After integrating along the thickness of the plate along the normal to the median surface, normal and shear efforts are expressed in terms of three unknown two-dimensional functions. The three-dimensional stress state of a symmetrically loaded thermosensitive plate was simplified to the two-dimensional state. For this purpose, we used only the hypothesis that the normal stresses perpendicular to the median surface are insignificant in comparison with the longitudinal and transverse ones. Displacements and stresses in the plate are expressed in terms of two two-dimensional harmonic functions and a particular solution, which is determined by a given temperature on the surfaces of the plate. The introduced harmonic functions are determined from the boundary conditions on the side surface of the thick plate. The proposed technique allows the solution of three-dimensional boundary value problems for thick thermosensitive plates to be reduced to a two-dimensional case.

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28

Singh, S. J., and S. P. Harsha. "Static Analysis of Functionally Graded Plate Using Nonlinear Classical Plate Theory with Von-Karman Strains." International Journal of Applied Mechanics and Engineering 23, no. 3 (August 1, 2018): 707–26. http://dx.doi.org/10.2478/ijame-2018-0039.

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Abstract The present study is based on the nonlinear bending analysis of an FGM plate with Von-Karman strain based on the non-linear classical plate theory (NLCPT) with in-plane displacement and moderate rotation. Non-linear bending analysis based on stresses and transverse deflections is then carried out for the plate for the complex solution obtained using an analytical method viz. Navier’s method. The equations of motion and boundary conditions are obtained using the Principle of Minimum Potential Energy (PMPE) method and material property is graded in thickness direction according to simple power-law distribution in terms of volume fractions of the constituents. The effect of the span-to-thickness ratio and FGM exponent on the maximum central deflection and stresses are studied. The results show that the response is transitional with respect to ceramic and metal and the complex solution predicts the real behavior of stresses and deflections in the functionally graded plate. The functionally graded plate is found to be more effective for moderately thick and thick plates, which is inferred by a complex nature of the solution. For FGM plates, the transverse deflection is in-between to that of metal and ceramic rich plates. The complex nature of the solution also gives information about the stress distribution in the thickness direction.

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29

Ahmed, Frih, Idder Abdelghani, Moulay Ali Abderrahmane, Abdeldjebar Rabia, Missoum Lakhdar, Fali Leyla, Boutadara Youcef, and Bassoud Abdelkader. "Bending behaviour of new sandwich structures for future constructions based on the equivalent single-layer trigonometric shear deformation theory." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 3 (December 30, 2024): e12892. https://doi.org/10.54021/seesv5n3-104.

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A novel single-layer trigonometric shear deformation theory (TSDT) is proposed for the static bending analysis of sandwich plates and cross-ply laminated composite plates. This theory incorporates the effects of transverse shear deformation and transverse normal strain, which are often neglected in classical plate theories. The TSDT employs a sinusoidal function for the in-plane displacement field and a cosine function for the transverse displacement field through the thickness of the plate. This kinematic assumption provides a more accurate representation of the deformation behavior compared to conventional higher-order shear deformation theories (HSDTs), while maintaining computational efficiency. The governing equations and associated boundary conditions are derived using the principle of virtual work. To validate the accuracy and efficiency of the proposed TSDT, numerical results are obtained for various benchmark problems and compared with those obtained from Reddy's higher-order shear deformation theory, classical plate theory, first-order shear deformation theory, and three-dimensional elasticity theory. The results demonstrate that the TSDT offers accurate predictions of deflections and stresses, particularly in the regions near the edges and interfaces of the layers.

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30

Sadrnejad. "Vibration Equations of Thick Rectangular Plates Using Mindlin Plate Theory." Journal of Computer Science 5, no. 11 (November 1, 2009): 838–42. http://dx.doi.org/10.3844/jcssp.2009.838.842.

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31

Vuksanovic, Djordje, and Marina Cetkovic. "Analytical solution for multilayer plates using general layerwise plate theory." Facta universitatis - series: Architecture and Civil Engineering 3, no. 2 (2005): 121–36. http://dx.doi.org/10.2298/fuace0502121v.

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32

Kim, Seung-Eock, Huu-Tai Thai, and Jaehong Lee. "A two variable refined plate theory for laminated composite plates." Composite Structures 89, no. 2 (June 2009): 197–205. http://dx.doi.org/10.1016/j.compstruct.2008.07.017.

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33

Dung, Dao Van, and Nguyen Thi Nga. "Nonlinear analysis of stability for imperfect eccentrically stiffened FGM plates under mechanical and thermal loads based on FSDT. Part 1: Governing equations establishment." Vietnam Journal of Mechanics 37, no. 3 (August 25, 2015): 187–204. http://dx.doi.org/10.15625/0866-7136/37/3/5884.

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In this paper, the buckling and post-buckling behaviors of eccentrically stiffened functionally graded material (ES-FGM) plates on elastic foundations subjected to in-plane compressive loads or thermal loads are investigated by an analytical solution. The novelty of this work is that FGM plates are reinforced by FGM stiffeners and the temperature, stiffener, foundation are considered. The first-order shear deformation plate theory is used. The thermal elements of plate and stiffeners in fundamental equations are introduced. Theoretical formulations based on the smeared stiffeners technique and the first-order shear deformation plate theory, are derived. The analytical expressions to determine the static critical buckling load and post-buckling load-deflection curves are obtained.

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34

ZENKOUR, ASHRAF M. "ON VIBRATION OF FUNCTIONALLY GRADED PLATES ACCORDING TO A REFINED TRIGONOMETRIC PLATE THEORY." International Journal of Structural Stability and Dynamics 05, no. 02 (June 2005): 279–97. http://dx.doi.org/10.1142/s0219455405001581.

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The displacement components are expressed by trigonometric series representation through the plate thickness to develop a two-dimensional theory. This trigonometric shear deformation plate theory is used to perform free-vibration analysis of a simply supported functionally graded thick plate. Lamé's coefficients and density for the material of the plate are assumed to vary in the thickness direction only. Effects of rotatory inertia are considered in the present theory and the vibration natural frequencies are investigated. The results obtained from this theory are compared with those obtained from a 3D elasticity analysis and various equivalent theories that are available. A detailed analysis is carried out to study the various natural frequencies of functionally graded material plates. The influences of the transverse shear deformation, plate aspect ratio, side-to-thickness ratio and volume fraction distributions are investigated.

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35

KHALFI, YACINE, MOHAMMED SID AHMED HOUARI, and ABDELOUAHED TOUNSI. "A REFINED AND SIMPLE SHEAR DEFORMATION THEORY FOR THERMAL BUCKLING OF SOLAR FUNCTIONALLY GRADED PLATES ON ELASTIC FOUNDATION." International Journal of Computational Methods 11, no. 05 (October 2014): 1350077. http://dx.doi.org/10.1142/s0219876213500771.

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A refined and simple shear deformation theory for thermal buckling of solar functionally graded plate (SFGP) resting on two-parameter Pasternak's foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories. It is assumed that the material properties of the plate vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the present plate theory based on exact neutral surface position is employed to derive the governing stability equations. The nonlinear strain-displacement relations are also taken into consideration. The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. The effects of the foundation parameters, plate dimensions, and power law index are presented comprehensively for the thermal buckling of solar functionally graded plates.

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36

Van, Vu Tan, Nguyen Huynh Tan Tai, and Nguyen Ngoc Hung. "Static bending and free vibration analysis of functionally graded porous plates laid on elastic foundation using the meshless method." Journal of Science and Technology in Civil Engineering (STCE) - NUCE 15, no. 2 (April 27, 2021): 141–59. http://dx.doi.org/10.31814/stce.nuce2021-15(2)-12.

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This paper presents a numerical approach for static bending and free vibration analysis of the functionally graded porous plates (FGPP) resting on the elastic foundation using the refined quasi-3D sinusoidal shear deformation theory (RQSSDT) combined with the Moving Kriging–interpolation meshfree method. The plate theory considers both shear deformation and thickness-stretching effects by the sinusoidal distribution of the in-plane displacements, satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without shear correction coefficient. The advantage of the plate theory is that the displacement field of plate is approximated by only four variables leading to reduce computational efforts. Comparison studies are performed for the square FGPP with simply supported all edges to verify the accuracy of the present approach. The effect of the aspect ratio, volume fraction exponent, and elastic foundation parameters on the static deflections and natural frequency of FGPP are also investigated and discussed. Keywords: meshless method; Moving Kriging interpolation; refined quasi-3D theory; porous functionally\break graded plate; Pasternak foundation.

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37

Ma, L. S., and T. J. Wang. "Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory." International Journal of Solids and Structures 41, no. 1 (January 2004): 85–101. http://dx.doi.org/10.1016/j.ijsolstr.2003.09.008.

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38

Quéré, S. "Constructal theory of plate tectonics." International Journal of Design & Nature and Ecodynamics 5, no. 3 (June 19, 2010): 242–53. http://dx.doi.org/10.2495/dne-v5-n3-242-253.

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39

Murty, A. V. Krishna. "Toward a consistent plate theory." AIAA Journal 24, no. 6 (June 1986): 1047–48. http://dx.doi.org/10.2514/3.9388.

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40

Ossadzow-David, Claire, and Maurice Touratier. "Multilayered Piezoelectric Refined Plate Theory." AIAA Journal 41, no. 1 (January 2003): 90–99. http://dx.doi.org/10.2514/2.1917.

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41

Hájek, Petr. "Orthotropy in Folded Plate Theory." International Journal of Space Structures 1, no. 4 (December 1985): 223–28. http://dx.doi.org/10.1177/026635118500100403.

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42

Vasiliev, V. V. "Modern conceptions of plate theory." Composite Structures 48, no. 1-3 (January 2000): 39–48. http://dx.doi.org/10.1016/s0263-8223(99)00071-9.

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43

Luo, Albert C. J. "A geometrically-nonlinear plate theory." Communications in Nonlinear Science and Numerical Simulation 4, no. 2 (June 1999): 136–40. http://dx.doi.org/10.1016/s1007-5704(99)90027-8.

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44

Ghosh, S. K. "Basic principles of plate theory." Journal of Mechanical Working Technology 14, no. 2 (March 1987): 251. http://dx.doi.org/10.1016/0378-3804(87)90074-x.

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45

Ren, J. G. "Bending theory of laminated plate." Composites Science and Technology 27, no. 3 (January 1986): 225–48. http://dx.doi.org/10.1016/0266-3538(86)90033-3.

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46

Touratier, M. "An efficient standard plate theory." International Journal of Engineering Science 29, no. 8 (January 1991): 901–16. http://dx.doi.org/10.1016/0020-7225(91)90165-y.

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47

Johannes, Meenen, and Altenbach Holm. "A General Refined Plate Theory." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 80, S2 (2000): 393–94. http://dx.doi.org/10.1002/zamm.20000801468.

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48

Pai, Perngjin F., and Ali H. Nayfeh. "A nonlinear composite plate theory." Nonlinear Dynamics 2, no. 6 (1991): 445–77. http://dx.doi.org/10.1007/bf00045438.

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49

E I, Adah, Eta E E, Ubi S E, Nwigwe E E, and Antia N S. "A Modified Design Stress Equation Based On Maximum Shear Stress Theory." Global Journal of Pure and Applied Sciences 29, no. 2 (November 30, 2023): 281–87. http://dx.doi.org/10.4314/gjpas.v29i2.17.

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Abstract (sommario):

The aim of this study was to formulate a new design stress equation for the analysis of two-dimensional plane elements using the maximum shear stress yield criterion known as the Tresca yield criterion. The existing Tresca yield equation was modified for a two-dimensional plane element to obtain a new general applied stress equation in terms of yield stress and stress factor. To get the specific applied stress equation for the twelve plate types considered, the polynomial shape parameters were solved to obtain the specific stress factor equation. To get the numerical value of the stress factor, a 1m by 1m mild steel of yield stress 250MPa, with deflection values taken at the point of maximum deflection, was analyzed. The numerical values of the stress factor for each plate type obtained were observed to be all less than unity, giving rise to a very high applied stress for plate types with no free edge and a moderately high stress for plate types with one free edge. This revealed the weakness of the existing yield criterion that may lead to failure. To improve this, a correction factor to take care of this limitation was introduced to the stress factor to have a factor of safety that will result in a design stress which is less than the yield stress of the material, by so doing ensuring safety. Therefore, the new design stress equation was found appropriate for predicting stress for the design of plane rectangular plates with one free edge, while this yield criterion is not advisable for use with plates without a free edge. 

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50

Sutyrin, V. G. "Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation." Journal of Applied Mechanics 64, no. 4 (December 1, 1997): 905–15. http://dx.doi.org/10.1115/1.2788998.

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The focus of this paper is the development of linear, asymptotically correct theories for inhomogeneous orthotropic plates, for example, laminated plates with orthotropic laminae. It is noted that the method used can be easily extended to develop nonlinear theories for plates with generally anisotropic inhomogeneity. The development, based on variational-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one-dimensional through-the-thickness analysis and a two-dimensional “plate” analysis. The through-the-thickness analysis provides elastic constants for use in the plate theory and approximate closed-form recovering relations for all truly three-dimensional displacements, stresses, and strains expressed in terms of plate variables. In general, the specific type of plate theory that results from variational-asymptotic method is determined by the method itself. However, the procedure does not determine the plate theory uniquely, and one may use the freedom appeared to simplify the plate theory as much as possible. The simplest and the most suitable for engineering purposes plate theory would be a “Reissner-like” plate theory, also called first-order shear deformation theory. However, it is shown that construction of an asymptotically correct Reissner-like theory for laminated plates is not possible in general. A new point of view on the variational-asymptotic method is presented, leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible while it is a Reissner-like. This uniquely determines the plate theory. Numerical results from such an optimum Reissner-like theory are presented. These results include comparisons of plate displacement as well as of three-dimensional field variables and are the best of all extant Reissner-like theories. Indeed, they even surpass results from theories that carry many more generalized displacement variables. Although the derivation presented herein is inspired by, and completely equivalent to, the well-known variational-asymptotic method, the new procedure looks different. In fact, one does not have to be familiar with the variational-asymptotic method in order to follow the present derivation.

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