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Zeitschriftenartikel zum Thema „Plate theory“

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Veröffentlicht am 4. Juni 2021

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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 (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. H

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2

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 (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 bas

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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 (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

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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 (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 pr

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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

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Toledano, A., and H. Murakami. "A Composite Plate Theory for Arbitrary Laminate Configurations." Journal of Applied Mechanics 54, no. 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 o

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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 (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 variationa

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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 (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

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Murakami, H. "Laminated Composite Plate Theory With Improved In-Plane Responses." Journal of Applied Mechanics 53, no. 3 (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 symm

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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 (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 deformatio

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Gilat, R., T. O. Williams, and J. Aboudi. "Buckling of composite plates by global–local plate theory." Composites Part B: Engineering 32, no. 3 (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 (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 rati

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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 (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)

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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 (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

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15

Bhimaraddi, Alavandi. "Nonlinear Dynamics of In-Plane Loaded Imperfect Rectangular Plates." Journal of Applied Mechanics 59, no. 4 (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 approac

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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 (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 (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 an

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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 (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 (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

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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 (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 (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 deflectio

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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 (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 p

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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 (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

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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 (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. Materi

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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 (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 l

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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 (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 differen

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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 (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 t

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Ahmed, Frih, Idder Abdelghani, Moulay Ali Abderrahmane, et al. "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 (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

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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 1: Governing equations establishment." Vietnam Journal of Mechanics 37, no. 3 (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

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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 (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 simpl

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

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

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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 (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

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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 (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 o

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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 (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

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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 (2004): 85–101. http://dx.doi.org/10.1016/j.ijsolstr.2003.09.008.

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Quéré, S. "Constructal theory of plate tectonics." International Journal of Design & Nature and Ecodynamics 5, no. 3 (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 (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 (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 (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 (2000): 39–48. http://dx.doi.org/10.1016/s0263-8223(99)00071-9.

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Luo, Albert C. J. "A geometrically-nonlinear plate theory." Communications in Nonlinear Science and Numerical Simulation 4, no. 2 (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 (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 (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 (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 (2023): 281–87. http://dx.doi.org/10.4314/gjpas.v29i2.17.

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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

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50

Sutyrin, V. G. "Derivation of Plate Theory Accounting Asymptotically Correct Shear Deformation." Journal of Applied Mechanics 64, no. 4 (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 a

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