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Journal articles on the topic 'High-Order Shear Deformation Theory'

Author: Grafiati

Published: 5 June 2025

Last updated: 2 August 2025

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1

Xie, Yan, Bin Deng, Jing Jing Chen, and Dao Kui Li. "High-Order Model of Thermo-Piezoelectric Composited Plate." Advanced Materials Research 721 (July 2013): 291–94. http://dx.doi.org/10.4028/www.scientific.net/amr.721.291.

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A finite element formulation is developed for laminated composite plate bonded with piezoelectric layers. To improve the accuracy of the prediction of the plate deformation, a high order shear deformation theory is used, whereas the through-the-thickness linear temperature field distribution is assumed. For the electric potential, a new high order theory has been used. Numerical results of a piezoelectric laminated plate show the significant impact of piezoelectric coupling and pyroelectric effects on the sensory response. Furthermore, the pyroelectric effects will influence the transverse she

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2

BENFRID, Abdelmoutalib, and Mohamed Bachir Bouiadjra. "Mathematical Approach for Verifying Buckling in Steel Plates." International Science and Technology Journal 35, no. 1 (2024): 1–12. http://dx.doi.org/10.62341/licase2078.

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A mathematical study was conducted to investigate the buckling of isotropic steel plates using instability theories. The First-Order Shear Deformation Theory (FSDT) and Higher-Order Shear Deformation Theory (HSDT) were employed to account for shear effects. These latter theories were adopted because they consider shear deformation with high precision, unlike classical theories that neglect this important action. The equilibrium equations, derived from Hamilton's principle, were used, and Navier-type solutions were preferred to calculate buckling loads under uniaxial or biaxial loading. Paramet

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3

Nguyen, Lieu B., Thi Bui Viet, and Hong-Yen Nguyen. "An isogeometric formulation with a three-variable high order shear deformation theory for free vibration analysis of FG porous plates reinforced by graphene platelets." Journal of Science and Technology in Civil Engineering (STCE) - NUCE 15, no. 2 (2021): 51–66. http://dx.doi.org/10.31814/stce.nuce2021-15(2)-05.

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We present a generalized three-variable high order shear deformation theory (THSDT) using isogeometric analysis (IGA) to analyze free vibration of functionally graded porous (FGP) plates reinforced by graphene platelets (GPLs) in this work. It is named as FGP-GPLs for a short. The proposed theory only has got three degrees of freedom (DOFs) per node as the same way of numerically solutions in three-dimensional (3D) solids. THSDT fulfills the classical plate theory (CPT), the first-order shear deformation theory (FSDT) and even the higher-order shear deformation theory (HSDT). IGA is chosen to

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4

Lan, Xiang Jun, and Zhi Hua Feng. "Analysis of Deflections and Stresses for Laminated Composite Plates Based on a New Higher-Order Shear Deformation Theory." Applied Mechanics and Materials 226-228 (November 2012): 1725–29. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1725.

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Based on the new simple third-order shear deformation theory, the deflections and stresses of the simply surported symmetrical laminated composite plates are obtained by using the principle of virtual work .The solutions are compared with the solutions of three-dimensional elasticity theory, the first-order shear deformation theory and the Reddy’s higher order shear deformation theory . Results show that the presented new theory is more reliable, accurate, and cost-effective in computation than the first-order shear deformation theories and other simple higher-order shear deformation theories.

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5

Guillén-Rujano, R., A. Hernández-Pérez, and F. Avilés. "Examination of the plate twist specimen for thick specially orthotropic laminated composites and sandwich plates by using first-order shear deformation theory." Journal of Sandwich Structures & Materials 21, no. 7 (2017): 2239–65. http://dx.doi.org/10.1177/1099636217748349.

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Analytical (closed-form) solutions are developed for the deflections and rotations of thick specially orthotropic plate twist specimens by using first-order shear deformation theory. Results are compared with outcomes from finite element method, previously reported experiments, and a classical laminated plate theory solution. A [(0/90)6]s cross-ply laminate and a sandwich panel with aluminum face sheets and a polyvinyl chloride (PVC) foam core are used as baseline materials. Overall, good agreement between first-order shear deformation theory and finite element method is obtained for complianc

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6

Shimpi, Rameshchandra P. "Zeroth-Order Shear Deformation Theory for Plates." AIAA Journal 37, no. 4 (1999): 524–26. http://dx.doi.org/10.2514/2.750.

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7

Shimpi, Rameshchandra P. "Zeroth-order shear deformation theory for plates." AIAA Journal 37 (January 1999): 524–26. http://dx.doi.org/10.2514/3.14205.

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8

Ray, M. C. "Zeroth-Order Shear Deformation Theory for Laminated Composite Plates." Journal of Applied Mechanics 70, no. 3 (2003): 374–80. http://dx.doi.org/10.1115/1.1558077.

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In this paper a zeroth-order shear deformation theory has been derived for static and dynamic analysis of laminated composite plates. The responses obtained by the theory for symmetric and antisymmetric laminates are compared with the existing solutions. The comparison firmly establishes that this new shear deformation theory can be used for both thick and thin laminated composite plates with high accuracy.

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9

Khoa, Ngo Nhu, and Tran Ich Thinh. "Finite element analysis of laminated composite plates using high order shear deformation theory." Vietnam Journal of Mechanics 29, no. 1 (2007): 47–57. http://dx.doi.org/10.15625/0866-7136/29/1/5590.

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A rectangular non-conforming element based on Reddy's higher-order shear deformation plate theory is developed. Although the plate theory is quite attractive but it could not be exploited as expected in finite-element analysis. This is due to the difficulties associated with satisfaction of inter-elemental continuity requirement and satisfy zero shear stress boundary conditions of the plate theory. In this paper, the proposed element is developed where Reddy's plate theory is successfully implemented. It has four nodes and each node contains 7 degrees of freedom. The performance of the element

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10

Merdaci, S., S. Boutaleb, H. Hellal, and S. Benyoucef. "Analysis of Static Bending of Plates FGM Using Refined High Order Shear Deformation Theory." Journal of Building Materials and Structures 6, no. 1 (2019): 32–38. http://dx.doi.org/10.34118/jbms.v6i1.66.

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This work deals with the analysis of the mechanical bending behavior of a rectangular plate simply supported on four sides (FGM), subjected to transverse static loading. The high order theory is used in this work, The developed models are variably consistent, have a strong similarity with the classical plate theory in many aspects, do not require correction to the shear factor, and give rise to variations transverse shear stresses such as transverse shear parabolically varies across the shear thickness and satisfies surface conditions without stresses. Equilibrium equations are obtained by app

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11

Merdaci, S., S. Boutaleb, H. Hellal, and S. Benyoucef. "Analysis of Static Bending of Plates FGM Using Refined High Order Shear Deformation Theory." Journal of Building Materials and Structures 6, no. 1 (2019): 32–38. https://doi.org/10.5281/zenodo.2609306.

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<strong>Abstract</strong>: This work deals with the analysis of the mechanical bending behavior of a rectangular plate simply supported on four sides (FGM), subjected to transverse static loading. The high order theory is used in this work, The developed models are variably consistent, have a strong similarity with the classical plate theory in many aspects, do not require correction to the shear factor, and give rise to variations transverse shear stresses such as transverse shear parabolically varies across the shear thickness and satisfies surface conditions without stresses. Equilibrium eq

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12

Slimane, Merdaci. "Analysis of Bending of Ceramic-Metal Functionally Graded Plates with Porosities Using of High Order Shear Theory." Advanced Engineering Forum 30 (November 2018): 54–70. http://dx.doi.org/10.4028/www.scientific.net/aef.30.54.

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This work consists of the analysis of the bending responses of porous Ceramic-Metal functionally graded (FG) rectangular plates are investigated according to high order shear deformation theory. The proposed theory contains four unknowns unlike the other theories which contains five unknowns, but it checks the boundary conditions without constraints on the upper and lower plate surfaces. Both the effect of shear strain and normal deformation are included in the present theory and so it does not need any shear correction factor. The equilibrium equations according to the porous FG plates Cerami

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13

A., Maji1, and Mahato2 P.K. "FREE VIBRATION ANALYSIS OF ORTHOTROPIC LAMINATED COMPOSITE PLATES USING FIRST ORDER SHEAR DEFORMATION THEORY." International Journal of Advances in Engineering & Scientific Research 4, no. 2 (2017): 71–83. https://doi.org/10.5281/zenodo.10775006.

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<strong>Abstract</strong><strong>: </strong>                                  <em>In this paper free vibration analysis of orthotropic laminated composite plates using first order shear deformation theory. The existing first-order shear deformation theory contains five unknowns but present first order shear deformation theory contains only four unknowns and has many similarity with the classical plate theory such as equation of motion, boundary c

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14

Li, Xinkang, Jifa Zhang, and Yao Zheng. "NURBS-Based Isogeometric Analysis of Beams and Plates Using High Order Shear Deformation Theory." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/159027.

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Isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) is developed for static analysis of beams and plates using the third-order shear deformation theory (TSDT). TSDT requires C1-continuity of generalized displacements; quadratic, cubic, and quartic NURBS basis functions are utilized to satisfy this requirement. Due to the noninterpolatory nature of NURBS basis functions, a penalty method is presented to enforce the essential boundary conditions. A series of numerical examples of thick and thin beams and plates with different boundary conditions are presented. Results are

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15

A., Maji, and Mahato P.K. "FREE VIBRATION ANALYSIS OF ORTHOTROPIC LAMINATED COMPOSITE PLATES USING FIRST ORDER SHEAR DEFORMATION THEORY." International Journal of Advances in Engineering & Scientific Research Vol.4, Issue 2, Feb-Apr-2017 (2017): pp 71–83. https://doi.org/10.5281/zenodo.580443.

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<em>In this paper free vibration analysis of orthotropic laminated composite plates using first order shear deformation theory. The existing first-order shear deformation theory contains five unknowns but present first order shear deformation theory contains only four unknowns and has many similarity with the classical plate theory such as equation of motion, boundary condition and stress resultant expressions. The equation of motion and boundary condition are derived from Hamilton’s Principle for the calculation of frequency analysis of orthotropic laminated composite plates. Analytical close

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16

Shimpi, R. P., H. G. Patel, and H. Arya. "New First-Order Shear Deformation Plate Theories." Journal of Applied Mechanics 74, no. 3 (2006): 523–33. http://dx.doi.org/10.1115/1.2423036.

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First-order shear deformation theories, one proposed by Reissner and another one by Mindlin, are widely in use, even today, because of their simplicity. In this paper, two new displacement based first-order shear deformation theories involving only two unknown functions, as against three functions in case of Reissner’s and Mindlin’s theories, are introduced. For static problems, governing equations of one of the proposed theories are uncoupled. And for dynamic problems, governing equations of one of the theories are only inertially coupled, whereas those of the other theory are only elasticall

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17

Otmane, Zerrouki, Merdaci Slimane, and Hadj Mostefa Adda. "Thermo-Mechanical Bending for Hybrid Material Plates Perfect-Imperfect Rectangular Using High Order Theory." Applied Mechanics and Materials 909 (September 28, 2022): 29–44. http://dx.doi.org/10.4028/p-ri86k0.

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In this paper, a higher order shear deformation theory is used to analyse the thermo-mechanical bending response of perfect-imperfect rectangular plates for hybrid ceramic and metal type (FGP) functionally graded plates with porosities. Based on the mixing law, the FG porous material qualities fluctuate with the thickness of the FGP layer. The equilibrium equations are found using the total potential energy approach. For simply supported (FGP) porous plates, the thermo-mechanical response is calculated. Analytical research shows the correctness of the existing high-order shear deformation theo

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18

ZENKOUR, A. M., M. N. M. ALLAM, and MOHAMMED SOBHY. "EFFECT OF TRANSVERSE NORMAL AND SHEAR DEFORMATION ON A FIBER-REINFORCED VISCOELASTIC BEAM RESTING ON TWO-PARAMETER ELASTIC FOUNDATIONS." International Journal of Applied Mechanics 02, no. 01 (2010): 87–115. http://dx.doi.org/10.1142/s1758825110000482.

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This article investigates the effect of transverse normal and shear deformations on a fiber-reinforced viscoelastic beams resting on two-parameter (Pasternak's) elastic foundations. The results are obtained by the refined sinusoidal shear deformation beam theory and compared with those obtained by the simple sinusoidal shear deformation beam theory, Timoshenko first-order shear deformation beam theory as well as Euler-Bernoulli classical beam theory. The effects of foundation stiffness on bending of viscoelastic composite beam are presented. The effective moduli methods are used to derive the

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19

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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20

Frishter, Lyudmila, and Al-Gburi Noora Saad Subhi. "Uniform Domain Equilibrium Equation with Finite Deformations." E3S Web of Conferences 410 (2023): 03007. http://dx.doi.org/10.1051/e3sconf/202341003007.

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In corner areas of structures, high stress values and gradients occur, and lead to stress concentrations. Infinite stress and deformations are determined by a solution of the linear elasticity theory problem in the area with a wedge-shape boundary notch. Infinite solutions of the elasticity problem occur under impact of forced deformations, when a surge of the deformation value reaches beyond the area boundary. Relative values of stress concentrations for corner area zones make no more sense. At finite displacements, high deformation and stress values occur in the corner zones of the area. For

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21

Eslami, M. R., and M. Shariyat. "A High-Order Theory for Dynamic Buckling and Postbuckling Analysis of Laminated Cylindrical Shells." Journal of Pressure Vessel Technology 121, no. 1 (1999): 94–102. http://dx.doi.org/10.1115/1.2883673.

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Using a high-order Reisner-Mindlin-type shear deformation theory in a power series form, the general large deformation form of the Green strain tensor for imperfect cylindrical shells is introduced. Then, based on Hamilton’s principle, the equations of motion are derived for laminated composite shells. Related constitutive equations are also proposed. In this formulation, temperature dependency of material properties is considered, too. No simplifications are made in solving the coupled nonlinear equations of motion. Finally, few examples of the well-known references are reconsidered for compa

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22

Bedia, Wafa Adda, Mohammed Sid Ahmed Houari, Aicha Bessaim, et al. "A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams." Journal of Nano Research 57 (April 2019): 175–91. http://dx.doi.org/10.4028/www.scientific.net/jnanor.57.175.

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In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. The advantage of this theory relies on its two-unknown displacement field as the Euler-Bernoulli beam theory, and it is capable of accurately capturing shear deformation effects, instead of three as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore,

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23

Cederbaum, Gabriel, Liviu Librescu, and Isaac Elishakoff. "Random vibration of laminated plates modeled within a high‐order shear deformation theory." Journal of the Acoustical Society of America 84, no. 2 (1988): 660–66. http://dx.doi.org/10.1121/1.396845.

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24

Liu, Ping, Kaida Zhang, and Yongwei Zhang. "Bending solution of high-order refined shear deformation theory for rectangular composite plates." International Journal of Solids and Structures 31, no. 18 (1994): 2491–507. http://dx.doi.org/10.1016/0020-7683(94)90033-7.

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25

Kołakowski, Zbigniew, and Jacek Jankowski. "Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures." Materials 13, no. 22 (2020): 5262. http://dx.doi.org/10.3390/ma13225262.

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For an isotropic square plate subject to unidirectional compression in the postbuckling state, components of transverse forces in bending, membrane transverse components and total components of transverse forces were determined within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), the classical plate theory (CPT) and the finite element method (FEM). Special attention was drawn to membrane components of transverse forces, which are expressed with the same formulas for the first three theories and do not depend on membrane deformations.

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26

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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27

D.H., Tupe, Dahake A.G., and Gandhe G.R. "Static Examination of Simply Supported Laminated Composite Beam with Varying Load Using Trigonometric Shear Deformation Theory." Indian Journal of Science and Technology 13, no. 10 (2020): 1188–99. https://doi.org/10.17485/ijst/2020/v13i10/149907.

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Abstract <strong>Objectives:</strong> To study the trigonometric shear deformation theory for the evolution of displacements and stresses of crossply simply supported laminated beam subjected to varying load. <strong>Methodology:</strong> A trigonometric shear deformation is used. The inplain displacement field uses a sinusoidal function in terms of the thickness coordinate to include the shear deformation effect. The theory satisfies the shear stress free boundary conditions on the top and bottom surfaces of the plate. The present theory obviates the need of a shear correction facto

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28

Auricchio, F., and E. Sacco. "Refined First-Order Shear Deformation Theory Models for Composite Laminates." Journal of Applied Mechanics 70, no. 3 (2003): 381–90. http://dx.doi.org/10.1115/1.1572901.

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In the present work, new mixed variational formulations for a first-order shear deformation laminate theory are proposed. The out-of-plane stresses are considered as primary variables of the problem. In particular, the shear stress profile is represented either by independent piecewise quadratic functions in the thickness or by satisfying the three-dimensional equilibrium equations written in terms of midplane strains and curvatures. The developed formulations are characterized by several advantages: They do not require the use of shear correction factors as well as the out-of-plane shear stre

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29

Senjanović, Ivo, Nikola Vladimir, Neven Hadžić, and Marko Tomić. "New first order shear deformation beam theory with in-plane shear influence." Engineering Structures 110 (March 2016): 169–83. http://dx.doi.org/10.1016/j.engstruct.2015.11.032.

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30

Mahajan, Aishwarya, Sagar Gaikwad, and Ajay Dahake. "Displacement in Deep Propped Cantilever Beam Subjected to Semi-elliptical Load." Proceedings of the 12th Structural Engineering Convention, SEC 2022: Themes 1-2 1, no. 1 (2022): 485–89. http://dx.doi.org/10.38208/acp.v1.538.

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A fifth order shear deformation theory considering transverse shear deformation effect is presented for displacement in propped cantilever beam. The considered displacement field accounts for non-linear variation corresponding to depth of beam. Governing equations and boundary conditions of the theory are obtained using the standard of virtual work. Numerical results for static deflection analysis for aspect ratio (length to depth) 2 to 50 for isotropic beam is obtained. The results of present theory are in close agreement with those of higher order shear deformation theories.

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31

Khaled, Zaiter, and Berrabah Hamza Madjid. "Study and comparison of the bending response of porous advanced composite plates under thermomechanical loads using different materials." Brazilian Journal of Technology 8, no. 1 (2025): e76492. https://doi.org/10.38152/bjtv8n1-005.

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This research focuses on the study and comparison of the thermomechanical bending behavior of porous advanced composite plates, particularly functionally graded materials (FGM), where the presence of porosity significantly influences their structural performance. A refined shear deformation theory is developed to analyze the bending response of porous FGMs under thermomechanical loads. The proposed model introduces a novel transverse shear function, separating transverse displacements into bending and shear components. This innovative approach simplifies the analysis, requiring fewer unknowns

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32

Rogacheva, Nelly. "THE REFINED THEORY OF ELASTIC PLATES AS ASYMPTOTIC APPROACH OF 3D PROBLEM." MATEC Web of Conferences 196 (2018): 02037. http://dx.doi.org/10.1051/matecconf/201819602037.

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The refined theory of elastic thin and thick plates is constructed by the asymptotic method for reducing three-dimensional (3D) equations of linear elasticity to two-dimensional ones without the use of any assumptions. The resulting refined theory is much more complicated than the known classical Kirchhoff theory: the required values of the refined theory vary in thickness of the plate by more complex laws; the system of partial differential equations of the refined theory has a higher order than the system of equations of the classical theory. A comparison of the obtained theory with the popu

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Chun, C. K., and S. B. Dong. "Shear Constitutive Relations for Laminated Anisotropic Shells and Plates: Part II—Vibrations of Composite Cylinders." Journal of Applied Mechanics 59, no. 2 (1992): 380–89. http://dx.doi.org/10.1115/1.2899531.

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In Part I of this paper, a system of shear constitutive relations was proposed for a first-order shear deformation theory of laminated anisotropic plates and shells. For laminated anisotropic structures, these shear constitutive equations involved the concept of generalized shear planes. Herein, an extensive parametric study is presented to assess the modeling capability of these shear constitutive relations in a class of laminated composite and sandwich cylinders. Classical theory results are also given in order to fully understand the influence of anisotropy on the accuracy and ranges of val

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34

Daouadji, Tahar Hassaine, Abdelouahed Tounsi, and El Abbes Adda Bedia. "A New Higher Order Shear Deformation Model for Static Behavior of Functionally Graded Plates." Advances in Applied Mathematics and Mechanics 5, no. 03 (2013): 351–64. http://dx.doi.org/10.4208/aamm.11-m11176.

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AbstractIn this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear

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Shimpi, Rameshchandra P., Rajesh A. Shetty, and Anirban Guha. "A simple single variable shear deformation theory for a rectangular beam." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 24 (2016): 4576–91. http://dx.doi.org/10.1177/0954406216670682.

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This paper proposes a simple single variable shear deformation theory for an isotropic beam of rectangular cross-section. The theory involves only one fourth-order governing differential equation. For beam bending problems, the governing equation and the expressions for the bending moment and shear force of the theory are strikingly similar to those of Euler–Bernoulli beam theory. For vibration and buckling problems, the Euler–Bernoulli beam theory governing equation comes out as a special case when terms pertaining to the effects of shear deformation are ignored from the governing equation of

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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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37

Ghazoul, Tahir, Mohamed Atif Benatta, and Mohamed Bachir Bouiadjra. "Static and dynamic behaviors of laminated composite plates resting on elastic foundation." Journal of Building Materials and Structures 9, no. 1 (2022): 12–21. http://dx.doi.org/10.34118/jbms.v9i1.1882.

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This present study consists to analyze the mechanical buckling and the free vibration stabilities of antisymmetric cross-ply and angle-ply laminated composite plates using a refined high order shear deformation theory of four variables against five in other high order theories. Among the advantages of this new theory it takes into consideration the shearing effect in the calculation of deformation without the need for shear correction factors and giving rise to a variation of the shear stresses along the thickness and satisfying the zero shear stresses condition in faces of the plate. The lami

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38

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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Bakhsheshy, Ali, and Hossein Mahbadi. "The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate." Noise & Vibration Worldwide 50, no. 9-11 (2019): 267–90. http://dx.doi.org/10.1177/0957456519883265.

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This article develops the modified couple stress theory to study the free vibration of bi-directional functionally graded microplates subjected to multidimensional temperature distribution. Third-order shear deformation and classical theories of plates are adapted for free vibration analysis of thick and thin microplates, respectively. Employing the third-order shear deformation theory, both normal and shear deformations are considered without the need for shear correction factor. Material of the bi-directional functionally graded microplate is graded smoothly through the length and thickness

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SUBHA, K., SHASHIDHARAN, S. SAVITHRI, and V. SYAM PRAKASH. "ASSESSMENT OF COMPUTATIONAL MODELS FOR LAMINATED COMPOSITE PLATES." International Journal of Computational Methods 04, no. 04 (2007): 633–44. http://dx.doi.org/10.1142/s0219876207001333.

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In this paper, results of the stress analysis of composite laminates subjected to mechanical load based on different higher order shear deformation theories are presented. Among the many equivalent single layer theories (ESL), the third-order shear deformation theory of Reddy is the most widely accepted model in the study of laminates. This model cannot represent shear stress continuity at the interfaces and zigzag nature of the displacement field. To improve the accuracy of transverse shear stress prediction, layer wise theories have proved to be very promising techniques. In all these theori

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Nami, Mohammad Rahim, and Maziar Janghorban. "Static analysis of rectangular nanoplates using trigonometric shear deformation theory based on nonlocal elasticity theory." Beilstein Journal of Nanotechnology 4 (December 30, 2013): 968–73. http://dx.doi.org/10.3762/bjnano.4.109.

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In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free boundary conditions of the rectangular plates and these stresses can be calculated from the constitutive equations. The effects of different parameters such as nonlocal parameter and aspect ratio are in

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Javed, Saira. "Frequency Response of Higher-Order Shear-Deformable Multilayered Angle-Ply Cylindrical Shells." Axioms 14, no. 3 (2025): 172. https://doi.org/10.3390/axioms14030172.

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This research is based on the frequency response of angle-ply laminated cylindrical shells under higher-order shear deformation theory. The higher-order shear deformation theory is used to model the displacement and rotational functions, which are approximated by cubic and quintic splines. The eigenvalue problem is obtained with the simply supported boundary condition. The frequency of cylindrical shells is analyzed by varying the circumferential node number, length, number of layers, and layer alignment. The competence of the formulation is verified by comparing it with the available results

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Kolakowski, Zbigniew, and Jacek Jankowski. "Some Inconsistencies in the Nonlinear Buckling Plate Theories—FSDT, S-FSDT, HSDT." Materials 14, no. 9 (2021): 2154. http://dx.doi.org/10.3390/ma14092154.

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Bending and membrane components of transverse forces in a fixed square isotropic plate under simultaneous compression and transverse loading were established within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), and the classical plate theory (CPT). Special attention was drawn to the fact that bending components were accompanied by transverse deformations, whereas membrane components were not, i.e., the plate was transversely perfectly rigid. In the FSDT and the S-FSDT, double assumptions concerning transverse deformations in the plat

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Sheinman, I., and M. Adan. "The Effect of Shear Deformation on Post-Buckling Behavior of Laminated Beams." Journal of Applied Mechanics 54, no. 3 (1987): 558–62. http://dx.doi.org/10.1115/1.3173069.

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A geometrical nonlinear theory of composite laminated beams is derived with the effect of transverse shear deformation taken into account. The theory is based on a high-order kinematic model, with the nonlinear differential equations solved by Newton’s method and a special finite-difference scheme. A parametric study of the shear effect involving several kinematic approaches was carried out for isotropic and anisotropic beams.

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Lim, Seongsik, Vivek Kumar Dhimole, Yongbae Kim, and Chongdu Cho. "Investigations for Design Estimation of an Anisotropic Polymer Matrix Composite Plate with a Central Circular Hole under Uniaxial Tension." Polymers 14, no. 10 (2022): 1977. http://dx.doi.org/10.3390/polym14101977.

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Composite plates with holes are common in engineering applications, such as the automotive and aerospace industries. Three-dimensional braided carbon/epoxy polymers are an advanced textile composite and are used in various structures due to their high damage resistance and relatively low manufacturing cost. When a braided polymer plate with a hole is used in engineering applications, it is necessary to know its mechanical behavior under loading conditions using analysis theory to design it better. However, the effects of stress distribution with shear deformation theories on the variable thick

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Sadeghian, Mostafa, Asif Jamil, Arvydas Palevicius, Giedrius Janusas, and Vytenis Naginevicius. "The Nonlinear Bending of Sector Nanoplate via Higher-Order Shear Deformation Theory and Nonlocal Strain Gradient Theory." Mathematics 12, no. 8 (2024): 1134. http://dx.doi.org/10.3390/math12081134.

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In this context, the nonlinear bending investigation of a sector nanoplate on the elastic foundation is carried out with the aid of the nonlocal strain gradient theory. The governing relations of the graphene plate are derived based on the higher-order shear deformation theory (HSDT) and considering von Karman nonlinear strains. Contrary to the first shear deformation theory (FSDT), HSDT offers an acceptable distribution for shear stress along the thickness and removes the defects of FSDT by presenting acceptable precision without a shear correction parameter. Since the governing equations are

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Kulkarni, Sudhakar A., and Kamal M. Bajoria. "Large deformation analysis of piezolaminated smart structures using higher-order shear deformation theory." Smart Materials and Structures 16, no. 5 (2007): 1506–16. http://dx.doi.org/10.1088/0964-1726/16/5/002.

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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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Suresh, J. K., and V. T. Nagaraj. "Higher-order shear deformation theory for thin-walled composite beams." Journal of Aircraft 33, no. 5 (1996): 978–86. http://dx.doi.org/10.2514/3.47044.

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Kardomateas, George A., Nunthadech Rodcheuy, and Yeoshua Frostig. "First-Order Shear Deformation Theory Variants for Curved Sandwich Panels." AIAA Journal 56, no. 2 (2018): 808–17. http://dx.doi.org/10.2514/1.j056306.

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