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Journal articles on the topic 'HSDT-higher order shear deformation theory'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

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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2

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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3

Sadr-Lahidjani, Mohammad Homayoun, Mohammad Hajikazemi, and Mona Ramezani-Oliaee. "Large Deflection Behavior of Relatively Thick Functionally Graded Plates under Pressure Loads Using Higher Order Shear Deformation Theory." Key Engineering Materials 471-472 (February 2011): 709–14. http://dx.doi.org/10.4028/www.scientific.net/kem.471-472.709.

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Large deflection analysis of thin and relatively thick rectangular functionally graded plates is studied in this paper. It is assumed that the mechanical properties of the plate, graded through the thickness, are described by a simple power law distribution in terms of the volume fractions of constituents. The plate is assumed to be under lateral pressure load. The fundamental equations for rectangular plates of FGM are obtained using the classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) for large deflection an

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4

Sadeghian, Mostafa, Arvydas Palevicius, and Giedrius Janusas. "Nonlinear Thermal/Mechanical Buckling of Orthotropic Annular/Circular Nanoplate with the Nonlocal Strain Gradient Model." Micromachines 14, no. 9 (2023): 1790. http://dx.doi.org/10.3390/mi14091790.

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This article presents the nonlinear investigation of the thermal and mechanical buckling of orthotropic annular/circular single-layer/bilayer nanoplate with the Pasternak and Winkler elastic foundations based on the nonlocal strain gradient theory. The stability equations of the graphene plate are derived using higher-order shear deformation theory (HSDT) and first-order shear deformation theory (FSDT) considering nonlinear von Karman strains. Furthermore, this paper analyses the nonlinear thermal and mechanical buckling of the orthotropic bilayer annular/circular nanoplate. HSDT provides an a

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5

Meski, Khaled, Belgacem Mamen, and Abderrahmane Menasria. "Analytical solutions for the thermo-mechanical bending of FG beams using a higher order shear deformation theory (HSDT)." MATEC Web of Conferences 394 (2024): 03004. http://dx.doi.org/10.1051/matecconf/202439403004.

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The aim of this paper is to analyze a thermo-mechanical behavior of functionally graded beam in thermal environment. Therefore, this research work investigates a thermal, mechanical and thermo-mechanical bending of functionally graded beam resting on simple supports and using a higher order shear deformation theory. the proposed kinematic uses only three variables, which is even less than the first order shear deformation theory (FSDT) and the conventional higher order shear deformation theories (HSDTs). The present model adopts a new displacement field, The material properties of the FG beam

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6

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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Xue, Ting, Xiansheng Qin, Shunqi Zhang, Zhanxi Wang, and Jing Bai. "Free vibration analysis of CNT reinforced plates using higher order shear deformation theory." Journal of Physics: Conference Series 2760, no. 1 (2024): 012022. http://dx.doi.org/10.1088/1742-6596/2760/1/012022.

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Abstract With the stringent requirements of lightweight and high stiffness in space technology and spacecraft, the research on frequency characters of carbon nanotubes (CNTs) reinforced structures is particularly urgent. In this paper, based on the Reissner-Mindlin higher-order shear deformation theory (HSDT), a vibration model for a CNT functionally graded (FG) plate is developed, and influences of the reinforcements distribution form, reinforcement volume fractions, and various boundary conditions of the structure are considered in this established model. Subsequently, the model’s convergenc

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8

Dao, Sy-Dan, Dang-Diem Nguyen, Trong-Hiep Nguyen, and Ngoc-Lam Nguyen. "An Analytical Solution for Energy Harvesting Using a High-Order Shear Deformation Model in Functionally Graded Beams Subjected to Concentrated Moving Loads." Modelling 6, no. 3 (2025): 55. https://doi.org/10.3390/modelling6030055.

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This study presents a high-order shear deformation theory (HSDT)-based model for evaluating the energy harvesting performance of functionally graded material (FGM) beams integrated with a piezoelectric layer and subjected to a moving concentrated load at constant velocity. The governing equations are derived using Hamilton’s principle, and the dynamic response is obtained through the State Function Method with trigonometric mode shapes. The output voltage and harvested power are calculated based on piezoelectric constitutive relations. A comparative analysis with homogeneous isotropic beams de

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9

Mahaboobali Nadaf, Dr. R. J. Fernandes. "Finite element solutions for bending analysis of simply supported two layered un-symmetric cross-ply (0/90) square plate under uniformly distributed transverse load." Tuijin Jishu/Journal of Propulsion Technology 44, no. 4 (2023): 2144–55. http://dx.doi.org/10.52783/tjjpt.v44.i4.1193.

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Laminated composite plates are extensively used in aerospace, military, civil infrastructure, and automotive industries due to their benefits, including superior fatigue resistance, high strength, and lightweight properties. Customizable fiber orientation, materials, and stacking patterns are additional advantages. Therefore, conducting rigorous analyses to evaluate deflections and stress levels in these plates is essential for maintaining structural integrity and optimal performance across various applications. The solutions presented in this study rely on the utilization of a higher-order sh

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10

Jung, Woo-Young, and Sung-Cheon Han. "Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates." Journal of Nanomaterials 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/208393.

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The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT). The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. T

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11

Sayyad, Atteshamuddin S., and Yuwaraj M. Ghugal. "On the Buckling of Isotropic, Transversely Isotropic and Laminated Composite Rectangular Plates." International Journal of Structural Stability and Dynamics 14, no. 07 (2014): 1450020. http://dx.doi.org/10.1142/s0219455414500205.

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This paper presents the uniaxial and biaxial buckling analysis of rectangular plates based on new trigonometric shear and normal deformation theory. The theory accounts for the cosine distribution of the transverse shear strain through the plate thickness and on the free boundary conditions on the plate surfaces without using the shear correction factor. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The Navier type solutions for the buckling analysis of simply supported isotropic, transversely isotropic, orthotropic and symmetric cross-

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Reddy, B. Sidda, J. Suresh Kumar, C. Eswara Reddy, and K. Vijaya Kumar Reddy. "Buckling Analysis of Functionally Graded Material Plates Using Higher Order Shear Deformation Theory." Journal of Composites 2013 (December 23, 2013): 1–12. http://dx.doi.org/10.1155/2013/808764.

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The prime aim of the present study is to present analytical formulations and solutions for the buckling analysis of simply supported functionally graded plates (FGPs) using higher order shear deformation theory (HSDT) without enforcing zero transverse shear stresses on the top and bottom surfaces of the plate. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. Material properties of the plate are assumed to vary in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents.

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13

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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14

Gadade, Appaso M., Achchhe Lal, and Bhairu N. Singh. "Progressive Failure Analysis of Laminated Composite Plate by Using Higher Order Shear Deformation Theory." Applied Mechanics and Materials 592-594 (July 2014): 1151–54. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.1151.

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A finite element analysis procedure is developed for progressive failure analysis of laminated composite plates under in plane tensile loading. A finite element model is based on higher order shear deformation theory (HSDT) with seven degrees of freedom. The degradation technique used for degradation of material properties of a failed ply is a ply discounting approach. The mode dependant Hashin and Lee failure criterion is used for the progressive failure analysis. The results of first ply failure load and last ply failure load are obtained for different stacking sequence of composite plate. T

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15

Javed, Saira. "A Numerical Solution of Symmetric Angle Ply Plates Using Higher-Order Shear Deformation Theory." Symmetry 15, no. 3 (2023): 767. http://dx.doi.org/10.3390/sym15030767.

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This research aims to provide the numerical analysis solution of symmetric angle ply plates using higher-order shear deformation theory (HSDT). The vibration of symmetric angle ply composite plates is analyzed using differential equations consisting of supplanting and turning functions. These supplanting and turning functions are numerically approximated through spline approximation. The obtained global eigenvalue problem is solved numerically to find the eigenfrequency parameter and a related eigenvector of spline coefficients. The plates of different constituent components are used to study

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16

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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17

Kadari, Belkacem, Aicha Bessaim, Abdelouahed Tounsi, Houari Heireche, Abdelmoumen Anis Bousahla, and Mohammed Sid Ahmed Houari. "Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations." Journal of Nano Research 55 (November 2018): 42–56. http://dx.doi.org/10.4028/www.scientific.net/jnanor.55.42.

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This work presents the buckling investigation of embedded orthotropic nanoplates by using a new hyperbolic plate theory and nonlocal small-scale effects. The main advantage of this theory is that, in addition to including the shear deformation effect, the displacement field is modeled with only three unknowns and three governing equation as the case of the classical plate theory (CPT) and which is even less than the first order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Nonlocal differential constitut

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18

Tai, Huynh Huu, Nguyen Van Hieu, and Vu Duy Thang. "Bending and free vibration behaviors of composite plates using the C0-HSDT based four-node element with in-plane rotations." Journal of Science and Technology in Civil Engineering (STCE) - NUCE 14, no. 1 (2020): 42–53. http://dx.doi.org/10.31814/stce.nuce2020-14(1)-04.

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In this paper the smoothed four-node element with in-plane rotations MISQ24 is combined with a C0-type higher-order shear deformation theory (C0-HSDT) to propose an improved linear quadrilateral plate element for static and free vibration analyses of laminated composite plates. This improvement results in two additional degrees of freedom at each node and require no shear correction factors while ensuring the high precision of numerical solutions. Composite plates with different lay-ups, boundary conditions and various geometries such as rectangular, skew and triangular plates are analyzed usi

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19

Kumar, Ajay, Pradeep Bhargava, and Anupam Chakrabarti. "Natural Frequencies and Mode Shapes of Laminated Composite Skew Hypar Shells with Complicated Boundary Conditions Using Finite Element Method." Advanced Materials Research 585 (November 2012): 44–48. http://dx.doi.org/10.4028/www.scientific.net/amr.585.44.

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In the present investigation, free vibration behaviour is studied for the laminated composite skew hypar shells having twist radius of curvature. A higher-order shear deformation theory is employed in the C0 finite element formulation. Higher-order terms in the Taylor’s series expansion are used to represent the higher-order transverse cross sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effect of transverse shear. The structural system is considered to be undamped. The correctness of the formulation is established by compa

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20

LAL, ACHCHHE, and B. N. SINGH. "EFFECT OF UNCERTAIN SYSTEM PROPERTIES ON THERMO-ELASTIC STABILITY OF LAMINATED COMPOSITE PLATES UNDER NONUNIFORM TEMPERATURE DISTRIBUTION." International Journal of Applied Mechanics 02, no. 02 (2010): 399–420. http://dx.doi.org/10.1142/s175882511000055x.

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Uncertainties in system properties are inherent in all engineering materials. This paper presents the second-order statistics of thermal buckling response of shear deformable laminated composite plate resting on elastic foundation with random system properties under nonuniform tent-like temperature distribution. The mathematical model based on higher-order shear deformation theory [HSDT] is presented. A C0 finite element method in conjunction with first-order perturbation technique is employed to derive the second-order statistics (mean and the standard deviation) of the thermal buckling tempe

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That-Hoang, Lan T., Hieu Nguyen-Van, Thanh Chau-Dinh, and Chau Huynh-Van. "Enhancement to four-node quadrilateral plate elements by using cell-based smoothed strains and higher-order shear deformation theory for nonlinear analysis of composite structures." Journal of Sandwich Structures & Materials 22, no. 7 (2018): 2302–29. http://dx.doi.org/10.1177/1099636218797982.

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This paper improves four-node quadrilateral plate elements by using cell-based strain smoothing enhancement and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of composite structures. Small strain-large displacement theory of von Kármán is used in nonlinear formulations of four-node quadrilateral plate elements that have strain components smoothed or averaged over the sub-domains of the elements. From the divergence theory, the displacement gradients in the smoothed strains are transformed from the area integral into the line one. The behavior of composite st

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22

Hoang Ton That, Lan. "Four-node quadrilateral C 0-element based on cell-based smoothed strains strategy and third-order shear deformation theory for functionally graded carbon nanotube reinforced composite plates." Rakenteiden Mekaniikka 56, no. 1 (2023): 1–23. http://dx.doi.org/10.23998/rm.119608.

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This study indicates the analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates using a four-node quadrilateral element related to the C0-type of Reddy’s third-order shear deformation theory (C0 HSDT) and cell-based smoothed strains (CS) strategy. Reddy’s theory is surely taking the advantages and desirable properties of the third-order shear deformation theory. Besides, FG-CNTRC plates with advanced material properties are changed from the bottom to top surface with four kinds of carbon nanotube (CNTs). Numerical results and comparison with other reference solu

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Hafizah, A. K. Nor, J. H. Lee, Z. A. Aziz, and K. K. Viswanathan. "Vibration of Antisymmetric Angle-Ply Laminated Plates of Higher-Order Theory with Variable Thickness." Mathematical Problems in Engineering 2018 (2018): 1–14. http://dx.doi.org/10.1155/2018/7323628.

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Free vibration of antisymmetric angle-ply laminated plates with variable thickness is studied. Higher-order shear deformation plate theory (HSDT) is introduced in the present method to remove the shear correction factors and improve the accuracy of transverse shear stresses. The thickness variations are assumed to be linear, exponential, and sinusoidal. The coupled differential equations are obtained in terms of displacement and rotational functions and approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically by employing the eigensolutio

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Dr., Mahaboobali Nadaf, and R. J. Fernandes Dr. "Bending Analysis of Cross-ply Laminated Composite Plates Using Higher Order Shear Deformation Theory Based on Finite Element Method." Journal of Scholastic Engineering Science and Management 2, no. 7 (2023): 14–26. https://doi.org/10.5281/zenodo.8052659.

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<strong>Laminated composite plates (LCP) possess exceptional characteristics, including superior fatigue response, high strength-to-weight ratio, making them extensively utilized in various industries such as automotive, military, civil infrastructure, and aerospace. The properties of these plates can be tailored by adjusting factors like material selection, orientation, and stacking pattern. Hence, it is crucial to analyze deflection and stress in order to ensure their optimal performance. In this study, a finite element method (FEM) -based analysis using the Higher Order Shear Deformation Th

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Sadeghian, Mostafa, Arvydas Palevicius, and Giedrius Janusas. "Nonlocal Strain Gradient Model for the Nonlinear Static Analysis of a Circular/Annular Nanoplate." Micromachines 14, no. 5 (2023): 1052. http://dx.doi.org/10.3390/mi14051052.

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A nonlinear static analysis of a circular/annular nanoplate on the Winkler–Pasternak elastic foundation based on the nonlocal strain gradient theory is presented in the paper. The governing equations of the graphene plate are derived using first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) with nonlinear von Karman strains. The article analyses a bilayer circular/annular nanoplate on the Winkler–Pasternak elastic foundation. HSDT while providing a suitable distribution of shear stress along the thickness of the FSDT plate, eliminating the defects of th

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Sayyad, Atteshamuddin S., and Yuwaraj M. Ghugal. "A Unified Shear Deformation Theory for the Bending of Isotropic, Functionally Graded, Laminated and Sandwich Beams and Plates." International Journal of Applied Mechanics 09, no. 01 (2017): 1750007. http://dx.doi.org/10.1142/s1758825117500077.

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In this paper, a displacement-based unified shear deformation theory is developed for the analysis of shear deformable advanced composite beams and plates. The theory is developed with the inclusion of parabolic (PSDT), trigonometric (TSDT), hyperbolic (HSDT) and exponential (ESDT) shape functions in terms of thickness coordinate to account for the effect of transverse shear deformation. The in-plane displacements consider the combined effect of bending rotation and shear rotation. The use of parabolic shape function in the present theory leads to the Reddy’s theory, but trigonometric, hyperbo

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Nguyen-Quoc, T., S. Nguyen-Hoai, and D. Mai-Duc. "An Edge-Based Smoothed Discrete Shear Gap Method for Static and Free Vibration Analyses of FG-CNTRC Plates." International Journal of Computational Methods 16, no. 04 (2019): 1850102. http://dx.doi.org/10.1142/s0219876218501025.

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In this paper, an edge-based smoothed stabilized discrete shear gap method (ES-DSG) is integrated with the C0-type high-order shear deformation plate theory (C0-HSDT) for free vibration and static analyses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates. The material properties of FG-CNTRC are assumed to be graded through the thickness direction according to several distributions of the volume fraction of carbon nanotubes (CNTs). The stiffness formulation of the ES-DSG based on C0-HSDT is performed by using the strain smoothing technique over the smoothing domains

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Belkhodja, Y., D. Ouinas, H. Fekirini, JA Viña Olay, and M. Touahmia. "Three new hybrid quasi-3D and 2D higher-order shear deformation theories for free vibration analysis of functionally graded material monolayer and sandwich plates with stretching effect." Advanced Composites Letters 29 (January 1, 2020): 096369352094186. http://dx.doi.org/10.1177/0963693520941865.

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The present investigation brings to the readers three new hybrid higher-order shear deformation theory (HSDT) models and analyses the functionally graded material (FGM) plates. The major objective of this work is to develop three HSDTs in a unique formulation by polynomial–hyperbolic–exponential and polynomial–trigonometric forms, propose the three new HSDT models, investigate the effect of thickness stretching by considering a quasi-three-dimensional theory and analyse the free vibration of isotropic and FGM monolayer and sandwich (symmetric as well as non-symmetric, with hardcore as well as

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Dinwoke, Onodagu P., Aginam C. Henry, and Uzodinma C. Franklin. "Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions." European Journal of Engineering and Technology Research 6, no. 7 (2021): 144–52. http://dx.doi.org/10.24018/ejeng.2021.6.7.2690.

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This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-

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Dinwoke, Onodagu P., Aginam C. Henry, and Uzodinma C. Franklin. "Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions." European Journal of Engineering and Technology Research 6, no. 7 (2021): 144–52. http://dx.doi.org/10.24018/ej-eng.2021.6.7.2690.

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This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-

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Belkhodja, Yamna, Djamel Ouinas, Fatima Zohra Zaoui, and Hamida Fekirini. "An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates." Advanced Composites Letters 29 (January 1, 2020): 096369351987573. http://dx.doi.org/10.1177/0963693519875739.

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Two assumptions have been made based on by this proposed theory, which come from recently developed exponential–trigonometric shape function for transverse shear deformation effect and a simple higher order shear deformation theory for plate, based on a constraint between two rotational displacements of axis parallel to the plate midplane, about the axes x, y Cartesian coordinates system, which caused fewer unknown number. For the application of this method, a displacement field extended as only bending membrane for transverse displacement is used, a governing equations of motion as a result a

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Wu, Chih-Ping, and Zhan-Rong Xu. "Strong and Weak Formulations of a Mixed Higher-Order Shear Deformation Theory for the Static Analysis of Functionally Graded Beams under Thermo-Mechanical Loads." Journal of Composites Science 4, no. 4 (2020): 158. http://dx.doi.org/10.3390/jcs4040158.

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The strong and weak formulations of a mixed layer-wise (LW) higher-order shear deformation theory (HSDT) are developed for the static analysis of functionally graded (FG) beams under various boundary conditions subjected to thermo-mechanical loads. The material properties of the FG beam are assumed to obey a power-law distribution of the volume fractions of the constituents through the thickness of the FG beam, for which the effective material properties are estimated using the rule of mixtures, or it is directly assumed that the effective material properties of the FG beam obey an exponential

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Zhang, Guiju, Caiyuan Xiao, Alireza Rahimi, and Mehran Safarpour. "Thermal and Mechanical Buckling and Vibration Analysis of FG-GPLRC Annular Plate Using Higher Order Shear Deformation Theory and Generalized Differential Quadrature Method." International Journal of Applied Mechanics 12, no. 02 (2020): 2050019. http://dx.doi.org/10.1142/s1758825120500192.

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This is the first research on the buckling and free vibration analysis of functionally graded graphene platelets reinforced composite annular plate resting on elastic substrate and subjected to nonlinear temperature gradient and mechanical load within the framework of higher order shear deformation theory (HSDT). Governing equations and boundary conditions are established by employing Hamilton’s principle. Generalized differential quadrature method is applied to obtain numerical solution. Considering nonlinear temperature gradient instead of the linear one and also the effects of elastic subst

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Javed, Saira. "Conical-Shaped Shells of Non-Uniform Thickness Vibration Analysis Using Higher-Order Shear Deformation Theory." Symmetry 16, no. 5 (2024): 620. http://dx.doi.org/10.3390/sym16050620.

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The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were used to analyse the frequency of conical-shaped shells. The differential equations, consisting of displacement and rotational functions, were approximated using spline approximation. A generalised eigenvalue problem was obtained and solved numerically for an eigenfrequency parameter and ass

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Trung, Nguyen Thoi, Phung Van Phuc, Tran Viet Anh, and Nguyen Tran Chan. "Dynamic analysis of Mindlin plates on viscoelastic foundations under a moving vehicle by CS-MIN3 based on C0-type higher-order shear deformation theory." Vietnam Journal of Mechanics 36, no. 1 (2014): 61–75. http://dx.doi.org/10.15625/0866-7136/36/1/2974.

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A cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed to improve the performance of the existing three-node Mindlin plate element (MIN3) for static and dynamic analyses of Mindlin plates. In this paper, the CS-MIN3 is extended to the C0-type higher-order shear deformation plate theory (C0-HSDT) and incorporated with damping-spring systems for dynamic analyses of Mindlin plates on the viscoelastic foundation subjected to a moving vehicle. The plate-foundation system is modeled as a discretization of triang

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Tomar, Sanjay Singh, and Mohammad Talha. "Thermo-Mechanical Buckling Analysis of Functionally Graded Skew Laminated Plates with Initial Geometric Imperfections." International Journal of Applied Mechanics 10, no. 02 (2018): 1850014. http://dx.doi.org/10.1142/s175882511850014x.

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The aim of the present study is to investigate thermo-mechanical buckling response of skew functionally graded laminated plates (FGLP) with initial geometric imperfections. The formulation has been performed using Reddy’s higher order shear deformation theory (HSDT) with the [Formula: see text] continuous displacement field. A nine-noded isoparametric element has been employed to discretize the domain of the plate. Variational principle has been used to derive the governing differential equation of the problem. Several examples with various comparison and parametric studies have been shown to

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TURAN, Muhittin, and Mahmut İlter HACIOĞLU. "Buckling Analysis of Functionally Graded Beams Using the Finite Element Method." Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 15, Special Issue 1 (2022): 98–109. http://dx.doi.org/10.18185/erzifbed.1199454.

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This study developed a finite element model according to higher-order shear deformation beam theory (HSDT) for the buckling analysis of functionally graded (FG) beams. Equilibrium equations of the FG beam are obtained from Lagrange’s equations. The beam element to be discussed within the scope of the study has 5 nodes and 16 degrees of freedom (DOF). As a result of the buckling analysis, the critical buckling load of the beam was obtained for various boundary conditions, power-law index (p), and slenderness (L/h). When the critical buckling loads obtained as a result of the analysis were compa

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Le, Truong Son. "Forced vibration analysis of sandwich plates with an auxetic honeycomb core and laminated composite three-phase skin layers resting on Kerr foundation." Journal of Military Science and Technology 103 (May 26, 2025): 110–20. https://doi.org/10.54939/1859-1043.j.mst.103.2025.110-120.

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This paper introduces isogeometric analysis (IGA) based on higher-order shear deformation theory (HSDT) for vibration analysis of sandwich plates resting on Kerr foundation (KF). The sandwich plates include the ultra-light of an auxetic honeycomb core layer and are reinforced by two laminated composite three-phase skin layers. The governing equation is derived from Hamilton's principle. The Newmark-β method is applied to solve the forced vibration of the sandwich plates by the code in Matlab software. The accuracy of the proposed method is verified through comparative examples. Additionally, t

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Ebrahimi, Farzad, Alireza Enferadi, and Ali Dabbagh. "Wave Dispersion Behaviors of Multi-Scale CNT/Glass Fiber/Polymer Nanocomposite Laminated Plates." Polymers 14, no. 24 (2022): 5448. http://dx.doi.org/10.3390/polym14245448.

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In this paper, wave propagation in multi-scale hybrid glass fiber (GF)/carbon nanotube (CNT)/polymer nanocomposite plates is studied for the first time by means of refined higher-order plate theory. The hybrid nanocomposite consists of CNTs and glass fibers (GF) as reinforcing components distributed within a polymeric matrix. A hierarchical micromechanical approach is used to predict the effective mechanical properties of the hybrid nanocomposite, including the three-dimensional (3D) Mori-Tanaka method and the rule of mixture. Moreover, a refined-type higher-order shear deformation theory (HSD

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Sadeghian, Mostafa, Arvydas Palevicius, Paulius Griskevicius, and Giedrius Janusas. "Nonlinear Analysis of the Multi-Layered Nanoplates." Mathematics 12, no. 22 (2024): 3545. http://dx.doi.org/10.3390/math12223545.

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This text investigates the bending/buckling behavior of multi-layer asymmetric/symmetric annular and circular graphene plates through the application of the nonlocal strain gradient model. Additionally, the static analysis of multi-sector nanoplates is addressed. By considering the van der Waals interactions among the layers, the higher-order shear deformation theory (HSDT), and the nonlocal strain gradient theory, the equilibrium equations are formulated in terms of generalized displacements and rotations. The mathematical nonlinear equations are solved utilizing either the semi-analytical po

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Pal, Priyaranjan. "The displacement view of a multilayered HSDT plate." Journal of Polymer Science and Engineering 4, no. 1 (2021): 863. https://doi.org/10.24294/jpse.v4i1.863.

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This paper presents the state of displacement of a multilayered composite laminate subjected to transverse static load with varying balance, symmetric and anti-symmetric angle-ply and cross-ply staking sequences. Higher-order shear deformation theory (HSDT) is considered in the finite element formulation of nine-noded isoparametric element with seven degrees of freedom at each node. The finite element formulation is transformed into computer codes. A convergence study is carried out first to obtain the optimal mesh size for minimizing the computational time. The maximum deflection at the cente

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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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Wu, Chih-Ping, and Kuan-Wei Li. "Multi-Objective Optimization of Functionally Graded Beams Using a Genetic Algorithm with Non-Dominated Sorting." Journal of Composites Science 5, no. 4 (2021): 92. http://dx.doi.org/10.3390/jcs5040092.

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A mixed layer-wise (LW) higher-order shear deformation theory (HSDT) is developed for the thermal buckling analysis of simply-supported, functionally graded (FG) beams subjected to a uniform temperature change. The material properties of the FG beam are assumed to be dependent on the thickness and temperature variables, and the effective material properties are estimated using either the rule of mixtures or the Mori–Tanaka scheme. The results shown in the numerical examples indicate the mixed LW HSDT solutions for critical temperature change parameters are in excellent agreement with the accur

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Dat, Le Thanh, and Pham Tan Hung. "Vibrational behavior in FG-GPLRC plates on elastic substrates using the moving Kriging meshfree method." Journal of Advanced Engineering and Computation 9, no. 2 (2025): 92. https://doi.org/10.55579/jaec.202592.500.

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The paper’s main purpose is to analyze the free vibration of graphene platelet-reinforced functionally graded metal foam plates using the C0-type higher-order shear deformation theory (C0-HSDT) with seven variables and the moving Kriging meshfree method (MKMM). Various types of porosity and graphene platelets distributions through the plate’s thickness are investigated in this study. Material properties of metal foam plates reinforced with graphene platelets are described using the Halpin-Tsai model. By applying Hamilton’s principle alongside the C0-HSDT, the governing equation for free vibrat

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Shegokar, Niranjan L., and Achchhe Lal. "Stochastic Nonlinear Free Vibration Analysis of Functionally Graded Beam Subjected to Thermal Loading with Random Material Properties." Advanced Materials Research 747 (August 2013): 551–54. http://dx.doi.org/10.4028/www.scientific.net/amr.747.551.

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This paper deals with the stochastic nonlinear free vibration response of functionally graded materials (FGMs) beam subjected to thermal loadings with uncertain material properties subjected to uniform and nonuniform temperature changes with temperature independent (TID) and dependent (TD) material properties. System properties such as material properties of each constituents material and volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strains using modified C0 contin

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Reddy, Ch Naveen, M. Bhargav, and T. Revanth. "Bending Analysis of Piezoelectric Functionally Graded Material Plates Using HSDT." Materials Science Forum 969 (August 2019): 116–21. http://dx.doi.org/10.4028/www.scientific.net/msf.969.116.

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This work investigates the complete analytical solution for functionally graded material (FGM) plates incorporated with smart material. The odjective of the present work is to determine bending characteristics of piezoelectric FGM plates with different geometrical parameters, voltages and boundary conditions for electro-mechanical loading. In this work an analytical formulation based on higher order shear deformation theory (HSDT) is presented for the piezoelectric FGM plates. The solutions are obtained in closed from using Navier’s technique for piezoelectric FGM plates a specific type of sim

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Jin, Guodong, Lei Ma, Hong Zhang, and Qingshan Wang. "Vibration Characteristics Analysis of Composite Laminated Annular/Circular Plate Using High-Order Shear Deformation Theory." Shock and Vibration 2021 (July 30, 2021): 1–19. http://dx.doi.org/10.1155/2021/5913860.

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In this paper, the free vibration behaviors of composite laminated annular and circular plates under complex elastic boundary constraints are investigated. Firstly, Reddy’s high-order shear deformation theory (HSDT) and Jacobi polynomial method are effectively combined to establish the unified vibration analysis model of composite laminated annular and circular plates. Secondly, the simulation of complex elastic boundary and coupling boundary is realized by using artificial virtual spring technology. Then, the energy equation of the composite laminated plate is established by using Rayleigh–Ri

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Subramani, Mageshwaran, Ananda Babu Arumugam, and Manoharan Ramamoorthy. "Vibration Analysis of Carbon Fiber Reinforced Laminated Composite Skin with Glass Honeycomb Sandwich Beam Using HSDT." Periodica Polytechnica Mechanical Engineering 61, no. 3 (2017): 213. http://dx.doi.org/10.3311/ppme.9747.

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In this paper, the vibration analysis of uniform laminated composite sandwich beam with a viscoelastic core was studied. The governing equation of motion of the laminated composite sandwich beam has been derived based on higher order shear deformation theory (HSDT) in finite element model (FEM). The developed finite element model has been validated in terms of natural frequencies with the experimental values and the available literature. Various parametric studies have been performed to examine the impact of the core thickness, ply orientation and aspect ratio of the uniform laminated composit

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Qin, Bin, Xing Zhao, Huifang Liu, Yongge Yu, and Qingshan Wang. "Free Vibration Analysis of Curved Laminated Composite Beams with Different Shapes, Lamination Schemes, and Boundary Conditions." Materials 13, no. 4 (2020): 1010. http://dx.doi.org/10.3390/ma13041010.

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A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expa

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Solanki, Manoj Kumar, Rahul Kumar, and Jeeoot Singh. "Flexure Analysis of Laminated Plates Using Multiquadratic RBF Based Meshfree Method." International Journal of Computational Methods 15, no. 06 (2018): 1850049. http://dx.doi.org/10.1142/s0219876218500494.

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The linear and nonlinear flexure analysis of laminated plates with twenty theories with the five variable higher order shear deformation theory (HSDT) is investigated using multiquadratic radial basis function based meshfree method. The mathematical formulation of the actual physical problem of the plate subjected to transverse loading is presented utilizing von Karman nonlinear kinematics. These non-linear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. The different results for deflection and stresses are obtained for thin to a thick pl

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