quasi-3D Shear Deformation Theory Research Articles

Free vibration analysis of nanocomposite plate in contact with fluid using a novel quasi-3D shear deformation theory and artificial neural network

This article presents an analytical approach leveraging a novel quasi-three-dimensional shear deformation theory to analyze the free vibration response of functionally graded graphene platelet-reinforced composite (FG-GPLRC) plates in a liquid medium. The study meticulously determines material properties using the Halpin-Tsai micromechanical model, offering a thorough characterization of these advanced nanocomposite structures. Differential motion equations, incorporating transverse shear and normal stresses, are derived via Hamilton’s principle. The natural frequencies of the nanocomposite plates are computed using Galerkin’s method and validated against published results, affirming their accuracy and reliability. The key innovation of this research is introducing a new trigonometric shape function, which exhibits superior precision compared to previously proposed shape functions and existing theories. Furthermore, an artificial neural network (ANN) model is developed to train the computed results, enabling precise prediction of the natural frequencies without further computational runs. The Bayesian Regularization algorithm, implemented in Matlab, is utilized for this purpose. Across different GPLs patterns and varying input parameters, the error percentage between the ANN model predictions and the results from the Galerkin’s method is consistently low, often below 0.1%. The ANN model demonstrates robust generalization by effectively predicting outcomes with input data beyond its training range. Additionally, it provides immediate computational results, eliminating the delays of traditional methods. The article also examines the effects of various factors, including material characteristics, geometric parameters, and the fluid medium, on the free vibration behavior of FG-GPLRC plates.

NGHIÊN CỨU PHÂN BỐ ỨNG SUẤT TẠI BIÊN NGÀM CỦA VỎ TRỤ FGM CHỊU TẢI TRỌNG TĨNH SỬ DỤNG LÝ THUYẾT BIẾN DẠNG CẮT BẬC CAO QUASI-3D

This article presents the results of investigating FGM closed cylindrical shells using quasi-3D higher-order shear deformation theory. The law of volume distribution of materials according to the power function. In this article, the results of the analysis of the stress state at the clamped boundary area of the FGM cylindrical shell subjected to radial local loads distributed according to different laws. The mathematical model and the calculation program in Maple are compared and verified with the published results. The article has shown that at the clamped boundary edge, the values of stress components increase sharply, and at the same time, the strong influence of the load parameters (the variation law, the size of the load area), the power-law index on the values and distribution of stress components in the boundary area is demonstrated.

Fundamental frequencies of cracked FGM beams with influence of porosity and Winkler/Pasternak/Kerr foundation support using a new quasi-3D HSDT

In this study, we have introduced, for the first time, a novel integral quasi-3D higher-order shear deformation theory (HSDT) employing a third-order shape function. This approach is employed to analyze the free vibration characteristics of a cracked porous functionally graded material (FGM) beam supported on a three-parameter elastic foundation (Winkler/Pasternak/Kerr). This new Quasi HSDT introduces a stretching effect that surpasses the capabilities of FSDT and other HDST. The employed shape function satisfies the conditions of shear stress nullity at both the higher and lower facets without the need for correction factors. The study incorporates a mathematical model representing Winkler/Pasternak/Kerr foundation types into the Hamiltonian to derive the equations of motion. The FGM beam studied in this paper is assumed to be composed of materials with a distribution that varies according to a power law along its height. Our results are compared with previous studies and we reinforce our findings with a parametric study assessing the impact of crack attributes on the natural frequencies of the FG plate. This study presents an advanced integral quasi-3D HSDT, applied for the first time, to analyze the behavior of FG beams resting on a three-parameter foundation.

Bending analysis of FGSP nanoplate resting on elastic foundation by using nonlocal quasi-3D theory

In this paper, the bending response of a functionally graded saturated porous (FGSP) nanoplate resting on the Pasternak elastic foundation is analyzed within the framework of quasi-3D higher-order shear deformation theory (quasi-3D HSDT) for the first time. The material properties are presumed to change gradually along the thickness direction following three patterns of porosity distribution: uniform, non-uniform symmetric, and asymmetric. The theory of poroelasticity developed by Biot is utilized in modeling the stress-strain relationships for the saturated condition. Moreover, the nanoscale effects of the structures are considered by Eringen's nonlocal elasticity theory. The governing equations are derived by using the principle of minimum potential energy according to quasi-3D HSDT, which ensures transverse shear stress-free on the upper and lower surfaces of the nanoplate. Based on the obtained closed-form solution, the impacts of the porosity distribution patterns, porosity coefficient, Skempton coefficient, geometrical parameters, elastic foundation, and nonlocal parameters on the bending behavior have been explored. According to the findings, when the pores are saturated by the fluid, the plate stiffness increases. Additionally, increasing the values of the nonlocal parameter for FGSP nanoplates leads to an increase in deflection and stresses. Finally, the present study quantitatively reveals the size-dependent effects of a saturated porous medium.

Vibration analysis of tri-directionally coated plate via thickness-stretching and microstructure-dependent modeling

In this study, the tri-directionally-coated functionally graded plate has different levels of microstructure and is modeled more accurately using nonclassical mechanics incorporating the intrinsic characteristic lengths as well as using a spatial variation of material properties. The free vibration behavior of the tri-directionally-coated functionally graded plate is investigated using a refined quasi-3D higher-order shear deformation theory in conjunction with nonlocal strain gradient theory. Based on the generalized field of displacement, the quasi-3D higher-order shear deformation theory is employed by reducing the number of variables from six to five variables. The equations of motion are performed based on the principle of Hamilton and solved by applying the Galerkin technique to cover various boundary conditions. Besides, the microstructure-dependent parameters, that is, the nonlocal parameter and the length scale parameter, also affect significantly the frequency of the tri-directionally-coated functionally graded plates. The multi-directionally-coated plate is softened when considering the nonlocal parameter; the multi-directionally-coated plate is, however, hardened when considering the length scale parameter.

Refined quasi-3D shear deformation theory for buckling analysis of functionally graded curved nanobeam rested on Winkler/Pasternak/Kerr foundation

In the present work, a novel refined three-variable quasi-3D shear deformation theory incorporates a correction factor is developed to analyze the buckling behavior of multi-directional functionally graded (FG) curved beams. The proposed displacement field is formulated in accordance with the Euler-Bernoulli beam theory. The research investigated two types of coated Functionally Graded (FG) nanobeams: Hardcore (HC) FG curved nanobeams and Softcore (SC) FG curved nanobeams. Three different material distributions are taken into consideration: a bidirectional material distribution referred to as “2D-FG,” a unidirectional transverse material distribution known as “T-FG,” and a unidirectional axial material distribution called “A-FG.” Eringen’s nonlocal elasticity theory is employed to capture small-scale effects. The total potential energy principle is utilized to derive the equilibrium equations of curved nanobeams. A novel solution, utilizing Galerkin’s method, has been developed to effectively address a range of boundary conditions. The curved FG beam is supported by an elastic foundation following the Winkler/Pasternak/Kerr model. A comprehensive analysis has been conducted to examine the impacts of various FG schemes, curved beam geometry, nonlocal parameter, elastic foundations, and various boundary conditions on the dimensionless critical buckling loads. This analysis aims to provide a comprehensive understanding of how each of these factors influences the critical buckling loads of the nanobeams.

Vibration Analysis of Thick Sandwich Plates with Saturated FG-Porous Core Using Quasi-3D Shear Deformation Theory

Vibration Analysis of Thick Sandwich Plates with Saturated FG-Porous Core Using Quasi-3D Shear Deformation Theory

Nonlinear Finite Element Model for Bending Analysis of Functionally-Graded Porous Circular/Annular Micro-Plates under Thermomechanical Loads Using Quasi-3D Reddy Third-Order Plate Theory.

A nonlinear finite element model for axisymmetric bending of micro circular/annular plates under thermal and mechanical loading was developed using quasi-3D Reddy third-order shear deformation theory. The developed finite element model accounts for a variation of material constituents utilizing a power-law distribution of a two-constituent material, three different porosity distributions through plate thickness, and geometrical nonlinearity. The modified couple stress theory was utilized to account for the strain gradient effects using a single material length scale parameter. Three different types of porosity distributions that have the same overall volume fraction but different enhanced areas were considered as a form of cosine functions. The effects of the material and porosity distribution, microstructure-dependency, the geometric nonlinearity, and various boundary conditions on the bending response of functionally-graded porous axisymmetric microplates under thermomechanical loads were studied using the developed nonlinear finite element model.

Static analysis of functionally graded saturated porous plate rested on pasternak elastic foundation by using a new quasi-3D higher-order shear deformation theory

Static analysis of functionally graded saturated porous plate rested on pasternak elastic foundation by using a new quasi-3D higher-order shear deformation theory

Simple quasi-3D and 2D integral shear deformation theories for buckling investigation of advanced composite plates

Simple quasi-3D and 2D integral shear deformation theories for buckling investigation of advanced composite plates

Spectral stochastic isogeometric analysis of bending and free vibration of porous functionally graded plates

In this paper, a systematic spectral stochastic isogeometric analysis (SSIGA) process is presented for the static bending and free vibration analyses of functionally graded (FG) plates with three-dimensional (3D) random porosity. The porosity is modeled as a Beta random field, represented compactly via the Karhunen-Loève expansion. A novel hierarchical locking-free quasi-3D shear deformation theory, called spectral displacement formulation (SDF), is proposed to approach exact 3D solutions and reflect more realistic effects of the random porosity field (RPF). Isogeometric analysis is utilized to meet the C1-continuity requirement of the SDF. The response surfaces of the porous FG plates are constructed non-invasively by the spectral collocation method. A new spectral stochastic post-processing process is developed to evaluate the probability characteristics of the responses and exclude the adverse convergence-in-probability property, which typically exists in sampling-based methods. Numerical examples illustrate the SSIGA process and demonstrate its effectiveness. The influences of the RPF parameters and the gradient index on the response statistics are investigated.

A refined quasi-3D theory for the bending of functionally graded porous sandwich plates resting on elastic foundations

An improved porosity distribution is introduced for the bending of a novel model of functionally graded (FG) sandwich plates via a refined quasi-3D shear and normal deformation theory. The sandwich plates are lying on Pasternak’s elastic foundation and exposed to sinusoidal mechanical loads. The shear and normal strains are both included, for that the shear correction factor is unnecessary. Depending on a specific function, the material properties of the sandwich plates vary continuously across the thickness direction. The equilibrium equations will be derived using the virtual work principle and solved using Navier’s method. The effects of the porosity parameter, inhomogeneity factor, elastic foundations parameters, length-to-thickness, and length-to-width ratios will be introduced. Comparison examples will be discussed to support the accuracy of the current theory. Further results will be introduced to provide benchmarks for comparison purposes.

Analytical investigation of wave propagation in bidirectional FG sandwich porous plates lying on an elastic substrate

This paper deals with the wave propagation analysis of bidirectional functionally graded (BDFG) porous sandwich plates lying on an elastic foundation within the framework of the quasi-3D shear deformation theory. The mechanical properties of the BDFG plates vary continuously in both axial and thickness directions according to a power law. The sandwich plate’s behavior is modeled by means of quasi-3D displacement field that contains undetermined integral terms and involves only four unknown functions. The BDFG porous sandwich plate is considered to be rest on two kinds of elastic foundation, variable and visco-elastic. The principle of Hamilton is used to reach motion equations of BDFG porous sandwich plates. Then, governing equations are derived for the wave propagation problem based on the present quasi-3D theory and solved analytically. The results of the present work are validated by comparing with those available in the literature works. A parametric study is conducted to show the effect of material gradation, core-to-thickness ratio, porosity volume fraction, and elastic foundation on the wave propagation. The results reveal that these parameters have a great influence on the wave propagation in porous BDFG sandwich plates resting on elastic foundations.

Buckling analysis of the porous sandwich functionally graded plates resting on Pasternak foundations by Navier solution combined with a new refined quasi-3D hyperbolic shear deformation theory

This article presents a numerical method for analyzing the compressive buckling of porous power-law functionally graded (PPFG) plates placed on Pasternak foundations, which is based on a novel refined quasi-3-dimensional hyperbolic shear deformation theory (RQHSDT) combined with the Navier solution technique. The RQHSDT employs a novel hyperbolic distribution of in-plane displacements through the plate thickness to account for non-linear variations in transverse shear stresses, satisfies the traction free boundary conditions on the top and bottom surfaces, and accounts for shear deformation and thickness stretching effects of the plates without the use of any shear correction factors. Unlike classical shear and normal deformation theories, the RQHSDT has only four variables in its displacement field, as opposed to five or more variables in other quasi-3D shear deformation theories, which reduces the number of unknown variables and governing equations in plate analyses and simplifies calculations. The governing equations of the buckling problem are derived using the virtual work principle. In problem solving, the Navier solution technique is used to obtain the exact solutions for the rectangular PPFG plates with simply supported edges subjected to in-plane loading. The accuracy of the proposed approach is confirmed by comparing the obtained results to those of previously published quasi-3D shear deformation theories. Using comprehensive parametric studies, the effects of gradient index, porosity fraction index, porosity distribution type, geometric parameters, two-direction compression ratio, and stiffness of foundation parameters on buckling of PPFG plates are investigated.

Coupled stress based formulation for static and dynamic analyses of a higher-order shear and normal deformable FG-GPL reinforced microplates

In this paper, size-dependent static bending and also free and forced vibration analyses of composite microplates are studied based on the modified couple stress theory (MCST) and quasi-3D sinusoidal shear deformation theory. The composite microplate is composed of epoxy reinforced with functionally graded graphene nanoplatelets (GPLs). The governing equations are derived utilizing Hamilton's principle and are solved for simply supported microplate using Navier's approach. The accuracy of the presented solution is confirmed and the effects of various parameters on the static and dynamic deflections and natural frequencies of the microplate are investigated including material length scale parameter and surface area, thickness, mass fraction, and distribution pattern of the GPLs. Numerical results confirm that subjoining the GPLs to the polymer reduces the static and dynamic deflections of the microplates and increases the natural frequencies. It is concluded that to achieve the highest reduction in the static and dynamic deflections and the highest growth in the natural frequencies, it is more helpful to use the GPLs with the larger surface areas and put them as far as away from the neutral surface of the microplate.

Investigation on the effect of porosity on wave propagation in FGM plates resting on elastic foundations via a quasi-3D HSDT

In this paper, wave propagation in functionally graded (FG) porous plates resting on Winkler-Pasternak foundation is studied using a quasi-3D shear deformation theory. The proposed theory has a new displacement field that includes indeterminate integral terms and contains fewer unknown variables taking into account the effect of transverse shear and thickness stretching. The parameters of the elastic foundation are introduced in the present formulation following the mathematical model of Pasternak. In addition, the effect of porosity is studied. The material of the FG plate is inhomogeneous and the material properties are assumed to vary continuously in the thickness direction according to a power law of the volume fraction. The equations governing wave propagation in the plates resting on an elastic foundation are derived using Hamilton's principle. Then, the dispersion relationship between frequency and wave number is solved analytically. A comprehensive numerical result is accomplished to evaluate the effects of the volume fraction index, the porosity, thickness ratio (h/a), and the wave number on the wave propagation in functionally graded porous plates are discussed in detail.

Thermoelastic response and boundary effect of cross-ply laminated cylindrical shells based on a quasi-3D type higher-order shear deformation theory

In the present study, the boundary effect and the thermoelastic response of laminated cylindrical shells with various boundary conditions are considered using the quasi-3D type higher-order shear deformation theory and the semi-analytical approach. The governing equations and their corresponding boundary conditions are derived based on the principle of virtual work. To obtain the static solution, these governing equations are solved by employing fundamental trigonometric series and the Laplace transform. The shell is subjected to a thermal load uniformly or sinusoidally distributed over the surface and linearly varying through the thickness. The present results are compared with other higher-order models in previous studies. The paper also exhibits the effects of the boundary condition, the relative thickness, the relative length, the laminated sequence, the relationships of elastic moduli, thermal expansion coefficients in the directions of principal material axes on the displacements, and the stresses of shells. The stress concentration effect is analyzed, and then the effects of several structural and material parameters on the distribution of stresses in the boundary zone are discussed in detail.

A quasi-three-dimensional isogeometric model for porous sandwich functionally graded plates reinforced with graphene nanoplatelets

The purpose of this study is to present a quasi-three-dimensional (quasi-3D) shear deformation theory for static bending and free vibration analyses of porous sandwich functionally graded (FG) plates with graphene nanoplatelets (GPLs) reinforcement. In addition, we propose a novel sandwich plate model with various outstanding features in terms of structural performance. The quasi-3D theory-based isogeometric analysis (IGA) in conjunction with refined plate theory (RPT) is first exploited to capture adequately the thickness stretching effect for porous sandwich FG plate structures reinforced with GPLs. The Non-Uniform Rational B-Splines (NURBS)-based IGA is employed in order to describe exactly the geometry models as well as approximate the unknown field with higher-order derivatives and continuity requirements while the RPT model includes only four essential variables. The sandwich FG plates consist of a core layer containing internal pores reinforced by GPLs and two functionally graded materials (FGMs) skin layers. Effective mechanical properties can be evaluated by employing the Halpin-Tsai model along with the rule of mixture. Various combinations of two porosity distributions and three GPL dispersions in the core layer are thoroughly investigated. Several numerical investigations are conducted to examine the effects of several key parameters on the static bending and free vibration behaviors of sandwich FG plate structures.

Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment

This paper presents a mathematical continuum model to investigate the static stability buckling of cross-ply single-walled (SW) carbon nanotube reinforced composite (CNTRC) curved sandwich nanobeams in thermal environment, based on a novel quasi-3D higher-order shear deformation theory. The study considers possible nano-scale size effects in agreement with a nonlocal strain gradient theory, including a higher-order nonlocal parameter (material scale) and gradient length scale (size scale), to account for size-dependent properties. Several types of reinforcement material distributions are assumed, namely a uniform distribution (UD) as well as X- and O- functionally graded (FG) distributions. The material properties are also assumed to be temperature-dependent in agreement with the Touloukian principle. The problem is solved in closed form by applying the Galerkin method, where a numerical study is performed systematically to validate the proposed model, and check for the effects of several factors on the buckling response of CNTRC curved sandwich nanobeams, including the reinforcement material distributions, boundary conditions, length scale and nonlocal parameters, together with some geometry properties, such as the opening angle and slenderness ratio. The proposed model is verified to be an effective theoretical tool to treat the thermal buckling response of curved CNTRC sandwich nanobeams, ranging from macroscale to nanoscale, whose examples could be of great interest for the design of many nanostructural components in different engineering applications.

Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory

The sandwich structures contain three or more layers attached to the core. In the current research, a three-layered sandwich microplate containing functionally graded (FG) porous materials as core and piezoelectric nanocomposite materials as face sheets subjected to electric field resting on Pasternak foundation is chosen as a model to investigate its vibrational behavior. To make the face sheets stiffer, they are reinforced by carbon nanotubes (CNTs) via different distribution patterns which result in changing their properties along the thickness direction. An innovative quasi-3D shear deformation theory with five unknowns, Hamilton’s principle, and modified couple stress theory are hired to gain equations of motion related to the abovementioned microstructure. Eventually, the evaluation of materials’ properties, geometry specifications, foundation moduli, and hygrothermal environment on vibrational behavior of such structures became easier using the presented results of the current study in figure format. As an instance, it is revealed that CNTs’ volume fraction elevation causes mechanical properties improvement, and in the following, natural frequency increment. Besides, considering the hygrothermal environment causes significant effects on the results.