quasi-3D Theory Research Articles

Study and comparison of the bending response of porous advanced composite plates under thermomechanical loads using different materials

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 and eliminating the need for shear correction factors, thereby reducing computational costs compared to traditional theories such as first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT), sinusoidal shear deformation theory (SSDT), and quasi-3D theory. The study examines the bending response of porous FGMs composed of various materials, including FGM 1 (Aluminum/Zirconia), FGM 2 (Ceramic/Zirconia), FGM 3 (Titanium/Silicon Carbide), FGM 4 (Stainless Steel/Zirconia), FGM 5 (Copper/Alumina), and FGM 6 (Nickel/Silicon Nitride). The results derived from the proposed theory are systematically compared with those obtained from other established theories to demonstrate its accuracy and computational efficiency. This work provides valuable insights into the behavior of porous FGMs and highlights the potential of the refined shear deformation theory for future applications in structural engineering.

Optimization of model order reduction for transient analysis of functionally graded plates using isogeometric analysis based on four-variable quasi-3D theory

Optimization of model order reduction for transient analysis of functionally graded plates using isogeometric analysis based on four-variable quasi-3D theory

The porosity effect on the buckling analysis of functionally graded plates under thermal environment using a Quasi-3D theory

Functionally graded porous structures are at the forefront of material innovation, providing a flexible solution to suit the wide range of requirements in modern engineering applications. The capacity of these materials to integrate customized porosity with variable mechanical properties not only improves performance but also promotes improvements in performance, efficiency, and durability. One of the main contributions of this research its a comprehensive method of including porosity effects in the thermal buckling load analysis of functionally graded plates. Also, this study aims to apply the Quasi-3D theory to investigate the influence of porosity on the thermal critical buckling load of functionally graded plates. The plates demonstrate microscopic heterogeneity, with material characteristics changing continually according to a modified polynomial function. The primary goal is to investigate how different porosity distributions (even, uneven, and logarithmic uneven) influence the thermal critical buckling load under different thermal load circumstances. The governing equations are derived using a Quasi-3D deformation theory that takes into account transverse normal strain. Navier’s method is used to investigate simply supported FG plates, both perfect and imperfect, under uniform, linear, and nonlinear thermal loads. Numerical simulations are used to calculate the thermal critical buckling for various geometries, thermal loading conditions and porosity characteristics. The results show that the porosity distribution has a substantial influence on increasing the thermal critical buckling load of FG porous plates. The model of even porosity distribution has the largest thermal critical buckling load, whereas the model of logarithmic-uneven porosity distribution has the lowest thermal critical buckling load, indicating that such distributions should be carefully considered in FGM design. The type of thermal loading condition applied to the plate has a significant impact on the thermal critical buckling of the plate. Moreover, various geometries, volume fraction index, and inclusion of thickness stretching are considered to examine the effect on the thermal critical buckling load response. Comparisons with literature are added to validate the accuracy of numerical findings. This research has the potential to offer comprehensive reference and useful guidance in the design and application of FG porous plate structures.

Buckling and bending analysis of porous FG beam using a simple integral quasi-3D theory

Buckling and bending analysis of porous FG beam using a simple integral quasi-3D theory

A four-unknown quasi-3D isogeometric approach for free vibration and bending analysis of piezoelectric 2D-FGPs

In this paper, an isogeometric analytical method based on quasi-3D shear deformation theory is proposed to analyze free vibration and the bending problems of bi-directional piezoelectric functionally graded plates (2D-FGPs). The formulated equations of motion for piezoelectric 2D-FGPs are derived by leveraging the fundamental equations intrinsic to piezoelectric materials and employing the Hamiltonian variational principle. The employed plate theory significantly diminishes the quantity of unknown variables and governing equations relative to extant quasi-3D theories. The higher-order continuity of the non-uniform rational B-splines (NURBS) satisfies the C1 continuity requirement of the quasi-3D theory. The effects of mechanical loads, boundary conditions, and applied voltages on the bending and free vibration responses of piezoelectric 2D-FGPs are investigated and discussed in detail through several numerical examples.

Finite element static analysis of functionally graded sandwich beams with porous core resting on a two-parameter elastic foundation based on quasi-3D theory

This paper presents for the first time an investigation into the static characteristics of FG sandwich beams with porous ceramic core and sandwich beams with FG porous core resting on a two-parameter Winkler-Pasternak elastic foundation using a new three-node higher-order finite element model with five degrees-of-freedom per node based on quasi-3D deformation theory, that accounts both the effects of transverse shear and normal deformations. The beams are subjected to uniformly distributed loads, and their material properties vary gradually through the thickness according to the power-law distribution. The governing equation of motion is derived from Lagrange’s equations. Uniform, symmetric, and asymmetric porosity patterns are considered. The accuracy of the proposed model is verified through comparisons with existing results. A comprehensive parametric study is carried out to explore the effects of various parameters such as boundary conditions, skin-to-core thickness ratio, power-law index, slenderness, porosity, and elastic foundation parameters on the displacements and stresses of FG sandwich beams. Benchmark results presented in this study can serve as a reference for future research endeavors on FG sandwich beams with porous cores.

Influence of porosity distribution on buckling behavior of FG sandwich plates using a quasi-3D refined plate theory

This paper uses a quasi-3D refined shear deformation plate theory to investigate the buckling response of supported functionally graded (FG) porous sandwich (SW) plates. The material properties of FG sandwich porous plates (SWPPs) are defined by a modified mixing rule, supplemented by an additional term representing the porosity in the thickness of the FG layer. By incorporating indefinite integral variables, the number of unknowns and governing equations of the current theory is reduced, making it easier to use. Three common types of sandwich porous plates are considered in the analysis: an isotropic FG porous plate, an FG face plate with a homogeneous core, and a homogeneous face plate with an FG core. The current method considers both normal and shear deformations and satisfies the transverse shear stress-free boundary conditions at the top and bottom surfaces of the plate. The equilibrium equations are derived using the principle of virtual displacements. These equations are then solved using the Navier-type method. The influence of thickness strain and several parameters, including mechanical loads, porosity coefficients, layer thickness ratios, geometric parameters, and gradient indices, are studied. The numerical results of the present theory are similar to the predictions of quasi-3D theories with more unknowns, in addition to being more accurate than those obtained by higher-order shear deformation theories. The findings support the idea that the suggested theory offers an easy and effective method for predicting the buckling behavior of FG porous sandwich plates. The results show that, without taking into account transverse normal deformations, the plate is softer and the critical buckling load decreases. On the other hand, with transverse normal deformations, the plate is stiffer, which increases the critical buckling load.

Thermally induced vibration of photovoltaic honeycomb-based-thermoelectric hybrid device

This paper presents a comprehensive investigation of thermally induced vibration (TIV) of elastically constrained photovoltaic honeycomb-based-thermoelectric hybrid device under space thermal environment. Based on four-variable refined quasi-3D higher-order theory as well as virtual boundary spring technique, the equation of motion of the hybrid device is derived by using Lagrange equation. The nonlinear temperature profile is obtained via finite difference scheme and the TIV responses are solved by employing Newmark approach. The effects of boundary condition, size of honeycomb cell, damping effect, thickness of insulation layer and radius of curvature on TIV of the hybrid device are studied. Results show that the TIV response of the hybrid device can be greatly weakened by replacing the dense thermoelectric leg with honeycomb-based thermoelectric leg. Designing the honeycomb cell as re-entrant architecture possesses a better suppression effect on TIV response. The amplitude of TIV reduces with increasing the thickness-length ratio and decreasing the height-length ratio of honeycomb cell. A larger thickness of insulation layer can weaken the TIV response. The oscillation of TIV response can be eliminated by fabricating hybrid device as circular cylindrical and hyperbolic parabolic shallow shells. The stiffer the boundary conditions, the less prone to TIV behavior of the hybrid device. The introduction of damping effect can suppress TIV response, but it simultaneously causes the occurrence of thermal snap. In general, the research provides several design references to weaken the TIV response of the hybrid device under space heat flux.

Thermal and thermo-mechanical post-buckling analysis of GNP-reinforced composite laminated plates

This research utilizes isogeometric analysis (IGA) method to analyze buckling and post-buckling responses of composite laminated plates embedded with graphene nanoplatelets (GNPs) subjected to three-dimensional (3D) conduction of heat or combined 3D heat conduction and mechanical edge compression. A formulation to determine temperature profile produced by 3D conduction of heat in the GNP-reinforced laminate is established, and a new function with smooth transition form of GNP volume fraction across the thickness is presented for dictating the volume fraction of layer. Shear deformable quasi-3D theory with the von Kármán type nonlinearity which takes initial geometric deformation and thermal effect into consideration is employed to construct the nonlinear equilibrium states. Four types of GNP arrangements encompassing uniform, O, X and V shapes are considered. The IGA approach presented, through the benchmark test, is evidenced to estimate the thermal buckling temperature accurately and to successfully trace the thermal post-buckling path. Additional parametric study is carried out to scrutinize the thermal and the thermo-mechanical post-buckling features of the GNP-reinforced composite laminated plates, and the new findings are sure to be served as the benchmark solutions.

Nonlinear temperature dependent and visco-elastic foundation effects on the free vibration of functionally graded sandwich plates with ceramic foam core

This paper investigates the vibrations of a functionally graded sandwich plate (FG sandwich plate) with a ceramic foam core resting on a viscoelastic foundation. The focus is on the influence of temperature changes on sandwich plates that have foam core and FG face sheet on the free vibration. The damping coefficient and different schemes of sandwich plate have been considered in the current work. The analysis uses a quasi-3D theory, which reduces the number of unknown displacements and simplifies the equations by incorporating integral terms. Two models are employed to represent the non-uniformity of the ceramic foam core. To account for the influence of the supporting layer, a viscoelastic foundation is included. The governing equations are derived using Hamilton’s principle and solved using the Navier solution method. The paper comprehensively discusses how the volume fraction index k, geometric properties, ceramic foam distribution, viscoelastic foundation, and different temperature rise profiles impact the vibration response of the FG sandwich plate.

A modified quasi-3D theory and mixed beam element method for static behaviour analysis of functionally graded beams

This paper develops a modified quasi-3D theory and the mixed beam element model for static analysis of functionally graded beams. The modified quasi-3D theory encompasses two innovations. Firstly, the accurate distribution of transverse shear stress is derived from the differential equilibrium equation that describes the relationship between stresses, rather than the traditional one derived from geometric relations and constitutive equations. Secondly, the effect of distributed loads associated with transverse stretching deformation, a factor typically overlooked in the existing quasi-3D theory-based beam models, is involved. In the development of beam finite element model, the mixed variational principle is firstly utilized to formulate the model of a quasi-3D theory-based beam element, where generalized displacements and internal forces are treated as two types of independent field quantities. Two numerical examples are conducted to investigate the validity and accuracy of the proposed theory and beam element. Numerical results indicate that the proposed mixed beam element can accurately predict the stress distributions over the cross-section and produce accurate displacement solutions. Meanwhile, it is noted that the effect of distributed loads related to the transverse stretching deformation should be correctly considered in the analysis of functionally graded beams based on quasi-3D theory.

Nonlinear vibration of sandwich beams made of FGM faces and FGP core under multiple moving loads using a quasi-3D theory

This study aims to investigate nonlinear dynamic behavior of sandwich beams constituted by functionally graded material (FGM) faces and functionally graded porous (FGP) core under the action of multiple moving loads. The energy equations based on a quasi-3D beam theory considering several functions of shear deformation were established for producing the nonlinear equations of motion used for describing dynamic responses of beams with various boundary conditions. By using the hybrid processes of the Newton-Raphson iteration procedure, the time-integration approach of Newmark-β, and the Gram-Schmidt-Ritz method, the new results of nonlinear analysis were explored and proposed. Several prime parameters such as the porous coefficient, sandwich thickness ratio, power law index and others that significantly affect the dynamic response of the beams were taken into investigations. It can be concluded that beams under one moving load have larger dynamic deflections compared to that under many moving loads. This is because the distance between the moving loads can produce a bending moment against the beam deformation.

Shape sensing of the thin-walled beam members by coupling an inverse finite element method with a refined quasi-3D zigzag beam theory

In structural safety field, the inverse finite element method (iFEM) is an effective methodology to reconstruct full-field displacement on beam, plate and shell structures, independently of the loading conditions and of the material properties. However, the current iFEM in principle requires uniform shear distribution over the thickness of beam, which is practically hardly possible due to these thin-walled beam with the general cross-section shape, such as I-section beam, hat-section beam and box-section beam, and there is no effective method to realize deformation online monitoring at home and abroad. To relieve this issue, a novel iFEM strategy is proposed to establish the shape sensing model of the thin-walled beam, where the thin-walled beam is replaced with an equivalent layered composite one based on a generalized layered global-local beam (GLGB) theory, and the improved quasi-3D zigzag shear deformation theory is presented to describe deformation field of the equivalent layered composite beam. The proposed iFEM method accounts for not only thickness stretching but also interlaminar continuity of shear stresses and displacements. Besides, the proposed iFEM formulation does not need any shear correction factors. Accuracy and effectiveness of the established shape sensing model are demonstrated through several case studies. The numerical results show that the proposed iFEM can accurately reconstruct the deformation of the thin-walled structure and the reconstruction accuracy can be improved by 5 %.

Quasi-3D flexural analysis of laminated composite plates resting on elastic foundations using higher-order displacement model

This work examines the impact of transverse strains on the static, vibration, and buckling analysis of laminated composite plates that are symmetric and anti-symmetric and rest on elastic foundations. This laminated plate theory, which is called a quasi-3D plate theory since it considers the effects of both transverse shear and normal strains, is provided here. The significance of nonclassical influences on plate deformation, such as shear deformation and thickness stretching, is sufficiently highlighted by the current theory. The theory demonstrates realistic transverse shear stress distributions across the laminated plate's thickness and complies with the traction-free boundary conditions at the upper and bottom surfaces of the plate. Hamilton's principle provides the current theory's equations of motion. For simply supported edges, the laminated plates supported by elastic foundations are investigated. For the aim of verification, the numerical results of the displacements, stresses, frequencies, and buckling load derived using the present theory are, if possible, compared with established literature. The current results and those derived from the other hypotheses found in the literature show a good degree of consistency. Additionally, the distributions of the interlaminar stresses in thickness direction of laminated composite plates sitting on elastic foundations are demonstrated.

A New Higher-Order Finite Element Model for Free Vibration and Buckling of Functionally Graded Sandwich Beams with Porous Core Resting on a Two-Parameter Elastic Foundation Using Quasi-3D Theory

A New Higher-Order Finite Element Model for Free Vibration and Buckling of Functionally Graded Sandwich Beams with Porous Core Resting on a Two-Parameter Elastic Foundation Using Quasi-3D Theory

Nonlocal quasi-3d vibration/ analysis of three-layer nanoplate surrounded by Orthotropic Visco-Pasternak foundation by considering surface effects and neutral surface concept

The present article deals with the application of refined plate theory and surface effects to investigate the nonlocal free vibration behavior of a functionally graded nano-plate composed of two piezoelectric face sheets resting on Orthotropic Visco-Pasternak. Surface and nonlocal effects are applied using the surface piezoelectricity and stress-strain gradient theories. Surface effects, refined quasi-3D higher-order theory, neutral surface position and in-plane mechanical preloads are considered to study piezoelectric sandwich nano-plate with a functionally graded core in this study for the first time, simultaneously. The size-dependent governing equations are derived based on 2D and 3D refined theory using Hamilton’s principle and different boundary conditions are studied and investigated according to the semi-analytical solution method. Comparing the results of the vibration behavior of 2D and quasi-3D models, local and non-local models, and also, examining different foundations simultaneously can be said as one of the innovations of the current research. Finally, a parametric study is presented to examine the effects of different parameters such as surface effects, small scale parameters, mechanical preloads, thickness stretching effects, neutral surface position, non-homogeneous coefficient, applied voltage, different foundation constants, boundary conditions, geometrical ratios and different theories in details. It is indicated that the inclusion of surface effects and thickness stretching effects leads to a significant influence on the vibration behavior of three-layered nano-scale plates. The presented results in this article may provide useful guidance for the design and development of the next generation of nano-devices.

A Quasi-3D theory for bending, vibration and buckling analysis of FG-CNTRC and GPLRC curved beams

This paper proposes a finite element model based on Quasi-3D theory, which includes both normal and shear effects, to study the bending, vibration, and buckling responses of FG-CNTRC and GPLRC curved beams. A two-node beam element satisfying C1 continuity requirement is utilized to compute displacements, critical buckling loads, and natural frequencies for beams with various boundary conditions. To evaluate the precision of the suggested model, various numerical examples are conducted. Next, a comprehensive parameter study is carried out to study the effects of distribution patterns and fractional volume of reinforced materials, open angles, aspect ratios, and boundary conditions. Numerous numerical results can serve as benchmarks for subsequent investigations.

Comprehensive analysis of bio-inspired laminated composites plates using a quasi-3D theory and higher order FE models

A comprehensive study is carried out by employing various finite element models (FEMs) for the bending, buckling stability and free vibration analyses of bio-inspired helicoidal composite plates with various lamination schemes. A higher order quasi-3D kinematic plate theory is developed to include a shear deformation effect. The variational formulation of the problem is exploited to derive the equations of motion, element stiffness, geometrical stiffness, and mass matrices based on a non-conforming rectangular element. Three different finite elements models are derived based on non-conforming elements with different number of nodes and degree of freedom. The developed finite element model has been validated with those found in the open literature. The effects of boundary condition, lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. Notably, for the lamination schemes investigated in this study, no shear locking phenomenon was observed in the analyses conducted using these FEMs. Dimensionless centre deflections, critical buckling loads and fundamental frequencies of bio-inspired helicoidal composite plates vary depending on the type of lamination scheme, boundary condition and aspect ratio. The new orientation schemes can replace the traditional ones to overcome the shear singularity and overcome the delamination defects.

Effects of porosity and nonlocality on the low- and high-frequency vibration characteristics of Al/Si3N4 functionally graded nanoplates using quasi-3D theory

Effects of porosity and nonlocality on the low- and high-frequency vibration characteristics of Al/Si3N4 functionally graded nanoplates using quasi-3D theory

High frequency analysis of the functionally graded sandwich nanobeams embedded in elastic foundations using nonlocal quasi-3D theory

This study focuses on the high frequency analysis of the functionally graded sandwich nanobeams resting on elastic foundations for the first time. In the current work, two types of sandwich structures, namely hard-core and soft-core sandwich beams, are considered. The elastic foundations are modeled using a two-parameter foundation model with a spring layer and a shear layer. For the size-dependent effects, the nonlocal elasticity theory is employed in conjunction with a quasi-3D theory. Hamilton's principle is applied to establish the governing equations of the motion of the nanobeams. A comprehensive parametric study is provided to demonstrate the free vibration behaviors of the sandwich nanobeams in both low and high frequency modes, with more focus on the high frequency analysis. Therefore, the present results contribute to a deeper understanding of the dynamic response of the functionally graded sandwich nanobeams in the high frequency range.