Hyperbolic Shear Deformation Theory Research Articles

Computer Simulation for Determination of Critical Buckling Temperatures of Sandwich Microplates with Cellular Core and CNT-RC Piezoelectric Patches via MSGT

This study introduces a computational simulation which leads to obtaining the critical buckling temperatures of a sandwich microplate which is modeled based on the modified strain gradient theory. This theory includes three material length scale parameters. The core of the microstructure is made from cellular materials which is treated with piezoelectric carbon nanotubes-reinforced composite patches. An advanced trigonometric hyperbolic shear deformation theory, eliminating the need for shear correction factors, is employed to analyze the microstructure. Thickness-dependent variations in structural characteristics are observed based on predefined functions. The equilibrium equations are derived using the virtual displacement principle. Fourier series functions provide an analytical way of solving these equations. The findings are verified by comparison with earlier research that was published and used fewer complex combinations. The study looks at how several important factors affect the structure’s reaction to thermal buckling.

On the isogeometric analysis of vibration and buckling of bioinspired composite plates using inverse hyperbolic shear deformation theory

Inspired by the remarkable energy absorption and damage tolerance capabilities observed in mantis shrimp crustaceans, this study delves into the intricate realm of biological composites with helicoidal structures. However, the effect of the relative orientation of fibers within the helicoidal structure matrix on the buckling and vibration characteristics still warrants comprehensive investigation for the better design of the bioinspired structures. For the first time, a Non-Uniform Rational B-Splines (NURBS)-based isogeometric analysis (IGA) framework termed NURBio is proposed to investigate the vibration and buckling characteristics of bioinspired laminated composite structures. The framework employs NURBS basis functions for exact complex geometric representation and field approximation and offers superior computational accuracy and efficiency as compared to conventional finite element method (FEM). The present analysis is underpinned by an inverse hyperbolic shear deformation theory (IHSDT) capable of accurately capturing the interlaminar stress distribution. This research investigates the performance of various bioinspired layup configurations encompassing recursive, exponential, semicircular, and Fibonacci helicoidal designs and compares them with those of unidirectional, and cross-ply laminates. A series of numerical examples on the buckling and vibration response of bioinspired composite plates are presented to demonstrate the versatility and efficacy of the proposed isogeometric framework. The influence of different layups, loading and boundary conditions, and geometric properties on the response of different bioinspired plate structures are meticulously examined. The study offers valuable insights into the design and optimization of high-performance bioinspired structures.

Effect of Micromechanical Models on Mechanical Behavior of Functionally Graded Plates Based on a Quasi-3D Hyperbolic Shear Deformation Theory

Five alternative micromechanical models (Voigt, Reuss, Tamura, LRVE, Hashin) are used to predict the valid material properties of a simply-supported functionally graded materials (FGM) plate. The free vibration and static behavior are studied based on a quasi-3D hyperbolic shear deformation theory considering the stretching effect. The profile of an FGM plate is assumed by the power-law, Sigmoid and exponential functions. The numerical results of an FGM plate behavior reveal via Navier-type solution. The temperature effects of the micromechanical models on the fundamental frequency and transverse displacement for an FGM plate are also discussed. By analyzing the influence of different micro-models on the mechanical behavior of an FGM plate, researchers can objectively understand the establishment and differences of structural micromechanical models. And considering the actual high temperature situation, the deformation prediction ability of the structure is predicted. This study provides theoretical guidance for the analysis and modeling of FGM structures for the purpose of engineering practice.

On nonlinear dynamic analysis of hyperbolic tangent FG-GPL-reinforced shallow spherical cap under supersonic flow

On nonlinear dynamic analysis of hyperbolic tangent FG-GPL-reinforced shallow spherical cap under supersonic flow

An Assessment of a New Hyperbolic Shear Deformation Theory for the Free Vibration Analysis of Cosine Functionally Graded Doubly Curved Shells under Various Boundary Conditions

An Assessment of a New Hyperbolic Shear Deformation Theory for the Free Vibration Analysis of Cosine Functionally Graded Doubly Curved Shells under Various Boundary Conditions

Three-dimensional flutter analysis of a novel circular sandwich plate employing hyperbolic shear deformation theory

Magnetorheological elastomers (MREs) Characterize a category of intelligent materials renowned for their distinct responsiveness to external magnetic fields, demonstrating swift alterations in their mechanical and rheological characteristics. The amalgamation of graphene platelets (GPLs) with MREs, termed GPL-reinforced MRE (GPL-MRE), heralds a novel material category imbued with the adaptive traits of MREs and the structural robustness inherent in GPLs. Such compositional innovation renders this material exceptionally suited for an array of applications across diverse structural frameworks. This research endeavors to scrutinize the flutter boundary of a smart circular sandwich plate featuring a core layer infused with GPL-MRE and variable stiffness composite laminated (VSCL) face layers within the context of supersonic airflow and resting upon a viscoelastic foundation. A novel hyperbolic shear deformation theory is invoked to delineate the displacement field of the sandwich plate. The mechanical properties of the mid-layer are delineated employing the Halpin-Tsai micromechanical methodology. The study probes the effect of supersonic airflow on the structure employing the first-order Piston theory (FPT) in polar coordinates. Hamilton's principle is utilized for deriving the equation of motion governing the structural dynamics in the Finite Element format. Paramount to this investigation is the exploration of assorted parameters and their impact on the flutter occurrence of the structure.

Frequency Analysis of Asymmetric Circular Organic Solar Cells Embedded in an Elastic Medium under Hygrothermal Conditions

This research represents the first theoretical investigation about the vibration behavior of circular organic solar cells. Therefore, the vibration response of asymmetric circular organic solar cells that represent a perfect renewable energy source is demonstrated. For this purpose, the differential quadrature method (DQM) is employed. The organic solar cell is modeled as a laminated plate consisting of five layers of Al, P3HT:PCBM, PEDOT:PSS, ITO, and Glass. This cell is rested on a Winkler–Pasternak elastic foundation and assumed to be exposed to various types of hygrothermal loadings. There are three different kinds of temperature and moisture variations that are taken into account: uniform, linear, and nonlinear distribution throughout the cell’s thickness. The displacement field is presented based on a new inverse hyperbolic shear deformation theory considering only two unknowns. The motion equations including hygrothermal effect and plate–foundation interaction are established within the framework of Hamilton’s principle. The DQM is utilized to solve these equations. In order to ensure the accuracy of the proposed theory, the present results are compared with those reported by other higher-order theories. A comprehensive parametric illustration is conducted on the impacts of different parameters involving the geometrical configuration, elastic foundation parameters, temperature, and moisture concentration on the deduced eigenfrequency of the circular organic solar cells.

A new higher-order shear deformation theory for flutter instability of a hybrid sandwich panel resting on a viscoelastic foundation

Magnetorheological elastomers (MREs) are smart materials characterized by their ability to adjust mechanical properties through the manipulation of applied magnetic fields, facilitating rapid and reversible tunability. The incorporation of reinforcing fibers introduces distinctive materials termed Magnetorheological Elastomer Composites (MRECs), combining tunability with enhanced rigidity. This study delves into the flutter analysis of a sandwich panel with a mid-layer composed of laminated MRECs and face sheets composed of functionally graded materials (FGMs) featuring porosity. The sandwich panel is situated on a viscoelastic foundation and exposed to a supersonic air current. Employing a higher-order (hyperbolic) shear deformation theory (HSDT), the displacement field of the sandwich plate is estimated. This selection eliminates the requirement for shear correction factors. The mechanical characteristics of the three sheets are determined using the Halpin-Tsai micromechanical method and the rule of mixture. The First-order Piston theory is employed to evaluate the effect of aerodynamic pressure and airflow damping on the sandwich panel. The derivation of the motion equation is achieved through Hamilton's principle. In order to solve the motion equation of the structure, the Finite Element Method (FEM) is utilized. The investigation systematically explores the influence of diverse parameters on the flutter boundary of the sandwich panel.

Analysis of vibro-acoustic characteristics of functionally graded sandwich microplates under thermal-electric effects

Based on the hyperbolic tangent parabola mixed shear deformation theory, the paper studied the sound radiation and the sound insulation of the functionally graded (FG) sandwich microplates under thermal-electric effects. The sandwich plate is composed of piezoelectric skin layers and FGM core layer. By using Hamilton’s principle, a size-dependent model considering the thermal-piezoelectric effects are established. The acoustic response and sound insulation are calculated with Rayleigh integral and solid-fluid coupling conditions. The accuracy of the presented method is verified by the numerical simulations. Then the effects of various parameters on the vibro-acoustic characteristics are analyzed and discussed. Numerical results show that the temperature variations, the length scale parameter to thickness ratio and the gradient index have great impacts on the FG sandwich microplates.

A hyperbolic theory for the analysis of laminated shallow shells with double curvature

In this paper, higher-order closed-form analytical solutions to the static bending and free vibration problems of laminated composite shells with double curvature are obtained using a hyperbolic shear deformation theory. The current theory is a modification of the shape function provided by Soldatos [30] in his well-known hyperbolic theory. The distributions of transverse shear stresses through the thickness of the shell are precisely predicted by the current theory satisfying traction free boundary conditions at the top and the bottom surfaces of the shell. Hamilton's principle serves as the foundation for the development of equations of motion. Navier's method is used for the analysis of simply-supported laminated shells under static and free vibration conditions. Displacements, stresses, and natural frequencies are presented for different shells with double curvature. The results from past investigations are compared to verify the accuracy and efficacy of the present hyperbolic shell theory.

Vibration and the Buckling Response of Functionally Graded Plates According to a Refined Hyperbolic Shear Deformation Theory

Vibration and the Buckling Response of Functionally Graded Plates According to a Refined Hyperbolic Shear Deformation Theory

Dynamic analysis of thick plates reinforced with agglomerated GNPs

In this work, the quasi-3D hyperbolic shear deformation theory (quasi-3D HSDT) is utilized to examine the dynamics of thick rectangular plates reinforced with rectangular nanofillers known as graphene nanoplatelets (GNPs). Agglomeration of the GNPs is incorporated and the mechanical characteristics like shear, elastic, and bulk moduli, Poisson's ratio, and density are analysed according to the mixture along with the Eshelby-Mori-Tanaka approach. Hamilton's principle is hired to derive the solving equations, the Navier approach is hired to present an analytical solution in the spatial domain, and the Newmark method is hired to provide an approximate solution in the time domain. The relevance of the dynamic response and the natural frequencies of the plate on several parameters are explored such as dispersion pattern and the GNPs percentage and agglomeration parameters. It is discovered that for a specific GNPs percentage, growth in the amount of agglomerated GNPs leads to lower natural frequencies and higher dynamic deflection. Meanwhile, for a specific mass fraction of the agglomerated GNPs, growth in the volume of clusters brings about higher natural frequencies and lower dynamic deflection.

Transient dynamic, energy absorption and out-phase/in-phase vibration response of coupled annular/circular SMA nanoplates assuming surface effects on frictional substrates

Shape and size are two important factors that affect the mechanical properties of nanostructures. Therefore, various forms of nano-scaled structures such as annular and circular ones have been applied in the engineering fields. Shape Memory Alloy (SMA), which can be used as the actuator because of its ability to change shapes, has potential applications in nano-electro mechanical system (NEMS). Dynamic behavior and the ability to absorb energy are two critical characteristics of advanced structures that are under static or various forms of dynamic loadings to be specific, this research numerically examined the in-phase/out-phase vibration, transient dynamic behavior under impulse load, and energy absorption in SMA annular/circular nanoplates with ferroelastic and pseudoelastic effects coupled together via damper and spring, placed between two frictional layers. In addition, an assumption of the Kuhn–Tucker phase transformation conditions was made. Moreover, the governing equations were derived based on Hyperbolic Higher Order Shear Deformation Theory (HHSDT) and solved using Differential Cubature Method (DCM). The constitutive equation of SMA proposed by Brinson was employed to model the pseudo-elastic behavior of SMA. Besides, Gurtin-Murdoch and modified couple stress theories were employed to calculate surface and micro-scale effects. As revealed by numerical achievements, under out-phase vibration mode, by increasing the surface effect coefficient to 0.4 when the annular nanoplate inner to outer radius ratio was 0.35, the natural frequency enhanced about 174%. As the material length scale parameter to thickness ratio was increased to 0.3 and the surface effects were considered, the energy absorption capacity was enhanced by nearly 28% and 23%, respectively.

Free vibration analysis of the structural integrity on the porous functionally graded plates using a novel Quasi-3D hyperbolic high order shear deformation theory

In this study, a novel quasi-three dimensional hyperbolic high-order shear deformation theory (quasi-3D HHSDT) is developed for free vibration analysis of porous functionally graded plates (FGPs). There are six unknowns in the current displacement field, and no shear correction factor is required. The mechanical properties are varied continuously through the thickness of porous FG plates using a modified power law function while considering the effect of porosities on the plate’s structural integrity. Two distinct porosity distribution models are considered, including even and uneven porosity distributions. The Navier technique is employed to obtain the closed-form solutions of motion's equations. An exhaustive parametric study is presented to show the influence of the different parameters on the fundamental frequencies.

Mechanical behavior analysis of FG-CNT-reinforced polymer composite beams via a hyperbolic shear deformation theory

Mechanical behavior analysis of FG-CNT-reinforced polymer composite beams via a hyperbolic shear deformation theory

A New Shear Deformation Theory in Axiomatic Framework for Bending and Buckling Analysis of Cross-Ply and Angle-Ply Laminated Composite Plates

Abstract In this study, a new higher order hyperbolic shear deformation theory for mechanical analysis of cross-ply and angle-ply multilayered plates is developed. Analytical solution to the static and buckling responses of symmetric and anti-symmetric composite laminates is presented. The proposed theory considers secant hyperbolic function of thickness coordinate in the displacement field. Also the developed theory assumes non-linear distribution of displacements and ensures that the top and lower surfaces of the plates have zero shear stresses. The equilibrium equations are obtained by applying the principle of virtual work. The stiffness characteristics of cross-ply and angle-ply laminates are taken into account when solving these governing equations. The closed-form Navier solution satisfying the corresponding boundary conditions is derived for simply supported (SS) composite plates. The results for non-dimensional deflections, and stresses of composite laminates under the effect of sinusoidal and uniform distributed load are thus obtained. The uni-axial and bi-axial loading force are used to evaluate critical buckling loads. Furthermore, the impact of span thickness ratio, aspect ratios, fiber orientation, modulus ratio, etc. on static and buckling analysis plates is also studied. The validity of present formulation is demonstrated by comparing our results with some of the available results in the literature.

Eigen value analysis of composite hollow shafts using modified EMBT formulation considering the shear deformation along the thickness direction

Composite hollow shafts are used in power transmission applications due to their high specific stiffness and high specific strength. The dynamic characteristics of these shafts are important for transmission applications. Dynamic modelling of these shafts is generally carried out using Equivalent Modulus Beam Theory (EMBT) and Layerwise Beam Theory (LBT) formulations. The EMBT formulation is modified by considering stacking sequence, shear normal coupling, bending twisting coupling and bending stretching coupling. It is observed that modified EMBT formulation is underestimating the shafts stiffness at lower length/mean diameter (l/dm) ratios. In the present work, a new formulation is developed by adding shear deformation along the thickness direction to the existing modified EMBT formulation. The variation of shear deformation along the thickness direction is found using different shear deformation theories, i.e., first-order shear deformation theory (FSDBT), parabolic shear deformation theory (PSDBT), trigonometric shear deformation theory (TSDBT), and hyperbolic shear deformation theory (HSDBT). The analysis is performed at l/dm ratios of 5, 10, 15, 20, 25, 30, 35, and 40 for carbon/epoxy composites, E-glass/epoxy composites, and boron/epoxy composite shafts. The results show that new formulation has improved the bending natural frequency of the composite shafts for l/dm < 15 in comparison with modified EMBT. The effect of new formulation is more significant for the second and third bending modes of natural frequencies.

Bending and Free Vibration Analysis of Porous-Functionally-Graded (PFG) Beams Resting on Elastic Foundations

The bending and free vibration of porous functionally graded (PFG) beams resting on elastic foundations are analyzed. The material features of the PFG beam are assumed to vary continuously through the thickness according to the volume fraction of components. The foundation medium is also considered to be linear, homogeneous, and isotropic, and modeled using the Winkler-Pasternak law. The hyperbolic shear deformation theory is applied for the kinematic relations, and the equations of motion are obtained using the Hamilton’s principle. An analytical solution is presented accordingly, assuming that the PFG beam is simply supported. Comparisons with the open literature are implemented to verify the validity of such a formulation. The effects of the elastic foundations, porosity volume percentage and span-to-depth ratio are finally discussed in detail.

A Hyperbolic Shear Deformation Theory for Natural Frequencies Study of Functionally Graded Plates on Elastic Supports

This study presents a hyperbolic shear deformation theory for free vibration of functionally graded plates on elastic foundations. The field of displacements is chosen based on the assumptions that axial and transverse displacements consist of components due to bending and shear. The components of the axial shear displacements give rise to the parabolic variation in the shear strain through the thickness, such that the shear stresses vanish on the plate boundaries. Therefore, the shear correction factor is not necessary. The material properties of the functionally graded plate are assumed to vary through the thickness according to the power law of the volume fraction of the constituents. The elastic foundation is modeled as a Pasternak foundation. The equations of motion are derived using Hamilton’s principle. The analytical solutions were established from Navier’s approach, and the results obtained are found to be in good agreement with the solutions of three-dimensional elasticity and with the solutions of the various plate theories. The effects of the power law index, the thickness ratio, and the foundation parameters on the natural frequency of the plates were also evaluated.

Mathematical Analysis of Transverse Displacement of Laminated Beam with Thermal Load

Objectives: This research emphasis on developing solution of transverse displacement for simply supported beam subjected to thermal load using hyperbolic shear deformation theory (HYSDT). Moreover, the significant transverse displacement analysis of single, three-layer orthotropic symmetric laminated beams exposed to sinusoidal thermal loads was taken under consideration with the aim to achieve exact solution for the above condition. Methodology: In this solution, we have used hyperbolic function in reference to thickness co-ordinate by considering shear deformation theory. The governing equations, boundary conditions were developed using principle of virtual work and thus exhibiting solution by Navier’s theory. Findin g: It is observed that by considering single, triple layer transverse displacement for simply supported beam subjected to thermal loading as well as applying hyperbolic shear deformation theory (HYSDT) has predicted transverse displacement of 0.269, 0.210 and 0.562 for ply angles such as 00, 900, 00/900/00 respectively with aspect ratio 20. In accordance with this we observed uniformity among the predicted values. Novelty: In this research we have introduced an advance function such as hyperbolic shear deformation theories (HYSDT) and transverse displacement for variable lengths and thickness of the beam was calculated by using MATLAB coding. Thus, achieving precise solution. Keywords: Sinusoidal load; hyperbolic shear deformation theory; governing differential equations; MATLAB coding; thermal load