Higher-order Shear Deformation Research Articles

Thermoelastic analysis of FG-CNTRC cylindrical shells with various boundary conditions and temperature-dependent characteristics using quasi-3D higher-order shear deformation theory

Abstract. This study focuses on performing static analysis of FG-CNTRC cylinder shells with various boundary restrictions, including thermomechanical responses. The governing equations are developed by taking into account the temperature-dependent material features, the quasi-3D high-order shear deformation hypothesis, and the normal transverse stress effect. The temperature gradient inside the thickness is expected to fluctuate, and the distribution pattern is derived by using the heat transfer equation and considering the temperature boundary limitations. A singular trigonometric series and the Laplace transform are used in an analytics solution to address basic equations. This study primarily examines the stress levels at the border region. The findings indicate that it is crucial to take into account the abrupt rise in stress at the boundary area, particularly when the shell’s relative length is small. The reciprocal impact of pressure and temperature load is also emphasized. Significant findings indicate that thermal load may either augment or diminish stress levels, contingent upon the orientation of the pressure and thermal load effect. The results of the study of this issue serve as the foundation for the calculation and design of relevant structures in practical applications. Furthermore, this serves as a foundation for the creation of more intricate issues in the forthcoming.

Free Vibration analysis of C/SiC blisk based on modified global mode method

The bladed disk is the core component which is under load in aero-engine, rocket engine and gas turbine. In recent years, the bladed disk has developed towards the direction of integrated bladed disk (blisk) and being applied with ceramic matrix composites. However, there is no accurate semi-analytical dynamic model to describe the dynamic characteristic of ceramic matrix composite blisk. In this paper, a new semi-analytical method, modified global mode method (MGMM) is proposed to model the 2D C/SiC laminated blisk. In proposed method, Chebyshev polynomials series are used to expand the displacements of the blades and disk, constraints between blades and disk is strictly satisfied by multi-modal transformation and integrated into governing equation, and high-order shear deformation theory is combined to establish the dynamic model of the blisk of 2D C/SiC laminated composite material. The proposed method avoids the matrix singular problem appearing in traditional global mode method when modeling of combined structure and makes the system perform dynamic analysis and mode prediction without mode extraction and reconstruction. Then, amplitude frequency response and modal experiment are carried out to verify the correctness and convergence of the proposed method. Finally, under the framework of proposed method, the effects of material parameters and geometric parameters on the modal characteristics of the blisk are analyzed. The results show that compared with the geometric parameters, the material parameters have less influence on the modal characteristics of blisk, additionally, a series of modal steering is observed. The work in this paper can provide theoretical guidance for the dynamic design of composite blisk.

An analytical modelling of free vibration in porous FG-CNTRC plate resting on elastic foundations

This paper presents an analytical investigation of the vibrations of porous functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate resting on elastic foundations. The plates are reinforced with randomly oriented straight carbon nanotubes, featuring four distinct reinforcement distribution patterns along the thickness. Material properties of the porous FG-CNTRC are graded along the thickness, with both symmetric and asymmetric porosity distributions considered. Utilizing high-order shear deformation theory (HSDT), the equations of motion are derived from Hamilton’s energy principle, and Navier’s method is employed for the solutions. The simply supported plate is assumed to rest on Winkler/Pasternak elastic foundations. The study examines the effects of various parameters, including CNT volume fractions, CNT distribution patterns, thickness ratio (a/h), aspect ratio (a/b), porosity coefficient, and elastic foundation parameters, on the dimensionless frequency parameter.

Nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells: Theoretical and experimental investigations

In this study, the nonlinear vibration behaviours of foam-filled honeycomb sandwich cylindrical shells (FHSCSs) are investigated theoretically and experimentally. Initially, a time-domain minimum residual (TDMR) method is first adopted for the analysis of nonlinear free and forced vibrations of the FHSCSs, which is based on a dynamical model developed, with the effective material parameters of the foam-filled honeycomb core being obtained by employing the Gibson method and the Hamilton equivalence technique. Based on the high-order shear deformation shell principle and von Karman's theory, the nonlinear natural frequencies and resonant responses are solved using the Broyden iterative approach and TDMR method. Furthermore, several literature results are utilized for the rough verification of such a method. Meanwhile, the FHSCS specimens are made manually and comprehensive tests with various base excitation energies are undertaken to provide a thorough validation of the current method. It can be found that the largest calculation errors of natural frequencies and resonant responses are 4.9 and 12.3%, respectively. Finally, the influences of the core form and base excitation amplitudes on the nonlinear vibration behaviours of the FHSCSs are examined. It can be noticed that the foam-filled FHSCS structure exhibits a more excellent anti-vibration capability compared to the non-foam-filled structure. The solving method, fabrication technique, and valuable findings in the current study highlight the path for the design and implementation of such advanced shells.

An enhanced quasi-3D HSDT for free vibration analysis of porous FG-CNT beams on a new concept of orthotropic VE-foundations

The original primary objective of this study is to conduct a comprehensive investigation into the free vibration behavior of beams with porosity, reinforced by carbon nanotubes (CNTs). These beams are supported by an arbitrary orthotropic variable elastic foundation (AOVEF). The focus lies on understanding how the presence of porosity and CNT reinforcement, coupled with the complex support provided by the AOVEF, influences the vibration characteristics of the beams. In addition, we intend to examine the impact of a number of micromechanical models on the vibration properties of these beams. Four carbon nanotube variables are introduced to symbolize several CNT variations. CNTs’ mechanical properties are examined through a variety of micromechanical models. Shear deformation effects are considered into account in the framework of higher-order shear deformation (HSDT) beam theory. The equations of motion are constructed using Hamilton’s concept and the equation system for the FG-CNT beam with supported ends is solved via the Navier methodology. A new approach in elastic foundation modeling is the Arbitrarily Orthotropic Variable Elastic (AOP-VE) foundation. It builds on the Winkler layer concept but introduces the idea of a variable response along the length of the beam foundation. Unlike the Winkler-Pasternak model, AOP-VE allows for control over the directional properties of the Pasternak foundation. The study looks into multiple aspects, involving various distribution kinds of CNTs, the impact of Winkler and Pasternak factors, mode values, side-to-length ratio, porosity, and angle variation. The results indicate that these parameters have a major effect on the inherent vibration features of FG-CNT beams. The study results in various novel findings that improve the understanding of the subject topic and set a standard for future studies.

Linear finite element formulation for free vibration and buckling analyses of multi-directional FGP doubly curved shallow shells in thermal environment

ABSTRACT This paper presents the free vibration and buckling analyses of multi-directional functionally graded porous doubly curved shallow shells resting on Pasternak elastic foundations in a thermal environment. For the first time, a linear finite element formulation using the refined high-order shear deformation theory, combined with the Hermitian function, is developed to compute the vibration and buckling behaviour of doubly curved shallow shells. Mechanical properties of MFGP material change according to the length, width and thickness directions and the porosity distribution including even and uneven. The doubly curved shallow shell is operated in uniform, linear and non-linear temperature environments. The convergence and accuracy of the proposed method are verified by comparing numerical results with published works. In addition, a comprehensive numerical investigation was carried out to evaluate the influence of parameters on the natural frequency and critical buckling behaviour of MFGP doubly curved shallow shells.

A nonlocal higher-order shear deformation approach for nonline ar static analysis of magneto-electro-elastic sandwich Micro/Nano-plates with FG-CNT core in hygrothermal environment

In this study, the nonlocal static analysis of Magneto-Electro-Elastic (MEE) sandwich micro/nano-plates with Functionally Graded Carbon Nanotubes (FG-CNTs) core in a hygrothermal environment is studied. The nonlocal static formulation is developed based on Reddy's High-order Shear Deformation theory (HSDT). The von Kármán nonlinear strains are used and the governing equations of the HSDT are derived accounting for Eringen's nonlocal stress-gradient model. The governing equations are solved using the Galerkin method, which involves expanding the displacement field based on orthogonal functions. The variation of the volume fractions through the thickness of FG-CNTs core layer has been computed using two different homogenization techniques: the rule of mixtures and the Mori–Tanaka scheme. A detailed parametric study to show the characteristics of the FG-CNTs core, nonlocal parameters, thermal and moisture changes, types of CNT reinforcement and volume fraction, electric and magnetic potentials, and geometric parameters. The results are compared with the first-order shear deformation theory (FSDT) and classical plate theory to show the accuracy of nonlocal High-order Shear Deformation theory(NHSDT) formulation.

Behavior of functionally graded carbon nanotube reinforced composite sandwich beams with pultruded GFRP core under bending effect

A novel generation of composite sandwich beams with laminated carbon fiber-reinforced polymer skins and pultruded glass fiber-reinforced polymer core materials was examined for their flexural behavior. The strength and failure mechanisms of the composite sandwich beams in flatwise and edgewise configurations were investigated using three-point static bending tests. These sophisticated composite structures must be designed and used in a variety of sectors, and our research provides vital insights into their performance and failure patterns. In comparison to the reference specimens (FGM-1), the carbon nanotube-reinforced specimens’ bending capacity was affected and ranged from −2.5% to 7.75%. The amount of the carbon nanotube addition had a substantial impact on the beams’ application level and load-carrying capacity. Particularly, the application of 0.5 wt% additive in the outermost fiber region of the beams, such as in FGM-4, led to an increase in the bending capacity. However, the stiffness values at the maximum load were decreased by 0.3%–18.6% compared to FGM-1, with the minimum level of the decrease in FGM-4. The experimental results were compared with the theoretical calculations based on the high-order shear deformation theory, which yielded an approximation between 11.99% and 12.98% by applying the Navier’s solution.

Forced vibration of a three-layer cylindrical shell with an auxetic core containing fluid under the influence of shock load using high-order shear deformation theories

Forced vibration of a three-layer cylindrical shell with an auxetic core containing fluid under the influence of shock load using high-order shear deformation theories

Bending and free vibration analysis of FG circular plates using a five unknown high order shear deformation theory

In this study, the bending and free vibrations of functionally graded material (FGM) circular plates are investigated using a new quadrilateral finite element based on a five-unknown high-order shear deformation theory. The proposed model accounts for a quadratic distribution of the transverse shear stress through the plate thickness and zero transverse shear stress at the top and bottom surfaces of the plate. The properties of the plate are changed through its thickness according to a power law in which the index varies from 0 value for a fully ceramic plate to infinity for a fully metallic plate. The concept of the physical neutral plane is introduced to avoid membrane-bending coupling. The total potential energy principle and the kinetic energy are used to derive the elementary rigidity and mass matrices. The performance and the convergence of the developed element are demonstrated through examples from the literature. Furthermore, the effect of various parameters, such as the power law index and the radius-to-thickness ratio, on the plate behavior is also considered.

Flutter and divergence zones of perovskite solar cell-based panels of aircraft wings in subsonic airflow

Solar-powered aircraft have advantages such as quite long flight time and resource conservation. In recent years, with the improvements in solar cell efficiency, lightweight structural design, microelectronics, and automation control technology, more and more countries and organizations have conducted research on solar-powered aircraft. Solar cells are an important component of solar-powered aircraft systems. Perovskite solar cells have the advantages of high flexibility, lightweight, and high specific power, making them the ideal material for solar-powered aircraft wings. To receive as much sunlight radiation as possible and improve the lift-to-drag ratio of the entire aircraft, solar-powered aircraft have a high aspect ratio, making them more sensitive to changes in airflow. Therefore, the stability zones and vibration of perovskite solar cell (PSC) panels in subsonic airflow were studied for the first time. Additionally, to enhance the novelty of the paper and present more comprehensive results, the effect of the nanomaterial properties of one-layered perovskite solar cell substrates reinforced by carbon nanotubes and graphene platelets on the flutter and divergence phenomenon was investigated. To accurately simulate the displacement field after the composite perovskite panel is bent, Reddy's high-order shear deformation theory was adopted. The PSC panel's aerodynamic-elastic coupling motion equations were established by combining Hamilton's principle with the linear potential flow theory and the Bernoulli equation. The dynamic equations were discretized using a meshless numerical method to obtain the generalized multi-parameter characteristic equations. The obtained natural frequencies and critical divergence speeds were compared with published literature to validate the correctness of the aerodynamic model and laminated board model. The divergence instability and flutter instability of the PSC nanocomposite panel were investigated for changing the thickness, nano-fillers, porosity, laying angle, and aspect ratio of the substrate. We showed, that the PSC panel has a divergence instability state first, and then flutter instability appears. Additionally, the substrate nanomaterial parameters of the PSC panel significantly affect shifting divergence and flutter zones. Interestingly, the corresponding natural frequency increases when flutter occurs with an increase in the porosity volume.

Vibrational Analysis of Magneto-viscoelastic Bi-directional Functionally Graded Beams Subjected to Complex Environments Based on a Novel High-Order Shear Deformation Theory

Vibrational Analysis of Magneto-viscoelastic Bi-directional Functionally Graded Beams Subjected to Complex Environments Based on a Novel High-Order Shear Deformation Theory

Dynamic analysis of GPLs reinforced microcapsules subjected to moving micro/nanoparticles using mathematical modeling and deep-neural networks

In the realm of engineering, the use of cylindrical microcapsules containing moving micro/nanoparticles is crucial. Therefore, biomechanical engineers must focus on increasing its stability so that it may be used in a variety of scenarios. Thus far, graphene nanoplatelets, or GPLs, have shown their efficacy as an epoxy reinforcement in enhancing the material's characteristics in comparison to plain epoxy. This indicates that GPL-reinforced epoxy has the potential for use as the fiber composite's matrix phase. Thus, bending data of the thick cylindrical microcapsule with GPL reinforcement under a moving load is reported in this study. A modified couple stress theory or MCST with a single length scale parameter is proposed for simulating the micro-size structure. The high-order shear deformation theory are used to represent the displacement fields while taking the shear-strain function into account. The space-dependent equations are solved using the Laplace transform approach and the double Fourier series, respectively, using forced vibration analysis. The results are compared and validated with another published study in the literature after the modeling and solution of the governing equations of the GPLs reinforced microcapsules exposed to moving micro/nano particles. With the help of the findings from the mathematical modeling section, deep neural networks (DNN) with output, input, and hidden layers are used to mimic the existing microcapsule in order to provide further verification and introduce machine learning methodologies for addressing engineering challenges. A cylindrical microcapsule under motion under a micro/nanoparticle may be modeled in the area of biomechanical engineering using the current outputs obtained from mathematical modeling and DNN sections.

HSDT mesh-free method for free vibration analysis of sandwich structures

The current study presents a meshless collocation method based on radial basis functions (MC-RBF) to analyze the vibrational response associated with a sandwich circular cylindrical nanopipe in a supersonic airflow and conveying fluid flow. The quasi-2D hybrid type of nonlocal strain gradient theory (QHNSGT) as a higher order shear deformation theory (HSDT) has been presented to model the size-dependent nanopipe equations extracted using the energy method for a sandwich nanopipe. The sandwich nanostructure is made of metal, ceramic, and bi-directional functionally graded (Bi-FG) material, respectively, lower, topper, and middle surfaces. By taking into account that the fluid flow is infinite, incompressible, uniform flow, Newtonian, laminar, as well as viscous, and with the help of the Navier-Stokes equation, the fluid-structure interaction is obtained. Also, the displacement fields are defined via the Quasi-2D hybrid type of high-order shear deformation theory. The governing equations are discretized via the MC-RBF method to obtain the natural frequencies. The verification section shows that the results of the current research are very near to the results of the published article in the literature. By using COMSOL multi-physics software, the results are verified, and the outputs show that the velocity of fluid flow has a significant role in the vibrational responses of the current composite structure.

Damping contribution of viscoelastic core on airborne sound insulation performance of finite constrained layer damping panels at low and middle frequencies

The airborne sound insulation performance of finite sandwich panels is often significantly worsened by resonant transmission components in low and middle frequencies. In this paper, damping contribution of viscoelastic core on sound transmission loss (STL) of finite constrained layer damping (CLD) panels is studied in narrow frequency bands. A fully coupled layer-wise approach is used with a generalized high-order shear deformation hypothesis that accounts for all types of deformations in the core. The influence of several parameters is investigated extensively. Results show that the adverse impact of the first-three odd-odd order modes, namely (1,1), (3,1), and (1,3) modes, as well as some higher-order modes on STL cannot be disregarded. The constrained viscoelastic core plays a crucial role in enhancing, or even eliminating, dips of STL spectrum at resonant frequencies. Additionally, it can considerably counterbalance a relatively broadband reduction of STL caused by the inter-modal coupling in middle frequencies. The damping mechanism can be divided into two aspects: (i) the reduction of modal amplitude by vibration energy dissipation, and (ii) the change of bending modal shapes. CLD treatment is a concise and effective way to achieve stable sound insulation performance.

Buckling analysis of sandwich plates reinforced with various loading of multi-walled carbon nanotubes

The current investigation aims to examine the buckling behavior of sandwich structures reinforced with faces containing varying weight percentages (wt.%) of multi-walled carbon nanotubes (MWCNT), through the combined employment of experimental and numerical analysis techniques. In particular, the numerical analysis is executed through the implementation of the generalized differential quadrature method (GDQM). The study first determines the mechanical properties of the pure and reinforced samples via experimental tests. The buckling equations of the sandwich plate are then derived using the Frostig approach and a high-order shear deformation theory (SDT) for the flexible core. The continuity conditions between the faces and the core are considered to obtain the structural equations of the system, and Lagrange coefficients are introduced to enhance the accuracy of the governing equations. Subsequently, the study investigates the impact of various parameters, such as core thickness, aspect ratio, different boundary conditions (BC), and the addition of MWCNT nanoparticles on the critical buckling load of the system, utilizing the mechanical properties obtained for the composite faces. The present investigation reveals that the incorporation of MWCNT into the composite matrix brings about notable enhancements in the mechanical characteristics of sandwich structures. Specifically, the elastic modulus and ultimate strength of the faces are found to increase following the addition of MWCNT. Additionally, the critical buckling load of the sandwich plates is observed to rise with an increase in aspect ratio and length-to-thickness ratio, while a decrease in axial load yields similar results. The clamped boundary condition has higher critical buckling loads than the simply supported boundary condition. The addition of MWCNT nanoparticles decreases the dimensionless critical buckling force as the b/a ratio increases. Finally, the reported results of the current investigation present noteworthy findings about the advancement and improvement of sandwich composite structures to meet various application requirements.

A novel model for buckling of composite shell: Ring stiffened shell and stiffened shell with cutout under hydrostatic pressure

Focusing on buckling problem under hydrostatic pressure of ring stiffened shells and shells with stiffened cutout fabricated by filament winding process, a new form of equilibrium equations is given in this paper based on high-order shear deformation theory (HSDT). A novel theoretical model is proposed based on Messager's model of geometrical imperfection. The model contains both ring stiffened shell model (RSSM) and stiffened shell with cutout model (SSCM). In this model, changes in the shells' thickness z˜k(x,y),k=1,2,…,n are described using a Fourier series representation, which is included in HSDT stiffness matrix A, B, D, E, F, H. To evaluate the critical buckling pressure pcr, the model is applied and compared with the conventional stiffened cylindrical shell (SCS) model. The results demonstrate a significant reduction in error, ranging from 71.08% to 81.22%, when using the proposed model for shells stiffened by a ring stiffener in the middle, as compared to the SCS model. This highlights the enhanced accuracy provided by the proposed model. The results indicate that small stiffened cutouts in thin shells and large stiffened cutouts in moderately thick shells have relatively small influence on the critical buckling pressure. Conversely, the presence of a ring stiffener in the middle has a more pronounced effect.

Large deflection analysis of FGM/magneto-electro-elastic smart shells with porosities under multi-physics loading

This present research concerns the large deflection of smart functionally graded porous magneto-electro-elastic (FGP-MEE) composite shell structures. The accurate modeling method, based on the high-order shear deformation hypothesis, addresses scenarios involving multiple physics. The novelty of the current research lies in the introduction of a novel numerical approach that efficiently handles the non-linear behavior of MEE shells subjected to complex multi-physics loading conditions and considering FGM composite with porosities. New numerical results, physical insights and finding have been provided in the present manuscript taking into account influences of several physical factors, such as mechanical loads, external electric voltages, magnetic potentials, volume fraction index, porosity coefficient, various porosity distributions and various boundary conditions. The novel FGP-MEE model suggested in this study is highly useful for the accurate development and design of FG-MEE structures.

Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

This article studies the free vibration responses of functionally graded material (FGM) porous nanoplates exposed to thermal load. The developed mathematical model includes a shear deformation, size-scale, and microstructure influence by a high-order shear deformation (HSDT) and nonlocal strain gradient (NGST) theories. The study considers four different porosity patterns across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The equation of motion of the FGM porous nanoplate, including the effects of thermal load, is derived with Hamilton's principle, and then solved analytically by employing the Navier method. For the free vibration responses of the nanoplate, the effects of nonlocal and strain gradient elasticities, temperature rise, porosity volume fraction and its distribution are analyzed.

Free Vibration Analysis of a Porous 2D Functionally Graded Beam Using a High-Order Shear Deformation Theory

Free Vibration Analysis of a Porous 2D Functionally Graded Beam Using a High-Order Shear Deformation Theory