Cylindrical Microshells Research Articles

Size-dependent finite element buckling analysis of porous cylindrical micro-shells reinforced by graphene platelets

This study introduces a spatial shear deformable rectangular element formulation to investigate the size-dependent buckling behavior of porous graphene platelets (GPL) reinforced micro-shells within the framework of the modified couple stress theory (MCST) for the first time in the worldwide term. The rectangular element, characterized by 4 nodes with 19 degrees of freedom each and possessing weak continuity of order C 1 , incorporates a length scale parameter enabling size-dependent analyses of shells. The research considers three distinct functions for the distribution of porosity combined with three different patterns of the GPL distribution (called by patterns A to C) along the micro-shell thickness. The elastic modulus of the nanocomposite in the absence of porosity is obtained using the Halpin-Tsai micromechanics model. Subsequently, the study meticulously validates the modeling accuracy and then investigates variations in the critical buckling load with respect to porosity distribution functions, distribution patterns of GPL, porosity coefficient, weight percentage of GPL, geometric parameters of the cylinder, and the length-scale parameter. The results reveal that the combination of the GPL pattern A with the first symmetric type porosity distribution yields the highest critical buckling loads. On the contrary, if the pattern B is combined with the second symmetric type of porosity distribution, the lowest critical buckling load will be observed. Given the accuracy of the results obtained and the versatility of the finite element method (FEM) in handling complex geometries together with diverse boundary conditions, the developed element holds promise for analyzing shells of various shapes under different boundary conditions.

Vibration analysis of a smart viscoelastic porous sandwich micro-shell with magnetorheological fluid core using the modified couple stress theory

In the current study, for the first time, the size-dependent vibration of a functionally graded (FG) porous sandwich cylindrical microshell with magnetorheological fluid core is investigated using modified couple stress theory (MCST) and the first-order shear deformation theory (FSDT). The microshell is made of FG porous material and for investigating the material properties, two types of porous distributions are considered. Based on FSDT and the MCST, the governing equations are derived using Hamilton’s principle regarding the energy dissipation due to the shear deformation of the magnetorheological core layer and the interaction between all layers. Different assumptions, based on the continuity in transverse shear stresses and slope of in-plane displacements, are considered in the theoretical formulation. The natural frequency and loss factor of the microshell with sliding simply supported boundary conditions are determined using Navier’s solution method. Finally, the influence of some parameters such as material length scale(l/h: 0-1), types of porous distributions (symmetric-asymmetric), porosity volume fraction (e0: 0-1), magnetic field intensity (B: 0-800) and aspect ratio (L/R: 1-8, R/h: 10-100) on the vibration damping characteristics of microshell, is investigated and validity of the results is studied.

3D Size-Dependent Dynamic Instability Analysis of FG Cylindrical Microshells Subjected to Combinations of Periodic Axial Compression and External Pressure Using a Hermitian C2 Finite Layer Method Based on the Consistent Couple Stress Theory.

This work develops a three-dimensional (3D) weak formulation, based on the consistent couple stress theory (CCST), for analyzing the size-dependent dynamic instability behavior of simply-supported, functionally graded (FG) cylindrical microshells that are subjected to combinations of periodic axial compression and external pressure. In our formulation, the microshells are artificially divided into nl layers. The displacement components of each individual layer are selected as the primary variables, which are expanded as a double Fourier series in the in-plane domain and are interpolated with Hermitian C2 polynomials in the thickness direction. Incorporating the layer-wise displacement models into our weak formulation, we develop a Hermitian C2 finite layer method (FLM) for addressing the current issue. The accuracy and the convergence rate of our Hermitian C2 FLM are validated by comparing the solutions it produces with the accurate two-dimensional solutions of critical loads and critical pressures of FG cylindrical macroshells and single-walled carbon nanotubes, which were reported in the literature. The numerical results show the effects of the material length-scale parameter, the inhomogeneity index, the radius-to-thickness and length-to-radius ratios, the load magnitude ratio, and the static and dynamic load factors on the first principal and first secondary instability regions of parametric resonance of simply-supported FG cylindrical microshells are significant.

A Hermitian Cn finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

AbstractWithin the framework of the consistent couple stress theory (CCST), we develop a Hermitian Cn (n = 1, 2) finite cylindrical layer method (FCLM) for carrying out the three‐dimensional (3D) analysis of the size‐dependent buckling and free vibration behaviors of simply supported, functionally graded (FG) piezoelectric cylindrical sandwich microshells. The microshells of interest are placed under closed‐circuit surface conditions and subjected to axial compression and electric voltages. We derive a 3D weak formulation based on Hamilton's principle for this study. In the resulting formulation, the microshell is artificially divided into nl microlayers, with the elastic displacement components and the electric potential selected as the primary variables. By incorporating a layer‐wise kinematic model into our weak formulation, we develop a Hermitian Cn FCLM, which can be used for analyzing FG piezoelectric cylindrical sandwich microshells. Each primary variable is expanded as a double Fourier series in the in‐surface domain and is interpolated in the thickness direction using Hermitian Cn polynomials. The accuracy and the convergence rate of our Hermitian Cn FCLMs are validated by comparing the solutions they produce for FG piezoelectric cylindrical macroshells and FG elastic cylindrical microshells with the relevant exact and approximate 3D solutions which have been reported in the literature. The material length scale parameter of our FCLMs is set at zero in the comparison made with the FG piezoelectric macroshells. In contrast, the piezoelectric and flexoelectric effects are ignored in the comparison made with the FG elastic microshells. The impact of some essential factors on the critical load, critical voltage, and natural frequency of simply supported FG piezoelectric cylindrical sandwich microshells is assessed. The important factors are identified as piezoelectricity, flexoelectricity, the material length scale parameter, the inhomogeneity index, the radius‐to‐thickness ratio, the length‐to‐radius ratio, and the magnitude of the applied voltage and the applied load.

Thermal buckling of piezoelectric graphene platelets reinforced cylindrical microshells using Navier’s and meshless methods

Thermal buckling analysis of a simply supported sandwich cylindrical microshell with piezoelectric layers reinforced with graphene platelets is presented in the current study. The motion equations of the piezoelectric microshell are derived in reference to the first-order shear deformation hypothesis alongside the modified couple stress theory. The critical buckling temperature difference of piezoelectric graphene platelets reinforced cylindrical microshells is derived from adopting Navier’s approach and the meshless method. The material properties of every layer for microcomposite shell layers reinforced by graphene platelets are estimated using Halpin–Tsai model. The comparison study is conducted to verify upcoming results. The goal is to investigate the effects of the applied voltage, the thickness of the piezoelectric layers, the distribution pattern, the weight fraction, the material length scale parameter, the length to radius ratio, and the thickness to radius ratio on the buckling of piezoelectric graphene platelets cylindrical microshell.

Analyzing the buckling of FGCNT-reinforced sandwich microshells in heart pacemakers: The impact of thickness stretching on third-order shear deformation

This study focuses on the buckling behavior of composite microshells inside pacemakers to select the most durable material. Due to the strong electromagnetic forces encountered by pacemaker microshells, comprehensive research is needed to identify suitable materials. This study analyzes the buckling behavior of a porous sandwich cylindrical microshell attached to electrodes, which is supported by an elastic foundation and reinforced with functionally graded carbon nanotubes. Three porosity models are considered for the core material, and the equilibrium equations are derived using Hamilton’s principle based on third order shear deformation theory. This study compares the critical buckling loads with those from the literature and examines the effects of various parameters, such as thickness stretching and non-stretching. The findings indicate that the thickness stretching effect has a significant influence on the critical buckling load. In addition, a lower functionally graded power index and higher porosity volume fraction result in higher critical buckling loads. These results are relevant for micro-electromechanical systems and can aid in the selection of appropriate materials for pacemaker microshells to improve their durability and performance.

A Size-Dependent Finite Element Method for the 3D Free Vibration Analysis of Functionally Graded Graphene Platelets-Reinforced Composite Cylindrical Microshells Based on the Consistent Couple Stress Theory

Within a framework of the consistent couple stress theory (CCST), a size-dependent finite element method (FEM) is developed. The three-dimensional (3D) free vibration characteristics of simply-supported, functionally graded (FG) graphene platelets (GPLs)-reinforced composite (GPLRC) cylindrical microshells are analyzed. In the formulation, the microshells are artificially divided into numerous finite microlayers. Fourier functions and Hermitian C2 polynomials are used to interpolate the in-surface and out-of-surface variations in the displacement components induced in each microlayer. As a result, the second-order derivative continuity conditions for the displacement components at each nodal surface are satisfied. Five distribution patterns of GPLs varying in the thickness direction are considered, including uniform distribution (UD) and FG A-type, O-type, V-type, and X-type distributions. The accuracy and convergence of the CCST-based FEM are validated by comparing the solutions it produces with the exact and approximate 3D solutions for FG cylindrical macroshells reported in the literature, for which the material length scale parameter is set at zero. Numerical results show that by increasing the weight fraction of GPLs by 1%, the natural frequency of FG-GPLRC cylindrical microshells can be increased to more than twice that of the homogeneous cylindrical microshells. In addition, the effects of the material length scale parameter, the GPL distribution patterns, and the length-to-thickness ratio of GPLs on natural frequencies of the FG-GPLRC cylindrical microshells are significant.

Enhancing vibration problem of temperature-dependent functionally graded cylindrical microshells using magneto-electro-elastic micropatches

Enhancing vibration problem of temperature-dependent functionally graded cylindrical microshells using magneto-electro-elastic micropatches

Three-dimensional nonlinear stability analysis of axial-thermal-electrical loaded FG piezoelectric microshells via MKM strain gradient formulations

The present study focuses on the moving Kriging meshfree (MKM) technique combined with the three-dimensional strain gradient continuum mechanics to analyze three-dimensional nonlinear stability response of thermo-electro-mechanical loaded functionally graded (FG) piezoelectric cylindrical microshells. The derived three-dimensional MKM model has the capability to present the transition of buckling mode containing different microsize-dependent gradient tensors. The microshells are made of a mixture containing PZT-4 and PZT-5H piezoelectric phases, the material properties of which vary continuously along the shell thickness and captured based on the power law composition scheme. With the aid of MKM strain gradient-based shell model, it is possible to satisfy the function property associated with Kronecker delta by putting the required boundary conditions directly at the associated nodes without any predefined mesh. The microsize-dependent nonlinear stability plots are obtained in the presence of modal transition relevant to various environment temperatures, external electric voltages, microstructural size dependency tensors, and power-law indexes. It is found that the stiffening character related to all three microstructural strain gradient tensors is more significant for the second nonlinear stability mechanical/electrical load in comparison with the first one. However, for the three-dimensional mechanical/electrical bifurcation load, the stiffening character of these gradient tensors becomes even lower than the first postbuckling load. Moreover, by applying an actuation via a positive voltage, the first three-dimensional critical buckling load and the associated end shortening reduce, while an actuation via a negative voltage results in to increase them. It is observed that by shifting to the postbuckling territory, the role of the electric actuation gets negligible.

A size-dependent shear deformable computational framework for transient response of GNP-reinforced metal foam cylindrical shells subjected to localized impulsive loads

In this study, the transient responses of functionally graded graphene nanoplatelet reinforced porous cylindrical microshells subjected to time-dependent localized distributed impulsive loads are investigated for the first time. The impulsive loads act vertically on the outer surface of the shell. The shell comprises graphene-nanoplatelet (GNP)-reinforced metal foam. In the current work, the internal pores are uniformly distributed with the graphene nanoplatelets, according to a given distribution, either uniformly or non-uniformly dispersed in the thickness direction of the shell, resulting in graded material properties. The effective elastic modulus of the nanocomposite is evaluated using the modified Halpin–Tsai micromechanics model combined with the extended rule of mixtures. A closed-cellular metal foam model is implemented to determine the mechanical properties of the porous nanocomposite. A modified couple stress-based hyperbolic shear deformable model is developed and implemented to capture the microstructure dependency of the mechanical behavior. The Lagrange equations in conjunction with double trigonometric functions are applied to derive the equations of motions of the microshells with simply supported boundary conditions. Further, the time-dependent dynamic responses are computed via modal superposition and the Newmark direct integration scheme. In the parameter study, the dynamic deflections of the microshell produced by various types of localized loads are compared, with the effects of internal pores, GNP distribution patterns, and external load parameters examined. It is found the circular-type and square-type localized loads yield very similar dynamic deflections. When adding a higher content of GNPs into the matrix, dispersing more GNPs near the top and bottom surfaces of the shell can effectively strengthen the shell stiffness, thereby considerably reducing the peak values of dynamic deflection.

Free Vibration Analysis of Graphene Platelets Reinforced Laminated Piezoelectric Cylindrical Micro-shells Using the Chebyshev–Ritz Formulation

Free Vibration Analysis of Graphene Platelets Reinforced Laminated Piezoelectric Cylindrical Micro-shells Using the Chebyshev–Ritz Formulation

Strain-gradient theory for shear deformation free-form microshells: Governing equations of motion and general boundary conditions

A first-order shear deformation (FOSD) free-form microshell model described in general curvilinear coordinates was developed within the complete framework of Mindlin’s form II linear isotropic strain-gradient theory (SGT), considering both strain-gradient and micro-inertia effects. The high-order governing equations of motion and consistent boundary conditions were simultaneously obtained through a variational formulation based on Hamilton’s principle. The established microshell model contains five strain-gradient material constants and one length parameter resulting from micro-inertia effects in addition to two classical Lamé constants, thereby capturing microstructure-induced size-dependent phenomena in both static and dynamic analyses. The constructed model within the general SGT can be flexibly reduced to those based on the modified strain-gradient, modified couple stress, and simplified strain-gradient theories. Moreover, by enforcing geometric restrictions, the general formulation for free-form microshells can be specialized for doubly curved microshells. Finally, the forced vibration results of a simply supported closed cylindrical microshell confirmed the reliability and accuracy of the proposed model and strain-gradient and high-order inertia effects on the size-dependent dynamic characteristics of microshells. Altogether, the presented mathematical formulations can provide a foundation for the in-depth understanding of microscale shell structures.

Dynamic stability analysis of functionally graded three-dimensional graphene foam cylindrical microshells under interior pressure based on modified strain gradient theory

Dynamic stability analysis of functionally graded three-dimensional graphene foam cylindrical microshells under interior pressure based on modified strain gradient theory

Free vibration analysis of a cylindrical micro-shell based on MCST

Dynamic analysis of a functionally-graded (FG) cylindrical micro shell is investigated in this work. Effect of small parameter in micro scale is included in fundamental relations based on modified couple stress theory (MCST). For more precise analyzing the structure, third-order shear deformation theory (TSDT) is employed as kinematic relations. The shell is made from FG materials, using power function law. A solution procedure based on an analytical method is developed for special boundary condition. The numerical results are computed in graphical form to seek how changes of main parameters of the study such as micro parameter, in-homogeneity index and some geometric values change the free vibration responses. As an important output of this paper, it is concluded that an increase in micro parameter leads to increase of natural frequency. Furthermore, increase of in-homogeneous index yields more soft structure and then decrease of natural frequency.

Combined axial and lateral stability behavior of random checkerboard reinforced cylindrical microshells via a couple stress-based moving Kriging meshfree model

Combined axial and lateral stability behavior of random checkerboard reinforced cylindrical microshells via a couple stress-based moving Kriging meshfree model

A couple-stress-based moving Kriging meshfree shell model for axial postbuckling analysis of random checkerboard composite cylindrical microshells

The current investigation intends to devise a couple stress continuum-based moving Kriging meshfree shell model for axial nonlinear buckling and postbuckling responses of random checkerboard composite cylindrical microshells. Accordingly, the graphene nanoplatelet reinforcements are supposed to be randomly dispersed based upon a checkerboard scheme within the resin matrix, the effective material properties of which are estimated based upon a probabilistic method. The modified couple stress continuum elasticity is implemented into the higher-order shear deformation shell theory incorporating geometrical nonlinearity. The established microstructural-dependent shell model is then numerically analyzed via the moving Kriging meshfree technique with the ability to take the essential boundary conditions into account accurately by employing proper moving Kriging shape function. By tracing the postbuckling paths, the snap-through phenomenon is observed. It is found that for a higher graphene nanoplatelet volume fraction, the significance of the stiffening character associated with the rotation gradient tensor increases. Furthermore, for a specific value of graphene nanoplatelet volume fraction, by reducing the length to width aspect ratio of graphene nanoplatelet reinforcements, the role of couple stress size dependency in the critical buckling load and critical shortening of an axially compressed cylindrical microshell becomes more important.

Free vibration analysis of simply-supported graphene platelets reinforced laminated piezoelectric cylindrical micro-shells

In this study, the micro-scale vibration analysis of the graphene platelets reinforced cylindrical micro-shells with piezoelectric layers is discussed. By simultaneous use of Hamilton’s principle and size-dependent modified couple stress theory, the governing equations of motion and the boundary conditions are derived. The natural frequencies for graphene platelets reinforced cylindrical micro-shell with piezoelectric layers are determined by the Navier’s approach. Three different graphene platelets distribution pattern are modeled in this study. The material properties of every layer of micro composite shell reinforced by graphene platelets are evaluated by Halpin–Tsai model. The present findings are validated with the available data in the literature. In addition, a parametric study is conducted to demonstrate the effects of the weight fraction, the distribution pattern, the material length scale parameter, the thickness of the piezoelectric layers, the length to radius ratio, the thickness to radius ratio, temperature change and the applied voltage on the natural frequency of piezoelectric GPL cylindrical micro-shell.

Thermo-electro-mechanical vibration and buckling analysis of a functionally graded piezoelectric porous cylindrical microshell

Thermo-electro-mechanical vibration and buckling analysis of a functionally graded piezoelectric porous cylindrical microshell

Acoustic wave transmission of double-walled functionally graded cylindrical microshells under linear and nonlinear temperature distributions using modified strain gradient theory

In this study, using modified strain gradient theory (MSGT) and the first-order shear deformation assumption (FSDA) framework, wave propagation through air-filled double-walled functionally graded (FG) cylindrical microshells subjected to linear and non-linear thermal loadings are investigated. MSGT has the advantage of having up to three scale parameters and can successfully reproduce size effects. The power-law model is used to express the distribution of material characteristics over the thickness of each shell due to characteristics varying by temperature, and the application of Hamilton’s principle results in deducing vibroacoustic equations in coupled relations. The size-dependent coupled vibroacoustic governing equations are solved using an analytical approach in conjunction with a double Fourier series, with the final result providing the appropriate Sound Transmission Loss (STL) equation. The developed solution’s accuracy and precision are examined by comparing it to data available from previous studies. Parameter studies reveal the impacts of temperature distribution, functionally graded index, incident angles, acoustic cavity depth, and length scale parameter on STL through double-walled FG cylindrical microshells.

Microstructural Size Dependency in Nonlinear Lateral Stability of Random Reinforced Microshells via Meshfree-Based Applied Mathematical Modeling

The prime objective of this research work is to develop an efficient small scale-dependent computational framework incorporating microstructural tensors of dilatation gradient, rotation gradient, and deviatoric stretch gradient to analyze nonlinear lateral stability of cylindrical microshells. The numerical strategy is established based upon a mixed formation of the third-order shear deformable shell model and modified strain gradient continuum mechanics. The graphene nanoplatelet reinforcements are assumed to be randomly dispersed in a checkerboard scheme within the resin matrix. Accordingly, to extract the effective material properties, the Monte Carlo simulation together with a probabilistic technique are employed. The numerical solution for the microstructural-dependent nonlinear problem is carried out via the moving Kriging meshfree method having the capability to accommodate accurately the essential boundary conditions using proper moving Kriging shape function. It is represented that the role of the stiffening characters related to the effect of microstructural dilatation gradient, rotation gradient, and deviatoric stretch reduces continuously by going to deeper territory of the load-deflection stability path. Moreover, it is indicated that among various microstructural gradient tensors, the stiffening character of the rotation gradient is higher than deviatoric stretch gradient, and the stiffening character of the latter is more considerable than the dilatation gradient tensor.