Sinusoidal Shear Deformation Theory Research Articles

Temperature-dependent thermal buckling and free vibration behavior of smart sandwich nanoplates with auxetic core and magneto-electro-elastic face layers

AbstractThis article addresses the thermomechanical thermal buckling and free vibration response of a novel smart sandwich nanoplate based on a sinusoidal higher-order shear deformation theory (SHSDT) with a stretching effect. In the proposed sandwich nanoplate, an auxetic core layer with a negative Poisson’s ratio made of Ti-6Al-4V is sandwiched between Ti-6Al-4V rim layers and magneto-electro-elastic (MEE) face layers. The MEE face layers are homogenous volumetric mixtures of cobalt ferrite (CoFe2O4) and barium titanate (BaTiO3). The mechanical and thermal material properties of the auxetic core and MEE face layers are temperature-dependent. Using Hamilton’s principle, governing equations are constructed. To characterize the size-dependent behavior of the nanoplate, governing equations are adapted with the nonlocal strain gradient theory (NSGT). By applying the principles of Navier’s technique, closed-form solutions are obtained. Parametric simulations are carried out to examine the effects of auxetic core parameters, temperature-dependent material properties, nonlocal parameters, electric, magnetic, and thermal loads on the free vibration and thermal buckling behavior of the nanoplate. According to the simulation results, it is determined that the auxetic core parameters, temperature-dependent material properties, and nonlocal factors significantly affect the thermomechanical behavior of the nanoplate. The outcomes of this investigation are expected to contribute to the advancement of smart nano-electromechanical systems, transducers, and nanosensors characterized by lightweight, exceptional structural integrity and temperature sensitivity. Also, the auxetic core with a negative Poisson’s ratio provides a metamaterial feature, and thanks to this feature, the proposed model has the potential to be used as an invisibility technology in sonar and radar-hiding applications.

Nonlinear bending behavior of functionally graded porous beams based on sinusoidal shear deformation theory

Nonlinear bending behavior of functionally graded porous beams based on sinusoidal shear deformation theory

The effect of the foam structure and distribution on the thermomechanical vibration behavior of sandwich nanoplates with magneto-electro-elastic face layers

This study examined the thermal vibration of a foam core nanoplate composed of ceramic silicon nitride (Si3N4) and metal biomaterial (Ti-6Al-4V) in the core layer, and cobalt-ferrite (CoFe2O4) and barium-titanate (BaTiO3) in the face layers. The constitutive equation is influenced by various factors, including nonlocal elasticity, thermal expansion, strain gradient elasticity, magnetostrictive, and electroelastic properties, as well as sinusoidal higher-order shear deformation theory (SHSDT) with stretching effect. The study found that the thermomechanical vibration behavior of nanoplates was influenced by the ratio of open cell foam to solid, nonlocal factors, thermal load, electrical and magnetic potentials, and different foam distribution.

A semi-analytical sinusoidal shear deformation theory for nonlinear dynamic response and vibration of CNT–FGM doubly curved shallow shells

A semi-analytical sinusoidal shear deformation theory for nonlinear dynamic response and vibration of CNT–FGM doubly curved shallow shells

Deterministic and stochastic flexural behaviors of laminated composite thin-walled I-beams using a sinusoidal higher-order shear deformation theory

In this study, a novel sinusoidal higher-order shear deformation thin-walled beam theory is presented to examine the effects of material properties and external load uncertainty on static responses of laminated composite thin-walled beams with open sections. The solution for the deterministic flexural analysis is based on Hamilton’s principle and Ritz-type exponential shape function series. Several mechanical parameters of laminated composite materials are randomized and plugged into the beam solver to investigate the thin-walled beam’s stochastic flexural behaviors. The computational cost and accuracy of the polynomial chaos expansion (PCE) method with both projection and linear regression approaches are presented and evaluated by comparing its results with crude Monte Carlo simulation (MCS). This comparison allows for a thorough assessment of the PCE method’s performance. Additionally, a sensitivity analysis is conducted to compare the relative significance of the uncertainty in material properties and loads on the stochastic responses. The supervised training of the artificial neural network based on the MCS beam data is also conducted and compared to the PCE and MCS methods. The findings about the stochastic outputs are introduced in various statistical metrics and illustrations to demonstrate the influences of material properties’ randomness on different laminated composite thin-walled beam configurations.

Active damping of multiscale composite shells using Sinus theory incorporated with Murakami’s zig-zag function

This article is divided into two main sections, the focus of the first is to develop a finite element model using the in-house MATLAB codes, implementing the sinusoidal shear deformation theory incorporating Murakami’s zig-zag function to encounter the inherent zig-zag effects of the laminated structures. The focus of the second is to investigate the active damping behavior of laminated multiscale hybrid fiber-reinforced composite (HFRC) smart shells via active constrained layer damping (ACLD) treatment using the proposed theory. The ACLD treatment layers comprise a constrained layer of viscoelastic material and an advance constraining layer of 1–3 piezoelectric composite material with vertically/obliquely oriented piezo-fibers, responsible for the active control. The computed numerical results of the laminated HFRC shell are analyzed and compared with the laminated base composite shell for symmetric/anti-symmetric cross-ply and anti-symmetric angle-ply. Moreover, we investigated the effect of carbon nanotube waviness and piezo-fibers orientation on the damping performance of the laminated HFRC/ACLD smart shell system. The analysis shows that the damping behavior of laminated HFRC shells improved due to the waviness of carbon nanotubes and that the orientation of piezo-fibers greatly influenced the effectiveness of the ACLD treatment patches. The proposed laminated multiscale HFRC/ACLD shell system with straight and wavy carbon nanotubes can be extensively used in structural health monitoring applications to actively control the mechanical vibrations induced in structures.

Buckling Behavior of a Functionally Graded Sandwich Plate

This research focuses on the buckling behavior of a porous Functionally Graded (FG) sandwich plate using the sinusoidal shear deformation theory and hyperbolic tangent and secant thickness stretching functions with novel displacement fields. The proposed model assumes a different thickness layer system with FGM on the top and bottom and a ceramic core. Hamilton's energy principle is applied to the FGM sandwich plates to understand their buckling behavior. The mesh convergence on Finite Element (FE) model is carried out, and the accuracy of the results is tested using the existing research. The present model results match reasonably well with the previously published literature. The impact of the transverse shear deformation, plate aspect ratio, size-to-thickness ratio, and volume fraction is investigated for different thickness layer systems.

Buckling analysis of plates using an efficient sinusoidal shear deformation theory

Mechanical buckling response of isotropic and orthotropic plates using the two variable refined plate theory is presented in this paper. The theory takes account of transverse shear effects and parabolic distribution of the transverse shear strains through the thickness of the plate; hence it is unnecessary to use shear correction factors. Governing equations are derived from the principle of virtual displacements. The nonlinear strain-displacement of Von Karman relations are also taken into consideration. The closed-form solution of a simply supported rectangular plate subjected to in-plane loading has been obtained by using the Navier method. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

Bending analysis of FGM plates using sinusoidal shear and normal deformation theory

This paper presents the bending analysis of functionally graded material (FGM) plates using sinusoidal shear and normal deformation theory. The in-plane displacements include sinusoidal functions in the thickness coordinate to consider the effect of transverse shear deformation, and transverse displacement includes the effect of transverse normal strain using the cosine function in thickness coordinate. The displacement field of the theory enforces to satisfy shear stress-free boundary conditions on the top and bottom surfaces of the plate with realistic variations across the thickness. Plate material properties vary across thickness directions according to a power law. The boundary value problem of the theory is derived using the principle of virtual work. Simply supported plate bending problems are solved using the Navier solution technique. Response of the plate is obtained with respect to the type of load, type of plate, aspect ratio, and power law index. The results of present theory are compared with those of quasi-3D discrete layer theory and semi-analytical solutions based on the theory of elasticity to ensure the accuracy of theory. The current theory showed excellent agreement with more exact theories in bending response.

Free vibration of axially loaded microbeam in MEMS based on sinusoidal shear deformation theory

Free vibration of an axially loaded silicon microbeam in MEMS under electrostatic actuation is studied on the basis of a sinusoidal shear deformation theory. Based on the modified couple stress theory (MCST) and von Kármán geometric nonlinearity, a nonlinear finite element formulation is derived and employed to construct the discrete nonlinear governing equations for the microbeam. The deflection of the microbeam at a given DC voltage is firstly calculated using the Newton Raphson based iterative procedure, and used to evaluate the tangent stiffness matrix. The natural frequencies of the microbeam corresponding the DC voltage are then computed. The influence of the applied voltage, the axial force as well as the material length scale parameter on the frequencies of the microbeam is studied in detail and highlighted. The dependence of the pull-in voltage upon the material length scale and the axial force is also examined and discussed.

Nonlinear dynamic analysis of the functionally graded graphene platelets reinforced porous plate under moving mass

Recent studies demonstrated that porous materials could gain satisfying improvements in some mechanical properties by adding graphene platelet (GPL) reinforcements. Following this result, the present work exhibits a semi-analytical method to investigate the nonlinear dynamic characteristics of the functionally graded GPLs reinforced porous (FG-GPLRP) plate under a moving mass. Two types of boundary conditions, i.e., simply supported (SSSS) and clamped (CCCC) edges, are incorporated in the study. Based on the refined sinusoidal shear deformation theory (RSSDT) and von Kármán nonlinearity, the governing equations are transformed into a group of ordinary differential equations for the deflection of the plate. Then, the dynamic behaviours of the plate can be investigated by operating the fourth-order Runge–Kutta approach. After verification, several numerical examples are displayed to illustrate the effects of porosity coefficient, GPLs content, Winkler–Pasternak foundation, damping, initial imperfection, and compression stress on the moving-load-bearing capability of the plate. The obtained results demonstrate that, without harming its moving load capacity, it is possible to decrease the mass of the FG-GPLRP plate to a satisfying extent by altering the porosity and GPLs content.

Free vibration and buckling analyses of a rectangular sandwich plate with an auxetic honeycomb core and laminated three-phase polymer/GNP/fiber face sheets

In this paper, the free vibration and uniaxial, biaxial, and shear buckling analyses of a sandwich plate with an auxetic honeycomb core and two laminated three-phase polymer/GNP/fiber face sheets are investigated. The sinusoidal shear deformation theory (SSDT) is utilized to model the plate, Hamilton’s principle is hired to derive the governing equations and boundary conditions, and a numerical solution is performed via the differential quadrature method (DQM). The effects of various parameters on the critical buckling loads and the natural frequencies of such a plate are examined such as the geometrical parameters of the auxetic honeycomb core, mass fractions of the GNPs and the fibers, and total thickness of the plate. Numerical results reveal that by increasing the thickness of the auxetic honeycomb core the critical buckling loads decrease and the natural frequencies experience an initial growth followed by a small reduction. It is concluded that the inclined angle in the auxetic honeycomb core has no remarkable effect on the critical buckling load, but affects the natural frequencies in all vibrational modes.

Expression of Concern: “Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory” [JCOMB, Volume 95, 15 June 2016, Pages 209–224

Expression of Concern: “Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory” [JCOMB, Volume 95, 15 June 2016, Pages 209–224

Nonlinear free vibration analysis of functionally graded plates and shell panels using quasi-3D higher order shear deformation theory

This paper presents the nonlinear free vibration behavior and response of functionally graded plates and shell panels under various boundary conditions. The displacement formulation followed uses a sinusoidal non-polynomial quasi-3D higher order shear deformation theory with six variables and, the parabolic transverse stress distribution functions are used to model stresses in the thickness direction. Present formulation employs the Green-Lagrange nonlinear strains along with Sander’s approximation to account for larger flexural response which could be experienced by the structure. An eight noded C0 continuous isoparametric finite element is used for numerical implementation of nonlinear finite element solver developed in MATLAB. Developed numerical formulation is employed to study and analyze the nonlinear free vibration response of the spherical, cylindrical and hyperboloid shell panels and the obtained results are seen to be consistent and good agreement with the literature thus establishing the effectiveness and accuracy of the present work.

Mechanical stress and deformation analyses of pressurized cylindrical shells based on a higher-order modeling

In this research, mechanical stress, static strain and deformation analyses of a cylindrical pressure vessel subjected to mechanical loads are presented. The kinematic relations are developed based on higher-order sinusoidal shear deformation theory. Thickness stretching formulation is accounted for more accurate analysis. The total transverse deflection is divided into bending, shear and thickness stretching parts in which the third term is responsible for change of deflection along the thickness direction. The axisymmetric formulations are derived through principle of virtual work. A parametric study is presented to investigate variation of stress and strain components along the thickness and longitudinal directions. To explore effect of thickness stretching model on the static results, a comparison between the present results with the available results of literature is presented. As an important output, effect of micro-scale parameter is studied on the static stress and strain distribution.

Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories

In this novel work, applying boundary shape function differential quadrature hierarchical finite element method (DQHFEM) will be employed to analyze frequency, damping, bending, and buckling of an embedded sandwich nanoplate using different plate theories such as refined zigzag theory (RZT), sinusoidal shear deformation theory (SSDT), first-order shear deformation theory (FSDT) and classical plate theory (CPT). The face sheets as well as the core layer of the sandwich structure respectively are formed by porous material and nanocomposites reinforced with graphene platelets (GPLs) considering various dispersion. According to the Halpin–Tsai micromechanics model, Young’s modulus, as well as the rule of mixture for density as well as Poisson’s ratio related to the face sheets, can be obtained. Further, for modeling the mentioned sandwich structure much more realistic, Kelvin–Voigt model is applied. In order to gain motion of equations, D’Alembert’s principle is utilized where size influences can be contemplated as well using higher-order strain gradient nonlocal theory. In this comprehensive research, diverse parameters featuring the influences of structural damping, strain gradient parameters, GPL volume percent, dispersion, viscoelastic medium, porosity, boundary edges, and geometric variables upon vibration, buckling, and bending behaviors correlative to this structure. It is ascertained that RZT is the most accurate theory among other mentioned theories in estimating the static and dynamic response of structure which needs no shear correction factors. Moreover, the presence of GPLs can make the entire sandwich structure stiffer and dispersion patterns of pores, as well as GPLs, can affect the vibration, buckling, and bending of the structure.

Strain gradient vibration analysis of piezoelectric composite microplate reinforced with FG-GPLs based on sinusoidal shear deformation theory

Here, the basic formulation of nonlocal strain gradient theory (SGT) and sinusoidal shear deformation theory (SSDT) are used to analyze the free vibration behavior of functionally graded graphene nanoplatelets reinforced piezoelectric composite (FG-GPLRPC) microplate. To provide a realistic model based on the Kelvin Voigt model, the material properties of the structure are assumed to be viscoelastic. The viscoelastic FG-GPLRPC microplate is resting on the orthotropic visco Pasternak foundation and is exposed to the electromagnetic field. Four different patterns of functionally graded distributions of GPLs, uniform distribution, and non-uniform distributions such as FG-A, FG-O, and FG-X are considered. The effective Young’s modulus, density, and Poisson’s ratio of FG-GPLRPC microplate are determined based on the Halpin–Tsai micromechanics model and the mixture rule, respectively. Finally, Hamilton’s principle is applied to obtain the equations of motion. The simply supported plate is assumed to study the dimensionless eigenfrequency with the analytical approach. The results are compared with other published papers to show the validity of the proposed approach. It is seen that growing the aspect ratio leads to about 33% increase and decrease in the system frequency for high and low damping coefficient values, respectively.

Modified couple stress theory application to analyze mechanical buckling behavior of three-layer rectangular microplates with honeycomb core and piezoelectric face sheets

The current study is aimed to analyze the mechanical buckling of a three-layered microplate made from honeycomb structures sandwiched between two piezoelectric face sheets. The microplate is located on an elastic foundation that stands both normal and shearing loads. Minghui and Jiuren relations were employed to determine the effective mechanical properties of the honeycomb core. The sinusoidal shear deformation theory (SSDT) was also employed as a higher-order theory with trigonometric shear deformation function to describe the displacement components. The governing equations were derived using the virtual displacement principle and modified couple stress theory (MCST) was employed to predict the results in micro dimension. Navier’s solution method was chosen to analytically extract the critical buckling loads for a simply supported edges microplate. The effect of the most important parameters such as geometrical specifications of the honeycomb core on the results was also considered and discussed. Nowadays the honeycomb structures are widely used in different areas of sciences and technologies due to their lightweight and high stiffness. Also, the piezoelectric materials are applied as sensors and actuators in smart engineering structures. Therefore, the outcomes of this study may help in designing and manufacturing more applicable structures and smart devices capable of tolerating loading conditions, especially in small dimensions.

Dynamic characteristics of composite micro lattice plates comprises of graphene nanoplatelets based on MCST theory

This paper investigates the free vibration characteristics of a stiffened micro lattice plate with the graphene nanoplatelets (GPLs) using the modified couple stress theory and sinusoidal shear deformation theory. The governing equations of motion are derived using the Hamilton’s principle. Solution procedure is developed based on Navier’s technique for simply-supported boundary conditions. The effect of geometrical parameters of the lattice structures and GPL weight fraction on the vibration response of the functionally graded (FG) micro lattice plates is analyzed. The numerical study reveals that by increasing the cell density, the natural frequency of the FG micro lattice plate approaches to the simple FG micro plate. Also, the effect of the size, distribution pattern of GPLs and material length scale parameter on the free vibration response of the FG GPLs-reinforced micro lattice plate is demonstrated in this study.

Effect of Porosity on the Thermal Buckling Analysis of Power and Sigmoid Law Functionally Graded Material Sandwich Plates Based on Sinusoidal Shear Deformation Theory

This work examines the effect of porosity distributions on thermal buckling analysis of functionally graded material (FGM) sandwich plates. To consider the porosity effect, five different types of distribution models, even, uneven, logarithmic uneven, linear uneven, and sinusoidal uneven are considered. It is assumed that the FGM faces of the sandwich plate are porous while the ceramic core is nonporous. To investigate the thermal buckling behavior of porous FGM sandwich plates, four different types of thermal loads, such as uniform, linear, nonlinear, and sinusoidal temperature rise along the thickness direction are considered. Effective material properties and thermal expansion coefficients of FGM sandwich plates are evaluated based on Voigt’s micromechanical model considering power law FGM (P-FGM) and sigmoid function FGM (S-FGM). The analytical solution is carried out using Hamilton’s variational principle considering the von Karman nonlinearity. The equilibrium and stability equations are derived based on sinusoidal shear deformation theory (SSDT). Numerical results are obtained to observe the influence of different porosity distributions, porosity coefficients, thermal loadings, and geometrical parameters over critical thermal buckling temperature.