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This paper investigates the influence of non-homogeneous elastic foundations on the free vibration characteristics of functionally graded graphene platelets reinforced composite plates submerged in fluid medium. A novel aspect of this study lies in exploring various distributions of the foundation, positioned either centrally within the plates or along their edges. The stiffness of the foundation is computed using Selvadurai's method, which accounts for subgrade soil properties and foundation depth. Material properties of the plates are examined by employing the rule of mixtures alongside the Halpin–Tsai micromechanical model. Hydrostatic pressure and free surface waves are not considered, given the assumption of an ideal and incompressible fluid. The theoretical framework is grounded in a novel inverse trigonometric shear deformation plate theory, where the transverse shear stress distribution is established using a newly developed inverse trigonometric function. The equations of motion are efficiently resolved through Galerkin's method. The efficacy of this approach lies in its utilization of integration to address the distribution issue of the foundation, obviating the need for deploying intricate algorithms. The proposed theory demonstrates enhanced accuracy in predicting natural frequencies compared to other published shear deformation plate theories. Moreover, this paper delves into the effect of material properties and the fluid environment on the natural frequencies of the structures. Particularly significant is our thorough investigation of the impact of variations in the locations, material properties, and sizes of the foundation on the free vibration of these plates, all of which bear great importance in structural design. [ABSTRACT FROM AUTHOR]

This paper studies the ultimate strength and progressive damage behavior of imperfect composite laminated plates under end-shortening strain using the semi-analytical finite strip method (FSM). Plates with various thicknesses and boundary conditions are perused. First-order shear deformation theory with the assumption of large deflections is considered. To analyze the failure in the laminates, the Hashin and Rotem failure criterion is used, and once the failure occurs, the material properties decrease instantaneously. Three different scenarios have been considered to apply material properties degradation in the failed ply: the complete ply degradation scenario, the strip degradation scenario (SDS), and the strip region degradation scenario. In the first scenario, the properties of the entire ply are degraded instantaneously after predicting the failure. In contrast, in the SDS, the reduction of material properties occurs only in the strip where the failure has occurred. In the third scenario, in order to increase the accuracy of damage analysis, each strip is divided into three regions, and material properties are degraded in the strip's region where the failure has happened. A convergence study is performed with regard to both the number of terms of displacement fields along the strip and the number of strips used across the laminates. To validate the damage responses, the results obtained by the proposed method have been compared with the finite element method (FEM) and available results in the literature. The introduced approach overcomes the limitations of previous methods, such as Ritz, in applying different boundary conditions and is much more suitable than the FEM in terms of simplicity of implementation and computational time. [ABSTRACT FROM AUTHOR]

This paper presents the delamination impact over the dynamic response of the variable angle tow (VAT) composite plates. The VAT plates with various fiber angles are constrained to different boundary conditions for parametric investigation, while delamination is made to present over two different locations with varying sizes. A comparative stochastic vibration study is performed to evaluate the contribution of composite properties to delaminated and intact plates. The randomness in the material properties is modeled with the efficient Latin hypercube sampling method. The polynomial neural network-based surrogate model, considered an efficient substitute for computationally expensive Monte Carlo simulation, is employed in the present work to examine the stochastic behavior of VAT plates. The contribution of the composite properties on the uncertain vibration characteristics is evaluated. It is observed from the investigations that the sensitivity of the composite properties varies significantly with the delamination. Lastly, a failure probability estimation is carried out with a developed polynomial neural network-based surrogate model to provide safe design estimation for various cases. [ABSTRACT FROM AUTHOR]

In this paper, a meshfree Jacobi point interpolation (MJPI) approach for the free vibration and stationary stochastic response analyses of heated composite laminated plate with varying thickness and curvilinear fiber is developed. The theoretical formulations for heated composite laminated plate with varying thickness and curvilinear fiber are established by using Hamilton's principle in framework of first order shear deformation theory. The effect of thermal stress generated by the temperature variation is considered based on the thermo-elastic theory. The displacement components of the plate are approximated by using the MJPI shape function. The boundary conditions considered in this study are achieved by using the artificial spring technique. The accuracy and reliability of the proposed MJPI shape function are confirmed by comparing with numerical results from the published literature and finite element software ABAQUS. Several comparisons show that the differences between the numerical results from current method, reference and ABAQUS software are less than 1%. Finally, the effects of different parameters such as temperature difference, fiber direction coefficient, thickness gradient and thickness power index on the free vibration and stationary stochastic response of the composite laminated plate are investigated. [ABSTRACT FROM AUTHOR]

With the special physical characteristics, graphene is considered as an excellent candidate for various engineering applications. Due to the electromechanical coupling properties and significant variations in material characteristics at the interfaces of adjacent layers, existing higher-order models reported in the literature may lack the necessary capability to achieve precise prediction of natural frequencies for piezoelectric graphene-reinforced composite plates. This paper will develop advanced plate theory for the vibration analysis of graphene-reinforced composite plates with a macro fiber composite piezoelectric layer. The number of displacement variables in the developed theory is independent of the layer number. In contrast to earlier higher-order theories, the proposed plate theory incorporates a modified interlaminar shear stress field that accounts for the electromechanical properties. Furthermore, the modified transverse shear stress field can be adsorbed in the equations of motion by means of Hamilton's principle, which can effectively improve the ability to predict natural frequencies of piezoelectric laminated plates. Using the exact solutions and the results obtained from other theories, the performance of the developed theory is evaluated. Compared with the existing higher-order models, the proposed theory is more accurate in predicting natural frequencies. Additionally, a parametric study is conducted for the influences of several significant parameters of graphene and the piezoelectric plate on the vibration responses of the smart composite plates with graphene reinforcements. [ABSTRACT FROM AUTHOR]

In this paper, a rectangular bistable composite laminated plate is studied through dynamic modeling, numerical simulation and experiment. A theoretical model is elucidated, elaborating the dynamic snap-through and nonlinear dynamics of the rectangular bistable composite laminated plate. The potential energy curve, the restoring force curve and the stiffness curve are graphically presented, exhibiting differences from those of square bistable plates. The two potential wells and the negative stiffness region are asymmetric. The dynamic snap-through elucidated by curvature and displacement is graphically presented in phase diagrams and time history diagrams. Due to the asymmetry of the double potential wells, the dynamic snap-through may be unidirectional rather than repeated, and the nonlinear dynamic responses around the two potential wells are asymmetric, which depends on initial positions. In frequency sweep, the frequency-amplitude response curves are characterized by the softening nonlinear stiffness effect and the hysteresis, where there are multiple peaks displaying the first several modes of the rectangular bistable plate around one stable state. The nonlinear dynamic responses are characterized by the periodic and chaotic vibrations, the 1/2 subharmonic resonance, the unidirectional dynamic snap-through and the repeated dynamic snap-through. When the excitation frequency is equal to the first mode frequency for the lower stable state or the third mode frequency for the upper stable state, the dynamic snap-through is found to occur. Linear mode frequencies can show the mechanism of the snap-through to a certain extent. At mode frequencies, sufficient energy is gathered to actuate the snap-through. Unlike square bistable plates, rectangular bistable plates may only be characterized by the unidirectional snap-through under the specific energy input, which depends on initial positions. For rectangular bistable plates, two opportune excitation frequencies that have to be selected can lead to the repeated snap-through. This research is beneficial to the development of aerospace structures, bistable energy harvesters and vehicle vibration isolation devices. Compared to the old work, this work is more in line with the actual situation, where a high aspect ratio morphing wing can adjust its airfoil according to different tasks based on rectangular bistable plates which are more suitable for potential applications in the future. [ABSTRACT FROM AUTHOR]

The analysis of a composite plate by refined plate theories is presented in this paper. The displacement fields of monolayer plate are expressed by means of Carrera unified formulation (CUF), and Taylor-like series expansion is employed along the thickness direction. The governing differential equation of monolayer plate is derived by Hamilton's principle, and the related element stiffness matrix, mass matrix, and load vector are obtained. The element matrix of composite plate is obtained by superimposing single-layer plate elements, and the global matrix is obtained in the finite element framework. Due to the shear locking phenomenon of thin plate, the higher-order model is revised by tensor component mixed interpolation (MITC). The accuracy and reliability of the present model are demonstrated by comparing with classical plate model (classical plate theory and first-order shear deformation theory) and a solid model generated in the commercial software ANSYS. Meanwhile, the geometric parameter optimization of composite plate is studied based on the constructed higher-order model by the multi-objective genetic algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear forced vibration responses of axially moving functionally graded carbon nanotube reinforced composite (FG-CNTRC) rectangular thin plates are investigated. In the frame of classical plate theory and von Kármán geometric nonlinear theory, the nonlinear partial differential equations of motion for axially moving FG-CNTRC plates are established by Hamilton's principle and discretized through the Galerkin method. The validity of the present model is verified by comparing the natural frequencies and the critical divergence velocity of the axially moving plate with the existing results in the literature. The frequency response curves (FRCs) of axially moving FG-CNTRC plates subjected to transverse harmonic concentrate excitation are calculated by using the incremental harmonic balance (IHB) method. The stability and bifurcation characteristics of period solutions obtained through the IHB method are analyzed by Floquet theory. The isolated detached resonance curves (DRCs) are observed inside the main continuous FRCs of axially moving FG-CNTRC plates. Saddle-node bifurcation, Hopf bifurcation, quasi-periodic motion and the internal resonance caused by the modal coupling effect are analyzed. The numerical results illustrate the effects of the CNT distribution, volume fraction, axially moving velocity, aspect ratio and width-to-thickness ratio on the nonlinear dynamic responses of axially moving FG-CNTRC plates. [ABSTRACT FROM AUTHOR]

By using an effective theoretical model, efficiency and accuracy of design for laminated plates can be significantly improved. However, the existing five-variable higher-order models will encounter difficulty to accurately produce interlaminar stresses, which will influence evaluation on interlaminar performance of laminated plates. Thus, this paper attempts to propose an efficient higher-order model with five variables, where the Legendre polynomial is introduced into in-plane displacement field at each layer. By enhancing compatible condition of displacements and equilibrium condition of stresses, the unknowns depending on the layer number have been eliminated. Differing from other existing five-variable higher-order models, the proposed model can describe the zig-zag effect of in-plane displacements, and fulfill continuity of transverse shear stresses at interfaces. The governing equations are further derived through the principle of virtual displacement, and analytical solutions for only simply-supported plates have been presented. To assess the capability of the proposed method, three-dimensional elasticity solutions have been employed for comparison, and other five-variable higher-order models from the literature have been also chosen for assessment. Numerical results show that the proposed model possesses the same computational efficiency as the selected five-variable models, but can predict more accurate results. In addition, the proposed model is employed to analyze bending behaviors of sandwich and composite plates, and accurate results can be also acquired. Therefore, the present model is proposed to design laminated plates. [ABSTRACT FROM AUTHOR]

This paper deals with the natural frequency and stability of axially moving functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular thin plates. Based on Reddy's first-order shear deformation theory, the partial differential equations of motion for axially moving FG-CNTRC plates in thermal environment are derived by Hamilton's principle and discretized by the Galerkin method. The in-plane displacement and inertia of the plate are retained in the dynamic model. By solving the complex eigenvalues of the gyroscope system, the variations of natural frequencies of the axially moving FG-CNTRC plates with axial moving velocity are obtained, and the stability of the plates is analyzed. The validity of the present model is verified by comparing the natural frequencies and the critical divergence velocity of the axially moving plate with the existing results in literature. The divergence and flutter type of instability, critical divergence velocity, and critical flutter velocity are studied. The numerical results reveal the effects of CNT distribution, volume fraction, aspect ratio, width-to-thickness ratio, and temperature rise on the natural frequencies of the plates. Additionally, the effects of geometry parameters on the critical divergence velocity and critical flutter velocity of axially moving FG-CNTRC plates are studied by plotting the instability regions. [ABSTRACT FROM AUTHOR]

Without regarding interlayer continuity of transverse shear stresses in the displacement expressions, traditional higher-order plate theories have difficulty in predicting continuous shear stress fields accurately for multilayered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates with independent CNT distributions in each layer. In this paper, a new higher-order continuous shear stress multilayered plate model is developed for high-accuracy analysis of FG-CNTRC plates. In the theoretical formulation, higher-order interpolation functions and piecewise descriptions are adopted for transverse shear stress fields. By fulfilling the interlayer continuity of shear stresses and displacements, the displacement expressions for FG-CNTRC plates are formulated. The accuracy of the proposed model is determined by two kinds of parameters: the order of assumed transverse shear stress fields and the number of subdivisions. Compared with traditional higher-order theories, the proposed model can accurately predict continuous transverse shear stresses for FG-CNTRC plates with different CNT configurations by constitutive relations directly. Additionally, a four-node rectangular plate element associated with the proposed model is formulated. Results show that the proposed model agrees well with the exact solutions and results from ANSYS. With the same amount of calculation, the proposed higher-order model has higher accuracy than the model with more subdivisions, especially for asymmetric plates with discontinuous CNT ply angle. [ABSTRACT FROM AUTHOR]

A static package design of a functionally graded porous plate in microscale which is coated by two polymeric piezoelectric carbon nanotubes reinforced composite (CNTRC) face sheets is provided in this study. The microstructure rests on the Pasternak foundation and is subjected to thermal load. Furthermore, face sheets are subjected to the electric field. With the aid of a quasi-3D hyperbolic shear deformation theory, governing equations of the microplate are derived and then its critical buckling loads are calculated. The properties of all layers alter continuously along with thickness direction due to the CNTs and pores distributions. The size effects are captured by the means of modified couple stress theory (MCST). By conducting the current study, the results emerged in detail to assess the effects of different parameters on buckling of structure. For instance, it is revealed that the highest and lowest critical buckling load and consequently stiffness, is due to the V–A and A–V CNTs dispersion type, respectively. Furthermore, it is revealed that by porosity coefficient enhancement, critical buckling load and consequently, stiffness are reduced dramatically. Current paper outcomes can be used in different fields of sciences such as optimum design of engineering structures or various high-tech industries as aerospace factories. [ABSTRACT FROM AUTHOR]

Based on Gurtin–Murdoch's theory, a new mechanistic laminated nanoplate model composed of nanocomposites under various boundary conditions is proposed, where the top and bottom surfaces of the laminated nanoplate are regarded as two-dimensional films which have independent surface elastic parameters. The influence of surface Lamé constants and residual stress on static bending and vibration properties for the laminated nanoplate is studied. In order to get approximate solutions of bending deflections and first-order frequencies for the laminated nanoplate with complex boundary conditions, the variational method is employed in this paper. The effectiveness of the presented variational method is verified by comparison with available results. Numerical results indicate that the effective bending stiffness of the laminated nanoplate considering surface effects is obviously different from the classical result. Moreover, the influences of surface effects on bending deflections and first-order frequencies are related to the surface elastic parameters and boundary conditions. The presented method and results provide a theoretical benchmark for other numerical and experimental methods to study nano laminates. [ABSTRACT FROM AUTHOR]

In this paper, the bending deformation, free vibration and forced vibration of one-dimensional hexagonal quasicrystal layered plates with imperfect interfaces are investigated. The generalized linear spring layer model is adopted to simulate the interface bonding defects caused by the slip or debonding of quasicrystal materials due to actual production or interlayer aging. The imperfect interface transfer matrix is established for one-dimensional hexagonal quasicrystal layered plates and the analytical solutions of phonon displacements, phonon stresses, phason displacements and phason stresses for static bending, the natural frequency for free vibration, and the displacements of phonon and phason fields for forced vibration under a harmonic excitation are then derived by the pseudo-Stroh formalism. Numerical examples are provided to analyze the influence of the stacking sequence and the imperfect interface parameter of two sandwich plates composed of crystal and quasicrystal materials on the bending deformation and vibrational response of layered quasicrystal composite plates. Furthermore, the presented three-dimensional plate model is applied to quasicrystal-coated aluminium-based composites in engineering practice. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic stability analysis of moderately thick viscoelastic plates is performed employing the Boltzmann integral law with constant bulk modulus. The remarkable and new point of the proposed method is that the frequency of a Mindlin viscoelastic plate subjected to simultaneous constant and harmonic in-plane compressive loads is explicitly predictable based on free vibration analysis of an elastic plate. Moreover, the damped part of frequency is easily calculated. Also, the critical excitation for which the system becomes unstable is determined. This method is completely new and significantly reduces the computational cost. The obtained results are compared with other existing results to show the efficiency and accuracy of the proposed method. This method is used to investigate the effects of viscoelastic properties and in-plane compressions on the steady-state responses of Mindlin viscoelastic plates under time-dependent compressive loads. [ABSTRACT FROM AUTHOR]

This paper presents the free vibration analysis of combined composite laminated conical–cylindrical shells with varying thickness using the Haar wavelet method (HWM). The displacement field of the combined shell is set based on the first-order shear deformation theory (FSDT), the displacement components, and rotation of individual shells including boundary conditions that are expanded by the Haar wavelet and Fourier series in the meridional and the circumferential direction. By solving the vibration characteristic equation discretized by the Haar wavelet, the vibrational results of combined shells are obtained. Then, the results of the proposed method are compared with those of published literature and finite element analysis (FEA). The results show that HWM has high convergence and high accuracy for the free vibration analysis of the combined composite laminated conical–cylindrical shells with varying thickness. Also, the effects of the parameters such as thickness variation parameters, material properties, geometrical dimensions, and different boundary conditions, on the vibrational behavior of the combined shells are investigated. Finally, new numerical results are provided to illustrate the free vibration behavior of the combined composite laminated conical–cylindrical shells with varying thickness. [ABSTRACT FROM AUTHOR]

In this paper, a new three-node triangular plate element is proposed to analyze laminated composite plates based on the higher-order shear deformation theory (HSDT). Originating from the MITC3+ shell finite elements, the displacement fields of the HSDT are interpolated by usual linear functions of the three-node triangular element and a cubic supplemented function associated with a node located at the centroid of the element. The transverse shear strain fields are separately approximated according to the MITC3+ shear-locking removal technique. The edge-based smoothed (ES) strain method is employed to improve the in-plane strain fields. Applying the divergence theorem, the surface integration of the in-plane stiffness matrices is transformed into the line integration on the boundary of the smoothing domains. The performance of the so-called ES-MITC3+ plate elements is validated through several numerical examples. The numerical results of the static, frequency and buckling analyses when this new element is used converge to the exact solutions and agree well with those given in other references. [ABSTRACT FROM AUTHOR]

The semi-analytical finite element (SAFE) method is widely used for studying properties of guided waves along composite waveguides. However, evaluating the modes associated to high wave numbers requires important mesh refinements and may significantly increase the computational cost. This paper presents a semi-analytical isogeometric analysis (SAIGA) to calculate the dispersion relation of functionally graded or multilayer plates coupling with fluids. High-order elements based on non-uniform B-splines (NURBS) basis functions are used. Several numerical examples are then studied for different problems in order to assess the efficiency of proposed method: (i) homogeneous plates; (ii) functionally graded plates; (iii) composite plates (with strong contrast of rigidity between layers); (iv) fluid-immersed plates. The results obtained are compared with the ones derived from analytical approaches and by the conventional SAFE method using Lagrange polynomials. For all cases, the dispersion curves evaluated by using enriched-NURBS basis functions achieve a significant better precision than using conventional Lagrangian functions (for the same number of degrees of freedom or the same order of shape functions), especially for the higher modes. The continuity of the stress shape modes at the interfaces is also shown to be much improved by using SAIGA. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic stiffness method (DSM) is developed for the vibration analysis of laminated cylindrical and conical shells, which are partially filled or surrounded by quiescent fluid. The Reissner and Naghdi's thin shell theory and incompressible fluid equations are employed on the structures and fluid, respectively, so as to characterize the fluid–structure coupling model. Shell elements with/without fluid loadings are derived and assembled by using the dynamic stiffness method. Numerical examples of the free vibration analysis for both empty and fluid-filled shells are validated against previous studies. Remarkable advantages regarding computational efficiency and accuracy of the DSM, especially in high-frequency domain, are presented through response curves compared with finite element calculations. As for partially fluid-filled or fluid-surrounded laminated shells, parametric studies are made to find the effects of material properties, fluid heights and semi-vertex angles on the dynamic characteristics. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the free and forced vibration behavior of a sandwich beam with functionally graded porous core and composite face layers embedded with shape memory alloy (SMA). Three different porosity patterns are assumed through the thickness direction of the core, and composite face layers are reinforced with carbon nanotubes (CNT). The sandwich beam is resting on an elastic foundation which is simulated by Vlasov's model. By using Hamilton's principle and first-order shear deformation theory, the governing equations of motion are derived. The analytical solution is presented to solve the equations of motion using Navier's solution. Results are verified with corresponding literatures. Finally, the effects of important parameters such as temperature, volume fraction of SMA, porosity distribution, weight fraction of CNT, and geometric parameters are explored in detail. [ABSTRACT FROM AUTHOR]

In the present paper, a flexible framework is developed for the optimization of composite laminate plates. In this framework, an optimization algorithm is employed to find the optimal stacking sequence design of the FE models by interfacing the Abaqus solver with MATLAB through a Python script. The Python script submits dimension, orientation, and diameter of the cutout combinations to Abaqus/CAE. The performance of the codes is validated by applying them to several problems of previous research. Three distinct types of boundary conditions, namely CCCC, SCSC, and SSSS, with different geometries comprising a square and rectangular plates with and without cutouts, are considered as optimal design problems. Besides that, analyses are performed on new symmetrical composites with 16 and 80 plies. The framework is equipped with the GA for optimizing the fiber orientations and maximizing the buckling capacities. The results are comprehensively discussed, showing a reasonable agreement with the literature. This code can easily be used by scientists and industry professionals as an automated tool for optimizing different finite element models and using any arbitrary optimization algorithm. [ABSTRACT FROM AUTHOR]

In the present study, nonlinear flutter and post-flutter behavior of a variable stiffness composite wing-like plate is investigated. The variable stiffness is obtained by varying fiber angles continuously according to a selected curvilinear fiber path function in the composite laminates. Flutter speed, limit cycle oscillations and bifurcation diagrams of the composite plate are explored for three different fiber path functions using the nonlinear structural model obtained based on the virtual work principle. The paper aims to exploit the ideal fiber paths with enhanced aeroelastic flutter and post-flutter properties for a composite plate in supersonic flow speed. First-order linear piston theory is applied to model the aerodynamics, and generalized differential quadrature is employed to solve the governing equations. Von Karman nonlinear strain theory is used to account for the geometric nonlinearities, and first-order shear deformation theory is employed to consider the transverse shear effects in the structural model. Time integration of the equation of motion is carried out using the Newmark average acceleration method. Different curvilinear fiber paths are introduced to enhance flutter instabilities and post-flutter behavior of the composite plate. Results demonstrate that the fiber orientation has a significant effect on the dynamic behavior of the plate and the asymmetric properties as well as the behavior of the limit cycle oscillation. [ABSTRACT FROM AUTHOR]

The newly developed penta-graphene is a two-dimensional (2D) carbon allotrope with promising mechanical properties. This paper investigates the nonlinear post-buckling and vibration of imperfect three-dimensional penta-graphene composite plates resting on elastic foundations and subjected to uniform external pressure and axial compressive load. The elastic constants of the single-layer penta-graphene are fully determined by the density functional theory by fitting the equation of strain energy to the density functional theory energy. Specifically, the elastic constant C 66 which has not been considered by other authors is also determined. The motion and compatibility equations are derived based on the classical plate theory taking into account von Karman geometrical nonlinearity, initial geometrical imperfection and Pasternak type elastic foundations. For nonlinear post-buckling, the Bubnov–Galerkin method is applied to obtain the load–deflection amplitude curves while the Runge–Kutta method and harmonic balance method are used to obtain the deflection amplitude–time curves and the amplitude–frequency curves for nonlinear vibration. Numerical results show the effects of geometrical parameters, initial imperfection and elastic foundations on the nonlinear post-buckling and vibration of the imperfect 2D penta-graphene plates. The present results are also compared to others to validate the accuracy of the applied method and approach. [ABSTRACT FROM AUTHOR]

In the present paper, for the first time the vibration behavior of hybrid composite conical shells reinforced with shape memory alloy (SMA) fibers is investigated. The temperature-dependent properties of SMA fibers and composite are accurately considered. Using the one-dimensional constitutive law of Brinson, thermo-mechanical properties such as recovery stresses, elasticity modulus and shear modulus with uniform temperature change are calculated for SMA fibers. Love's first approximation classical shell theory with von-Kármán type of geometrical nonlinearity is used in conjunction with Hamilton's principle for deriving the equations of motion. A semi-analytical solution is presented so that trigonometric functions are applied in the circumferential direction, and the generalized differential quadrature method is used to discretize the equations of motion along the longitudinal direction. Finally, parametric studies are done to investigate the effects of volume fraction, pre-strain, location of SMA fibers, boundary conditions, semi-vertex angle of the cone, and temperature on the vibration characteristics of the SMA hybrid composite conical shells. It is shown that a proper utilization of SMA fibers significantly increases the fundamental frequency and vibration control of the SMA hybrid composite conical shells. [ABSTRACT FROM AUTHOR]

Particle-reinforced composites (PRCs) are usually studied by some averaging or homogenization techniques. In this, the effective properties are derived by assuming that particles are dispersed within composites according to some given (probabilistic) distribution. Such approaches restrain the possibilities of studying the contribution of exact location and parameters of individual particles to the overall behavior of composites. In this paper, we attempt to fill this gap by deriving the mesoscopic model of such composites corresponding to a continuum with point inhomogeneities. We start from a fully microscopic model where the composite is regarded as a continuum with spherical inclusions. Letting the diameter of inclusions decrease to zero, material parameters of the composite are represented in terms of the Dirac distribution. The Mindlin–Reissner–von Kármán thick plate theory is considered as a particular case, and closed-form formulas are obtained for the plate stiffness coefficients. Numerical analysis of a thick composite plate reinforced over its mid-surface justifies the theoretical derivations. [ABSTRACT FROM AUTHOR]

This research investigates the nonlinear thermal stability responses of functionally graded graphene-reinforced composite (FG-GRC) laminated plates with embedded circular and elliptical delamination as well as edge delamination, subjected to a uniform temperature rise and a variety of mechanical boundary conditions. The thermomechanical properties of the GRCs are estimated using the extended Halpin–Tsai micromechanical model that incorporates efficiency parameters to take into account nanoscale size and surface effects of the graphene reinforcement. The von Karman geometrical nonlinearity is adopted in a solution based on the third-order shear deformation theory. The nonlinear equilibrium equations derived by the minimum total potential energy principle are solved using the Ritz method in conjunction with the Newton–Raphson iterative procedure. Parametric studies reveal that the types of graphene distribution pattern and geometry of delamination zones have a substantial effect on the thermal equilibrium paths and buckling temperature of the GRC delaminated plates. FG-X graphene sheet pattern raises the critical buckling temperature and compressive strength of the baselaminate and reduces the nonlinear thermal postbuckling deflection; however, it causes a significant increase in normal stress distribution at the top and the bottom surfaces of the delaminated plates. [ABSTRACT FROM AUTHOR]

This study presents the vibroacoustic analysis of a hybrid epoxy composite panel reinforced with advanced multi-walled carbon nanotubes (MW-CNTs) and luffa fibre. The vibroacoustic responses were obtained numerically, and the model validity was verified with experimental values. The responses were analysed under the stimulus of harmonic point excitation, considering ambient conditions, using a coupled finite element–boundary element (FE–BE) model. To ensure the accuracy and stability of the numerical model, the different structural responses, including natural and thermal frequency, of hybrid composite plates, were evaluated and compared with data from published literature. In addition, experimentation was conducted, and the results were compared with the numerically derived model to demonstrate the model's effectiveness. Furthermore, several numerical examples were solved using the numerical model to illustrate its applicability and enhance understanding. The results obtained from the experimental investigation showed that adding luffa fibre and MW-CNTs to the composite panel improved its sound transmission loss and absorption coefficient. Overall, the results suggest that the hybrid composite panel has excellent vibroacoustic performance and can be used in various engineering applications that require lightweight, high-strength materials with good damping and noise reduction properties. [ABSTRACT FROM AUTHOR]

In this work, the nonlinear post-buckling of an advanced porous nanocomposite plate with and without imperfection subjected to a hygro-thermo-mechanical load and lying on elastic foundation is carried out using third-order shear deformation theory (TSDT). Also, a modified form of a Halpin-Tsai (M-H-T) micromechanical model is proposed to characterize the mechanical properties of graphene oxide powder (GOP)-reinforced polymer nanocomposite. To this aim, the influence on random distribution, non-straight shape and agglomerated state of the GOPs is adequately incorporated into the M-H-T model. Also, two porosity distributions including symmetric and asymmetric are considered. Both the linear and nonlinear influence of temperature and moisture concentration on the bending response are probed. Large deflection theory is considered to extract the stress field and displacement field for the perfect and imperfect nanocomposite plate. Navier solution is used to solve the large deflection nonlinear equations. Numerical results are validated by existing results in the literature. A parametric investigation is established to discuss the effects of the temperature rise and moisture concentration, elastic foundation coefficients, nanoparticle geometry, aspect ratio, porosity distributions, and geometry imperfection on the GOP-reinforced polymer composite post-buckling behaviors. [ABSTRACT FROM AUTHOR]

The interface thermoelastic behavior of multi-layered structures under severe loads is a particularly important issue. Different from the previous generalized thermoelastic model, the Dual-Phase-Lag generalized thermoelastic model considering interface conditions is reestablished based on peridynamics in this manuscript. The model inherits the nonlocality of peridynamics, captures the thermal barrier at the interface, and can better deal with the discontinuous behavior at the interface. The monolithic algorithm is used for numerical model validation that is a sandwich plate subjected to thermal shock and subsequent calculation. On this basis, the influence of parameters, such as the horizon size, temperature gradient relaxation time, on the thermoelastic response behavior is studied. The thermoelastic responses with cracks and crack propagation at the interface were also carried out. It helps to better understand the effect of interfacial cracks in laminated plate subjected to thermal shocks. Finally, the analysis results are summarized. [ABSTRACT FROM AUTHOR]

The optimal design of multilayer substrates containing the cutout under compressive loads is fundamental to achieving maximum buckling resistance compared to structural weight, especially in aerospace structures. In this study, buckling and post-buckling behavior of composite laminated plates with orthogonal and symmetrical lay-up containing cutouts with different diameters have been investigated experimentally, semi-analytically, and numerically. Based on the first-order shear deformation theory, a finite strip method is developed to study the buckling of the composite laminates with cutout semi-analytically. A finite element method was used for numerical analysis. The required mechanical properties were obtained from standard tests. The current study results show that the size of the cutout diameter doesn't have a considerable effect on the elastic rigidity of the plate. Still, the buckling load decreases significantly by increasing the cutout diameter. Also, the plate's buckling load and elastic rigidity are increased considerably by increasing the number of composite layers. The thickness of the plate has more effect on the buckling load than the diameter of the cutout. The present study shows a good correlation between the results of buckling behavior derived from semi-analytical and finite element methods with experimental results. [ABSTRACT FROM AUTHOR]

Uncertainties caused by the deviation of functionally graded reinforcements from the ideal linear distribution form are unavoidable during the manufacturing process, and this can significantly influence the vibrational behavior of carbon-based nanocomposite plates. In this context, this work aims to carry out a detailed parametric study on the free vibration response of laminated composite plates made of multi-layer carbon-based nanocomposite plies, considering both linear and nonlinear distribution forms of the nano-reinforcements. Materials constituting the plies are nano-reinforcement-based carbon nanotubes (CNTs) embedded in a polymer matrix. The CNTs are assumed to be either uniformly distributed (UD) or functionally graded (FG) across the ply thickness. Two types of laminated plate arrangements are comparatively investigated. The effective material properties such as elastic modulus and mass density are derived using the extended rule of mixture, whereas the governing equations are obtained through the combination of the Lagrange equation of motion and the first-order shear deformation theory (FSDT). The natural frequencies of the carbon nanotube-reinforced composite (CNTRC) laminated plates are obtained using the finite element method. The accuracy of the present numerical model is validated by comparing our results with those published in the open literature. The obtained numerical results show that both the plate layout arrangement and how the CNT fillers are dispersed along the ply thickness have a remarkable influence on the CNTRC laminated plates. [ABSTRACT FROM AUTHOR]

In the present work, for the first time, a general analytical solution is developed and applied for functionally graded (FG) composite laminated plates with circular cutouts under various in-plane loading conditions. The stress resultants are expressed in a simple and elegant form. Firstly, the extension is achieved by first introducing arbitrarily oriented uniaxial, biaxial, and shear loading conditions into Greszczuk's solution. Then, the expressions of effective moduli of unsymmetrical laminated plates, obtained by the layer lumping method, are introduced in the present solution. The FG plate can be discretized into a large number of skinny orthotropic layers such that a continuous gradation of their mechanical properties can be obtained. The material properties of the FG plate are graded continuously through the thickness direction according to a power-law function. The robustness and accuracy of the proposed analytical solution are ascertained by comparing its results with analytical findings using the complex variable method and those predicted by the finite element method (FEM). This comparison demonstrates a good level of agreement between these results. Results also show the validity of the proposed solution for both symmetric and non-symmetric FG-laminated plates. Moreover, a comprehensive parametric study is examined and discussed in detail to show the effects of various parameters such as gradation of the material properties and applied loading on the orientation of material axes and the stress distribution around the cutout. The present analytical findings can serve as a benchmark for future research on the modeling of multilayered perforated FG plates. [ABSTRACT FROM AUTHOR]

This work intends to present a novel numerical approach for studying the vibration behaviours of variable angle tow (VAT) composite structures in their quasi-static nonlinear equilibrium states. This methodology is able to predict the buckling load, to investigate the natural frequencies variation for progressively higher loads, and to provide a means for verifying experimental Vibration Correlation Technique results. The use of VAT composites, in which the fibre orientations are allowed to vary along with a curvilinear pattern within each lamina, dramatically increases the design space and provides a significant improvement in buckling performance and benefits in the postbuckling regime. This study has been performed using an innovative methodology based on the well-established Carrera Unified Formulation able to describe several kinematic models for two-dimensional structures. In detail, layerwise theories are employed to characterize the complex phenomena that may appear in VAT composite structures. All Green-Lagrange strain components are employed because far nonlinear regimes are investigated. Furthermore, the geometrical nonlinear equations are written in a total Lagrangian framework and solved with an opportune Newton–Raphson method along with a path-following approach based on the arc-length constraint. Different VAT composite structures have been analyzed to validate the proposed approach and provide some benchmark solutions. The computed equilibrium paths are compared with results obtained using the commercial code ABAQUS. The results document the good accuracy and reliability of the presented methodology and show this numerical tool's potentialities. [ABSTRACT FROM AUTHOR]

Considering the excellent physical properties, graphene can be regarded as an ideal reinforcing material for composite structures today. Nevertheless, the existing higher-order models neglecting the continuity conditions of interlaminar stresses may lose capability to analyze precisely the stability of functionally graded graphene-reinforced composite (FG-GRC) laminated thick plates. For FG-GRC laminated structures, the compatibility conditions of interlaminar stresses will directly affect the accuracy of critical loads. As a result, an appealing plate theory with only seven unknowns is suggested for buckling analysis of FG-GRC laminated thick plates. The compatibility requirements of interlaminar shear stresses between adjacent layers are satisfied in the proposed model. Improved transverse shear stresses are obtained using a preprocessing approach based on the three-dimensional (3D) equilibrium equation and Reissner's mixed variational theorem (RMVT). The performance of the suggested model is assessed by using the 3D elasticity solutions and the results obtained from some existing models. Numerical results indicate that the proposed model can reliably predict critical loads of laminated and sandwich plates. Additionally, the impact of the graphene distribution pattern, staking sequence, volume fraction, boundary conditions, thermal environment, and geometric parameters of the plate on the buckling behavior of FG-GRC laminated plates is explored. [ABSTRACT FROM AUTHOR]

We study interactions between mechanical loads and distributions of charge carriers as well as current densities in the bending of a sandwich plate with a piezoelectric dielectric layer between two nonpiezoelectric semiconductor layers. A set of two-dimensional plate equations is derived from the underlying three-dimensional macroscopic theory of piezoelectric semiconductors when the plate is in bending with shear deformation under transverse mechanical loads. It is shown that the distribution and motion of the mobile charges in the semiconductor layers are sensitive to and can be manipulated by mechanical loads. In particular, local electric potential barriers/wells form when the plate is under local mechanical loads, and the potential barriers/wells affect the distributions of the current densities in the semiconductor layers. Thus the sandwich plate exhibits couplings between mechanical loads and the distribution/motion of mobile charges and can be used for electromechanical semiconductor devices with broad applications in sensing and transduction. [ABSTRACT FROM AUTHOR]

A size-dependent piezoelectric-piezomagnetic bi-layered composite plate bending model is established based on the modified strain gradient theory and layerwise theory, where the governing equations and corresponding definite solution conditions are firstly derived by the Hamilton variational principle. And then, the meshless collocation method coupled with the method of polynomial particular solutions is tentatively to solve this bending problem. Finally, the influences of size effect, applied coupling loads, structure dimension, and foundation parameters on the bending properties of piezoelectric-piezomagnetic bi-layered composite plates are systematically discussed by some typical numerical examples. Moreover, the bending analyses under different boundary conditions and proportions of component materials are further carried out, and some interesting conclusions are obtained. [ABSTRACT FROM AUTHOR]

Free vibrations of shallow sandwich shells resting on elastic foundations are investigated. It is assumed that the shell consists of three layers of defined thickness. The core is made of ceramics or metal, while the upper and lower layers are made of functionally graded material (FGM). The volume fractions of metal and ceramics are described by the power law. Hence, estimation methods for higher accuracy remain a challenge. The elastic foundation is described by two-parameter Pasternak's model. Both higher-order shear deformation shell theory (HSDT), which includes interactions with elastic foundation, and the R-functions theory combined with the variational Ritz method are used to study shells with arbitrary planforms. The numerical study is carried out in the framework of the refined third-order theory. The proposed method and developed numerical techniques have been validated on test problems for FG shell with rectangular planform. Furthermore, new results for shallow shells with a cut-out of the complex form are obtained. The effects of the gradient index, boundary conditions, thickness of core and face sheet layers, as well as elastic foundations on fundamental frequencies, are investigated. In addition, we demonstrate how the divergence of the results varies with the gradient index. The considered studied cases show that the natural frequencies depend on the foundation parameters, the thickness of the layers, boundary conditions, and the thickness arrangement. [ABSTRACT FROM AUTHOR]

In the present article, the vibration analysis of laminated composite plates strengthened with multi-walled carbon nanotubes (MWCNTs) is performed, employing the finite element method. Rule of mixtures and the Halpin–Tsai model are utilized to ascertain the elastic properties of the nanocomposite matrix. The effect of random orientation, the curved state, and the agglomeration of carbon nanotubes in the epoxy resin on mechanical properties is investigated. Classical lamination theory is also implemented to theoretically estimate the natural frequencies for validation purposes. Then, the natural frequencies of the laminated composite plates are determined by the numerical method for various parameters involved in the design process. The effect of MWCNTs' inclusion on the natural frequencies of the carbon nanotube-based laminated plate, taking into account the reformed micromechanical Halpin–Tsai model, is finally investigated. The outcomes of the research are in compliance with experimental values and theoretical evidence available in the bibliography. [ABSTRACT FROM AUTHOR]

A new model for predicting elastic flexural wave band gaps in periodic composite plate structures containing interconnected, star-shaped, transversely isotropic, magneto-electro-elastic (MEE) inclusions is developed using a microstructure-dependent Mindlin plate model. The Floquet–Bloch theorem and the plane wave expansion method for periodic media are employed to solve the non-classical wave equations and to determine the band gaps incorporating the microstructure effect. The current non-classical model recovers its classical elasticity-based counterpart as a special case if the microstructure effect is suppressed. A parametric study is performed to demonstrate the newly developed model. The numerical results of the study show that the microstructure effect on band gaps is large when the plate is very thin. In addition, the unit cell edge length, inclusion geometry and MEE coupling have significant effects on band gap sizes, and large band gaps can be generated by tailoring the controlling parameters. [ABSTRACT FROM AUTHOR]

This communication provides initial information and understanding of the manner in which a newly developed theoretical mechanism (Soldatos in Int J Solids Struct 202:217–225, 2020) is applied in specific boundary value problems met in polar linear elasticity of fibrous composites and thus enables the determination of the spherical part of the couple-stress tensor. In this context, it tests the applicability of the implied mechanism/method in the case that a rectangular plate reinforced by a single family of unidirectional fibres is subjected to pure bending. The problem solution is obtained for either non-polar or polar material behaviour, where fibres are considered perfectly flexible or resistant in bending, respectively, and provides clear evidence of the correctness of the principal argument that underpins the proposed method. Namely, that the general rotation field of the plate deformation differs from the fibre rotation field. That newly discovered method enables an extra energy term that emerges in the strain energy function of the fibrous composite plate to relate with the spherical part of the couple-stress tensor outside conventional equilibrium conventions. It thus leads to the determination of the spherical part of the couple-stress and its distribution throughout the plate body in a complete and comprehensive manner. [ABSTRACT FROM AUTHOR]

Estimation of the effective homogenized properties is an essential step in the application of carbon nanotube (CNT)-reinforced composites. The difference between the experimental results and continuum-based homogenization schemes has motivated this work to present a modified Mori–Tanaka homogenization approach for CNT-reinforced nanocomposites. The agglomeration of CNT fibres in the matrix phase and slight weakening of the CNT–matrix interface are considered, which are incorporated in the effective homogenized properties of the nanocomposites using a two-parameter agglomeration model and interface spring-layer model, respectively. The nanotube fibres in the well-dispersed form are considered as cylindrical inclusions in the isotropic polymeric matrix. The bundled structure of CNTs is first modelled as cylindrical inclusions in the matrix and later as cumulative spherical inclusions in the hybrid matrix. Further, the effective material properties of nanocomposites are used to study the free vibration response of cylindrical panels reinforced with CNT fibres. Efficient higher-order shear and normal deformation theory is adopted, and fundamental natural frequencies are evaluated for a different set of agglomeration and interface weakening parameters using an analytical approach. The results show a significant reduction in the material stiffness as well as the natural frequency with increasing degree of agglomeration. At the same time, a slightly weakened interface is found less severe for stiffness reduction. An analysis of straight aligned CNTs highlighted their larger vulnerability to agglomeration than randomly distributed CNTs in the matrix. [ABSTRACT FROM AUTHOR]

This study proposes a new plate formulation based on a generalized layerwise theory in the isogeometric analysis (IGA) framework to investigate the bending and free vibration behavior of a laminated composite plate. All degrees of freedom in the isogeometric formulation are only associated with the displacements (i.e., rotation-free). In IGA, NURBS functions are used both to construct the geometry and to approximate the field variables. Merits of utilizing IGA include: the exact geometrical description, high accuracy and efficiancy, higher-order smoothness. The displacement-based layerwise theory assumes an individual displacement field expansion inside each layer, and the transverse displacement component is regarded to be C 0 -continuous at the layer interfaces, thus yielding a more precise description of the stress states. The C 0 continuity enforcement across the thickness in the present formulation is easily implemented by virtue of the knot insertion technique of IGA. The capability of the present isogeometric layerwise formulation in analyzing the static and dynamic responses is evidenced by conducting some numerical tests available in the open literature and comparing the computed outcomes with the reference data. [ABSTRACT FROM AUTHOR]

In this study, natural frequencies and vibrational mode shapes of variable stiffness composite skewed plates are optimized applying a genetic algorithm. The variable stiffness behavior is obtained by altering the fiber angles continuously according to two selected curvilinear fıber path functions in the composite laminates. Fundamental frequency and related mode shapes of the plates are optimized for two different fiber path functions using the structural model obtained based on the virtual work principle. A three-layer composite skewed plate with four types of boundary conditions and different plate geometries is considered as case study in this research. Diverse sweptback angles as well as different aspect ratios are considered as various plate geometries. The present study aims to calculate the best fiber path with maximized fundamental frequency or in-plane strengths for a composite skewed plate. The generalized differential quadrature method of solution is employed to solve the governing equations of motion. Moreover, the linear kinematic strain assumptions are used, and the first-order shear deformation theory is employed to generalize the formulation for the case of moderately thick plates including transverse shear effects. Numerical results demonstrate the effect of the fiber angles, boundary conditions, and diverse geometries on the natural frequencies of the composite plate. The optimal fiber angles of each layer are presented for the above cases in free vibration analysis. It is verified that the application of optimized curvilinear fibers instead of the traditional straight fibers introduces a higher degree of flexibility, which can be used to adjust frequencies and mode shapes. [ABSTRACT FROM AUTHOR]

In this work, we have investigated the nonlinear instability behavior of a thin laminated composite circular plate subjected to a tensile periodic load. A nonlinear system with quadratic and cubic nonlinear terms, referred to the effect of large deflection, is obtained. The method of multiple time scales is used to obtain periodic solutions for the second- and third-order systems, which directly leads to the solvability conditions of the two orders including the nonlinearity terms. Different cases of resonance with the instability criteria are taken into account. For the numerical application, the effect of the tensile periodic load was studied on a plate of graphite fabric-carbon material. [ABSTRACT FROM AUTHOR]

A geometric transformation method based on discrete singular convolution (DSC) is firstly applied to solve the buckling problem of a functionally graded carbon nanotube (FG-CNT)-reinforced composite skew plate. The straight-sided quadrilateral plate geometry is mapped into a square domain in the computational space using a four-node DSC transformation method. Hence, the related governing equations of plate buckling and boundary conditions of the problem are transformed from the physical domain into a square computational domain by using the geometric transformation-based singular convolution. The discretization process is achieved via the DSC method together with numerical differential and two different regularized kernels such as regularized Shannon's delta and Lagrange-delta sequence kernels. The accuracy of the present DSC results is first verified, and then, a detailed parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of the skew plate and skew angle on the axial and biaxial buckling responses of FG-CNTR composite skew plates with different boundary conditions. Some new results related to critical buckling of an FG-CNT-reinforced composite skew plate are also presented, which can serve as benchmark solutions for future investigations. [ABSTRACT FROM AUTHOR]

The buckling and parametric resonance characteristics of laminated composite spherical sandwich shell panels with viscoelastic material (VEM) core are investigated in the present analysis considering full geometric nonlinearity in the Green–Lagrange sense. The study includes the longitudinal strain and normal strain in the transverse direction along with transverse shear deformation of the VEM core. The core displacements are considered to be varying linearly along the thickness and those of the face sheets follow first-order shear deformation theory. An eight-noded sandwich shell finite element of the serendipity family is adopted to discretize the sandwich shell panel domain. The finite element-based equation of motion is derived using Hamilton's principle in the form of the Mathieu–Hill-type equation. The dynamic instability regions are obtained by applying Hsu's criteria-based Saito–Otomi conditions to the transformed equation motion. An in-house finite element-based code is developed in the MATLAB platform to solve the stability problem and to establish the stability regions. A parametric study is carried out to investigate the influence of different system parameters on the critical buckling load and the parametric resonance of the sandwich shell panels. It is noted that an increase in core and constraining layer thicknesses increases the critical buckling load of the sandwich shell panels. The stability boundaries are observed to shift toward a higher-excitation-frequency region in the stability diagram with an increase in constraining layer thickness and a decrease in aspect ratio. [ABSTRACT FROM AUTHOR]

A semi-analytical solution of thermal buckling and postbuckling equilibrium paths of rectangular composite plates subjected to localized thermal heating over the plate area with uniform temperature rise through its thickness is reported here. The plate is either simply supported or clamped for out-of-plane displacements and immovable for in-plane displacements. The thermal buckling of the composite plate subjected to localized thermal loading is solved in two steps as the prebuckling stress distributions within the plate are not known a priori. In the first step the explicit analytical expressions for these in-plane prebuckling stress distributions within the composite plate are developed by solving the thermoelasticity problem using Airy's stress function. Using the computed in-plane stress distributions within the plate, the plate nonlinear stability equations are formulated using a variational principle. First-order shear deformation theory incorporating von-Kármán geometric nonlinearity is used to model the plate. The generalized differential quadrature method in conjunction with the modified Newton-Raphson method is used to solve the nonlinear governing partial differential equations for nonlinear thermal stability of composite plates. The influence of aspect ratio, area of heated region, and the boundary conditions on the critical buckling temperature and equilibrium paths are examined. [ABSTRACT FROM AUTHOR]