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Graphene is a highly conductive and exceptional material that has shown potential for significantly improving the piezoelectric and mechanical properties of piezoelectric matrix. This paper examines the stability of composite plates surface bonded with graphene‐reinforced composite piezoelectric (GRCP) actuators. However, the significant differences in material characteristics at the interfaces will pose some challenges in analyzing the buckling behavior of piezoelectric composite plates by means of existing higher‐order shear deformation theories. To address this issue, a refined plate theory is developed for the buckling analysis of piezoelectric composite plates. The developed theory includes a new interlaminar shear stress field that precisely describes the distribution of interlaminar shear stresses, which differs from earlier higher‐order theories. It should be emphasized that the finite element formulation can be simplified by removing the second‐order derivatives of in‐plane displacement parameters from interlaminar shear stresses. In terms of the developed theory, a four‐node C0 quadrilateral plate element is introduced to examine the buckling behavior of piezoelectric composite plates. Furthermore, the modified interlaminar shear stress field is absorbed into the strain energy, significantly improving the ability to predict the critical loads of composite plates with GRCP actuators. The refined plate model is evaluated through the utilization of three‐dimensional (3D) elasticity solutions and results obtained from other associated theories. Numerical results demonstrate that the refined plate model is capable of producing favorable results, and a comprehensive examination is conducted to analyze the effects of significant parameters on the buckling behaviors of piezoelectric composite plates. This study sets a solid foundation for future research and development on the application of graphene‐reinforced composite piezoelectric actuators in composite structures. Highlights: Buckling analysis of composite plates with GRCP actuators is conducted.A refined plate theory with modified interlaminar shear stresses is developed.The ability to predict critical loads can be significantly improved.The finite element formulation can be simplified based on the proposed model.Comprehensive parametric studies on buckling behavior are caried out. [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]

Graphene is recognized as one of the most alluring reinforcements for composite materials due to its exceptional mechanical capabilities. However, the existing models disregarding the compatible requirements of interlaminar stresses in the literature may meet severe challenges for the dynamic analysis of functionally graded graphene-reinforced composite (FG-GRC) laminated thick plates. If transverse shear deformations cannot be described accurately, the prediction of natural frequencies for FG-GRC laminated plates will be seriously and directly affected. Accordingly, an attractive plate theory in conjunction with the analytical approach and finite-element formulation is proposed for free vibration analysis of FG-GRC plates. An improved transverse shear stress field is acquired in terms of the three-dimensional (3D) elasticity equations and the Reissner mixed variational theorem (RMVT). The performance of the suggested model was evaluated using 3D elasticity solutions and the results obtained from other models. Numerical results showed that the suggested model can produce promising results for the thick laminated and sandwich plates. Additionally, a thorough investigation was conducted to study the effects of several graphene parameters, including volume fractions, distribution patterns, span-to-thickness ratios, aspect ratios, boundary conditions, and stacking sequences, on the dynamic responses of FG-GRC laminated plates. [ABSTRACT FROM AUTHOR]

Nowadays, graphene is considered as one of the most ideal reinforcements for composite materials due to the outstanding mechanical properties. From the literature survey, it is found that the researches on interlaminar stress analysis of functionally graded graphene reinforced composite (FG-GRC) laminated structures are scarce in literature. If transverse shear deformations are unable to be described accurately, the reasonable design of FG-GRC laminated structures will meet severe challenges due to the differentiation of material properties at the adjacent layers. Thereby, such issue is less studied by using the efficient models, so an advanced mixed-form plate theory is to be proposed for transverse shear stress analysis of FG-GRC laminated plates. The proposed theory can meet beforehand compatible conditions of transverse shear stresses at the interfaces of adjacent laminates and only contains seven independent displacement variables. By applying the three- dimensional (3D) equilibrium equations and the Reissner mixed variational theorem (RMVT), the accurate transverse shear stresses are obtained. The 3D elasticity solutions and the results computed by using the chosen models are selected to appraise the capability of the proposed model. Numerical results show that the proposed plate model can yield accurately transverse shear stresses without any post-processing procedure. In addition, the effects of graphene volume fraction, graphene distribution pattern, lamination sequence, span-to-thickness ratio and aspect ratio on the displacements and stresses of the FG-GRC laminated plates are thoroughly investigated. [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]

In this article, an accurate mixed zigzag theory (HZZTM) is proposed for free vibration analysis of laminated composite and sandwich plates. In-plane displacements in the proposed zigzag theory nonlinearly distribute through the thickness and exhibit an abrupt discontinuity of slope at interfaces, which coincide with three-dimensional analysis. In order to obtain the accurate transverse shear stresses, a preprocessing approach based on the three-dimensional (3D) equilibrium equations and the Reissner mixed variational theorem (RMVT) is used. It is significant that the second-order derivatives of in-plane displacement variables have been removed from the transverse shear stress fields, such that the finite element implementation is greatly simplified. Thus, based on the proposed zigzag model, a computationally efficient C0-type three-node triangular plate element with linear interpolation function is proposed for free vibration analysis of thick laminated composite and sandwich plates. Moreover, the accurate transverse shear stresses are introduced in the dynamic equilibrium equation by employing the Hamilton's principle, which can actively improve the accuracy of natural frequencies of the laminated composite plates with different thickness and material properties at each ply. Performance of the proposed model is assessed by comparing with several benchmark solutions. Agreement between the present results and the reference solutions is very good, and the proposed model only includes the seven displacement variables which can demonstrate the accuracy and effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

An accurate and computationally attractive global-local higher-order theory (GLHT) is developed for the linearly elastic analysis of cross-ply multilayered composite plates. The theory is derived using the kinematic assumptions of GLHT in conjunction with the Reissner mixed variational principle. For a low-order linear element, it is difficult to accurately compute the transverse shear stresses even applying the three-dimensional equilibrium equation post-processing technique. The reason for this difficulty is that the higher-order derivatives of displacement variables are included in the transverse shear stress fields after using the post-processing technique. Thus, by employing the Reissner mixed variational principle, the higher-order derivatives of displacement variables have been removed from the transverse shear stress components before the finite element procedure is implemented. Based on the mixed GLHT, a computationally efficient C0-type three-node triangular plate element with linear interpolation function is proposed for the analysis of multilayered composite plates. The advantage of the present formulation is that no post-processing approach is needed to calculate the transverse shear stresses while maintaining the computational accuracy of a linear plate element. Performance of the proposed element is assessed by comparing with several benchmark solutions. Numerical results show that the present elements can robustly and accurately predict the displacements and stresses of multilayered composite plates. [ABSTRACT FROM AUTHOR]

Graphene is considered to be a desirable reinforcement material for composite materials due to its exceptional mechanical properties. However, there is a lack of research on the interlaminar stress analysis of graphene reinforced composite plates bonded with a macro fiber composite (MFC) actuator subjected to electro- mechanical loads. Inaccurate descriptions of interlaminar shear deformations can significantly affect the mechanical performance of the MFC piezoelectric graphene reinforced composite plate due to the electro-mechanical coupling feature and abrupt change in material properties at the interfaces of neighboring layers. To address this issue, this study proposes an attractive plate model for the analysis of MFC piezoelectric laminated plate. The three-dimensional (3D) elasticity equations and the Reissner mixed variational theorem (RMVT) are employed to improve the precision of interlaminar shear stresses. The 3D elasticity solutions and results obtained from other models are used to evaluate the proposed model. Furthermore, this study thoroughly investigates the effect of several significant parameters on the deformations and stresses of the MFC piezoelectric plates with reinforcements. [ABSTRACT FROM AUTHOR]

In this paper, an efficient improved C 0 -type global–local model (IGLM) considering transverse normal strain is proposed to study the hygrothermal response of thick cross-ply laminated composite plates. Based on the interlaminar continuity conditions of in-plane displacement and transverse shear stresses, layer-dependent variables could be reduced. Employing shear stress free condition at the upper and the lower surfaces, derivatives of transverse displacement are eliminated from the displacement field, so that C 0 interpolation functions are only required for the finite element implementation. As a result, the number of variables is independent of the number of layers of the laminate. To assess the proposed model, the classical quadratic eight-node isoparametric element is presented, in which the interelement C 0 continuity conditions are satisfied. Comparing the results from available three-dimensional elasticity theory and those computed from the ninth-order model, it is found that the simple C 0 finite elements could produce promising deformations and stresses for thick cross-ply laminated composite plates with different boundary conditions under hygrothermal loadings. [ABSTRACT FROM AUTHOR]

Graphene is regarded as one of the most attractive reinforcements for composite materials attributing to the extraordinary physical characteristics. However, existing models in the literatures might meet severe challenges for the interlaminar stress prediction of functionally graded graphene reinforced composite (FG-GRC) laminated thick plate integrated with piezoelectric fiber reinforced composite (PFRC) actuator under electro-mechanical loadings. If transverse shear deformations cannot be described accurately, the mechanical performance of FG-GRC laminated plate with PFRC actuator will be significantly impacted by the electro-mechanical coupling effect and the sudden change of material characteristics at the interfaces. Thereby, a new electro-mechanical coupled plate model with only seven independent displacement variables is to be proposed in this paper. Employing the Reissner mixed variational theorem (RMVT), the precision of the transverse shear stresses considering the electro-mechanical coupling effect can be improved. Moreover, the second-order derivatives of in-plane displacement parameters have been removed from the transverse shear stress components, which can greatly simplify the finite element formulation. Thus, based on the proposed electro-mechanical coupled plate model, a simple C0-type finite element formulation is developed for interlaminar shear stress analysis of FG-GRC laminated thick plate with a PFRC actuator. The 3D elasticity solutions and the results obtained from other models are used to assess the performance of the proposed finite element formulation. Additionally, comprehensive parametric studies are achieved for the influences of graphene volume fraction, distribution pattern, electro-mechanical loading, boundary conditions, lamination scheme and geometrical parameters of the plate on the deformations and stresses of the FG-GRC laminated plate with a PFRC actuator. • A new electro-mechanical coupled plate model is developed in this paper. • The improved transverse shear stresses considering the electro-mechanical coupling effect are derived. • Interlaminar stress analysis of FG-GRC laminated plates with a PFRC actuator is conducted. • Comprehensive parametric studies on the FG-GRC laminated plate with a PFRC actuator are carried out. [ABSTRACT FROM AUTHOR]

With the advantage of outstanding mechanical characteristics, carbon nanotube (CNT) is nowadays considered as one of the most ideal reinforcements for composite materials. Mechanical properties of functionally graded carbon nanotube reinforced composite (FG-CNTRC) structures have been extensively investigated in the published literature. However, analytical results on transverse shear stresses of smart FG-CNTRC plates subjected to electro-mechanical loadings are scarce in literature. To fill this gap, a refined plate theory is proposed for bending analysis of laminated FG-CNTRC plates integrated with a piezoelectric fiber reinforced composite (PFRC) actuator. The kinematic assumptions of the proposed plate theory are obtained by superimposing an efficient zigzag function on the first-order shear deformation theory. Laminated FG-CNTRC plates with four distribution types of CNT through the thickness are considered. The governing equations are obtained by using the principle of minimum potential energy and the Navier's method is used to solve the boundary value problem. The present results are compared with the three-dimensional (3D) elasticity solutions and the results computed by using the chosen models. Numerical results show that the proposed zigzag function can effectively improve the accuracy of proposed plate model in predicting the displacements and stresses. In order to understand clearly the static behaviors of smart FG-CNTRC plates, the influences of electro-mechanical loading, CNT distribution through the thickness direction, CNT volume fraction and span-to-thickness ratio are thoroughly investigated. • The laminated FG-CNTRC plates integrated with a PFRC actuator are analyzed by using an efficient zig-zag model. • The proposed zig-zag model can accurately predict the displacements and stresses of smart FG-CNTRC plates. • Laminated FG-CNTRC plates with four distribution types of CNT through the thickness are considered. • The effects of electro-mechanical loading, CNT distribution, volume fraction and span-to-thickness ratio are investigated. [ABSTRACT FROM AUTHOR]