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This work presents an efficient and original high-order shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

A non-local plate model is proposed based on Eringen's theory of non-local continuum mechanics. The basic equations for the non-local Kirchhoff and the Mindlin plate theories are derived. These non-local plate theories allow for the small-scale effect which becomes significant when dealing with micro-/nanoscale plate-like structures. As illustrative examples, the bending and free vibration problems of a rectangular plate with simply supported edges are solved and the exact non-local solutions are discussed in relation to their corresponding local solutions.

To address the interfacial failure problem while maintain the main advantageous features in layered sandwich structures, a novel functionally graded (FG) porous plate is proposed where the continuous gradient in material properties based on a graded porosity offers a smooth stress distribution along the plate thickness so that the remarkable stress mismatch that leads to interfacial failure in the conventional sandwich structures can be avoided. The FG porous plate is assumed to be made of closed-cell Aluminium foams with Young's modulus, shear modulus, mass density and Poisson's ratio varying across the thickness. The mechanical property of closed-cell solids is used to determine the relationship between porosity coefficient and mass density coefficient. Based on the first-order shear deformation plate theory, the governing equations are derived and then solved by employing Chebyshev polynomials based Ritz method. The uniaxial, biaxial and shear buckling loads, bending deflections and stresses are obtained for fully clamped and simply supported porous plates. Numerical results show that compared with the conventional layered sandwich plate with a uniform porous core, the proposed FG porosity can eliminate the stress mismatch and yield significantly improved buckling and bending performances, promoting the advance and application of porous structures in multiple engineering areas.

In this article, isogeometric analysis (IGA) based on the modified nonlocal couple stress theory (MNCST) is introduced to study bending and free vibration characteristics of functionally graded (FG) nanoplates placed on an elastic foundation (EF). The MNCST is a combination of nonlocal elasticity theory and modified couple stress theory to capture the small-size effects most accurately, hence this theory considers both softening and stiffening effects on responses of FG nanoplates. A higher order refined plate theory is adapted, because it satisfies parabolic distributions of transverse shear stresses across the nanoplate thickness and equals zero at the top and bottom surfaces without requiring shear correction factors. The governing equations are obtained using Hamilton's principle from which deduce the equations determining the natural frequency and displacement of the FG nanoplates. Several comparison studies are conducted to verify the proposed model with other results in the literature. Furthermore, the influence of nonlocal parameters, material length parameters, boundary conditions, material volume exponent on the bending, and free vibration response of FG nanoplates are fully studied.

This paper investigates the low-velocity impact response of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene nanoplatelets (GPLs) in which GPLs are randomly oriented and uniformly dispersed in the polymer matrix within each individual layer with GPL weight fraction following a layer-wise variation along the plate thickness. The micromechanics-based Halpin–Tsai model is used to evaluate the effective material properties of the GPL-reinforced composite (GPLRC), and the modified nonlinear Hertz contact theory is utilized to define the contact force between the spherical impactor and the GPLRC target plate. The equations of motion of the plate are derived within the framework of the first-order shear deformation plate theory and von Kármán-type nonlinear kinematics and are solved by a two-step perturbation technique. The present analysis is validated through a direct comparison with those in the open literature. A parametric study is then performed to study the effects of GPL distribution pattern, weight fraction, geometry and size, temperature variation as well as the radius and initial velocity of the impactor on the low-velocity impact response of functionally graded GPLRC plates.

A semi-analytical methodology on the sound transmission of stiffened laminated plate under different reinforcement forms is developed to explore its sound insulation performance under the action of a plane sound wave load, in accordance with the classical laminated plate theory and in consideration of stiffener flexion and torsional motions. The formula of acoustic transmission loss is obtained by utilizing spatial harmonic expansion and the virtual work principle. Subsequently, the predicted values of proposed methodology are validated by the existing models. Eventually, some characteristic parameters are considered to investigate their effects on sound insulation behavior.

The purposes of this paper are to study bending, buckling, and vibration by considering micro-scale effects using the Kirchhoff thin-plate theory and to consider small deflections, neglecting higher-order nonlinear terms. The governing equations for the bending, buckling, and vibration of the system are obtained using the equilibrium method coupled with the Kirchhoff thin-plate theory and a modified couple stress theory (MCST). The concept of the equivalent bending stiffness (EBS) of micro-thin plates is proposed to describe the scale effect. The Navier method is used to obtain analytical solutions for the bending, buckling, and free vibration of thin plates under simply supported boundary conditions with scale effects. The numerical results are presented to investigate the influence of scale effects on deflection, critical buckling load, buckling topography, and thin-plate natural frequency. The results show that the scale effect increases the equivalent stiffness of the thin plate, which leads to a decrease in deflection, a larger critical buckling load, and an increase in natural frequency, but does not affect the buckling topography. The MSCT is invalid when the thickness is greater than 10 times the scale effect parameter, thus defining the scope of application of the scale effect. This research study may contribute to the design of micro-scale devices such as MEMSs/NEMSs.

In this article, the free vibration response of sandwich plates with porous electro-magneto-elastic functionally graded (MEE-FG) materials as face sheets and functionally graded carbon nanotube-reinforced composites (FG-CNTRC) as core is investigated. To this end, four-variable shear deformation refined plate theory is exploited. The properties of functionally graded material plate are assumed to vary along the thickness direction of face sheets according to modified power-law expression. Furthermore, properties of FG-CNTRC layer are proposed via a mixture rule. Hamilton’s principle with a four-variable tangential–exponential refined theory is used to obtain the governing equations and boundary conditions of plate. An analytical solution approach is utilized to get the natural frequencies of embedded porous FG plate with FG-CNTRC core subjected to magneto-electrical field. A parametric study is led to fulfill the effects of porosity parameter, external magnetic potential, external electric voltage, types of FG-CNTRC, and different boundary conditions on dimensionless frequencies of porous MEE-FG sandwich plate. It is noteworthy that the numerical consequences can serve as benchmarks for future investigations for this type of structures with porous mediums.

In this paper, the bending behavior of rectangular plates with stepped thickness resting on an elastic half-space foundation is investigated through an analytic method. Combined with the bending theory of the rectangular thin and moderately thick plate, the stepped rectangular plate is divided into upper and lower plates, and the Fourier series is used to obtain the analytical solution of the deflection of the plate and the interaction force between the plate and foundation. The influence of the elastic modulus of the plate, plate theory, and the dimension of the plate on the deflection of the stepped rectangular plate is also discussed. The results show that the analytical solution is basically the same as the existing research results, and it is also verified by the analysis results of the models established by ABAQUS software. The deflection at the center of the stepped rectangular plate increases with the increase of the elastic modulus of the upper plate and the decrease of the side length of the upper plate, while the plate theory has little effect on the deflection of the plate. This method not only overcomes some of the disadvantages of numerical methods but also eliminates the assumptions of the Winkler foundation model and the two-parameter foundation model, thus obtaining a more reasonable and accurate bending performance of the stepped rectangular plate resting on the elastic half-space foundation.

In recent years, research and applications of bioinspired structures in advanced engineering fields have gained increased attention from the research community, thanks to their fascinating properties. In this study, we address an efficient computational approach for performing nonlinear static and dynamic analyses of functionally graded plates based on triply periodic minimal surface architectures for the first time. We named a functionally graded triply periodic minimal surface (FG-TPMS) plate. A key idea of modelling FG-TPMS plates is to rely on the four-unknown refined quasi-3D plate theory, von-Kármán assumptions, and NURBS-based isogeometric analysis. The nonlinear behavior of three TPMS structures including Primitive (P), Gyroid (G), and I-graph and Wrapped Package-graph (IWP) under various conditions are intensively studied in this work. To estimate the effective mechanical features of the TPMS architectures, we utilize a two-phase fitting model with respect to the relative density. The influence of several parameters of TPMS structures on the nonlinear static and dynamic characteristics is evaluated. In addition, four types of dynamic loads including rectangular, triangular, half-sine, and explosive blast are also considered here. The key contribution of this study is the development of an efficient and powerful nonlinear numerical model to explore the static and dynamic behavior of TPMS architectures-based FG plates. The present method not only effectively accounts for the thickness stretching effect but also includes the consideration of structural damping, thereby facilitating a more accurate solution to engineering problems under real-world conditions. Furthermore, the current results indicate that FG-TPMS plates exhibit a superior energy absorption capacity compared to isotropic ones of the same weight under geometric nonlinearity conditions. Finally, the findings obtained from this study enhance our understanding of nonlinear behavior as well as provide valuable design strategies for future advanced engineering structures based on TPMS architectures.