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AbstractThis work presents a static and vibration analysis of a porous functionally graded (FG) microplate using a simplified quasi-3D plate formulation and a modified couple stress theory that requires only one material length scale parameter. The theory contains only five unknowns, incorporating undetermined integral variables in accordance with the first-order shear deformation theory (FSDT). The model satisfies the zero traction boundary conditions on the upper and lower surfaces of the microplate. The governing equations are obtained via Hamilton’s principle and subsequently solved using Navier-type closed-form solutions. The proposed theoretical model is validated by comparing it with existing models in the literature to demonstrate its efficacy. The influence of the length scale parameter, the power law index, shear and normal deformation effects, porosity factors, and plate thickness on the responses of microplates is examined through the presentation of numerical examples. The findings show that taking size effects into account increases the stiffness of the microplate, which in turn reduces deflections and raises natural frequencies. Conversely, the normal and shear deformation influences have the opposite impact. [ABSTRACT FROM AUTHOR]

In this paper, a comprehensive dynamical analysis of porous-reinforced carbon nanotube (CNT) nanocomposite beams on viscoelastic foundations is presented. Using a three-unknown shear beam theory, the two-nodded finite element model was formulated and adapted for both C1 and C0 continuities for displacement variables. This model captured the distinct characteristics and interactions of the porous medium, CNT reinforcements, and the intrinsic damping introduced by the viscoelastic foundation. The dynamical investigation incorporates both free and forced vibration analysis, and the Newmark method is employed for time-dependent analysis, ensuring accurate temporal behavior prediction. The study also emphasizes the impact of different CNT distribution patterns and porosity variations on the mechanical properties of the beams, particularly in terms of stiffness and damping characteristics. Further depth is added by analyzing the interactions between beams and both Winkler and Pasternak foundation models, with findings that highlight the importance of foundation parameters in the overall dynamic response. The results shed light on the critical role each component plays in the composite beam’s dynamic response, offering insights for potential innovative designs and applications in both advanced structural engineering and nanotechnology domains. [ABSTRACT FROM AUTHOR]

The current investigation proposes an enhanced finite element beam model to assess the dynamic behavior of functionally graded sandwich beams with variable cross-sections. By integrating the shear effect, this beam model integrates both C0 and C1 continuities to generate elementary matrices using an efficient three-unknown shear deformation beam theory. The model focuses on advanced sandwich beams with functionally graded material face-sheets and metallic cores, exploring various geometric arrangements. The originality of this study addresses variable cross-sections in sandwich beams, evaluating the influence of material composition and geometric configurations on free and forced vibration responses, including different boundary conditions. The methodology uses the eigenvalue method for examining free vibration and applies Newmark's algorithm for solving forced vibration problems. The current model expands the scope of analysis compared to previous models that primarily focus on uniform cross-sections and conventional material distributions. The developed model incorporates non-uniform geometrics, material gradient parameters, and advanced finite element analysis to enhance precision and efficacy through detailed parametric investigations and comparisons with existing literature. This contribution significantly improves the mechanical modeling of composite sandwich structures, particularly those incorporating functionally graded materials and complex geometrical aspects. [ABSTRACT FROM AUTHOR]

The current inquiry aims to scrutinize the porosity's effect on the buckling response of carbon nanotube reinforced composite (CNTRC) imperfect beams. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. Single-walled carbon nanotubes (SWCNTs) are distributed and aligned in a polymeric matrix with various reinforcement patterns to create CNTRC porous beams. The material properties of the functionally graded beam determined using the mixture rule are assumed to vary according to the power law distribution of the volume fraction of the constituents. The mathematical models presented in this study are validated through numerical comparison with existing results. The new buckling results of carbon nanotube-reinforced porous beams are analyzed considering the influence of several parameters, including volume fraction, aspect ratios, degree of porosity, and types of reinforcement. The results stipulate that the above parameters play a significant role in the critical buckling load variation. It is proclaimed that the critical buckling load dwindled as porosity increased and that the X-CNT reinforced beam has a high resistance against buckling compared to other reinforcement types. [ABSTRACT FROM AUTHOR]

This paper investigates the free vibration of functionally graded material (FGM) sandwich plates supported by different boundary conditions and influenced by a three-parameter viscoelastic foundation and hygro-thermal changes. Three types of FGM sandwich plates are studied and discussed, in which the FGM layers vary according to the power law rule and consist of ceramic and metal materials. An efficient and simple four-variable integral higher-order shear deformation theory (HSDT) is employed to model the analytical solution of the considered problem. Hamilton principle is implemented to obtain the plates' governing equations and to derive the eigenvalue equation for the free vibration study. The model is verified by comparing numerical results with previous studies on the vibration of exponentially graded plates. New results are presented in this paper showing the influences of different boundary conditions, hygro-thermal changes, viscoelastic parameters, vibration modes, material exponents, and geometric dimensions. [ABSTRACT FROM AUTHOR]

AbstractThis paper uses a quasi-3D refined shear deformation plate theory to investigate the buckling response of supported functionally graded (FG) porous sandwich (SW) plates. The material properties of FG sandwich porous plates (SWPPs) are defined by a modified mixing rule, supplemented by an additional term representing the porosity in the thickness of the FG layer. By incorporating indefinite integral variables, the number of unknowns and governing equations of the current theory is reduced, making it easier to use. Three common types of sandwich porous plates are considered in the analysis: an isotropic FG porous plate, an FG face plate with a homogeneous core, and a homogeneous face plate with an FG core. The current method considers both normal and shear deformations and satisfies the transverse shear stress-free boundary conditions at the top and bottom surfaces of the plate. The equilibrium equations are derived using the principle of virtual displacements. These equations are then solved using the Navier-type method. The influence of thickness strain and several parameters, including mechanical loads, porosity coefficients, layer thickness ratios, geometric parameters, and gradient indices, are studied. The numerical results of the present theory are similar to the predictions of quasi-3D theories with more unknowns, in addition to being more accurate than those obtained by higher-order shear deformation theories. The findings support the idea that the suggested theory offers an easy and effective method for predicting the buckling behavior of FG porous sandwich plates. The results show that, without taking into account transverse normal deformations, the plate is softer and the critical buckling load decreases. On the other hand, with transverse normal deformations, the plate is stiffer, which increases the critical buckling load. [ABSTRACT FROM AUTHOR]