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The post-buckling behavior of a hybrid functionally graded (FG) rectangular plate reinforced with carbon nanotubes (CNT) is presented. The mathematical model developed based on transverse displacement variation of second-order in third-order shear deformation theory, hence referred to as modified third-order shear deformation theory (MTSDT). Transverse shear stress is imposed zero on top and bottom surface of plate. 2D C0 finite element (FE) formulation model developed based on MTSDT. Inhouse MATLAB code developed of present FE formulation. The rectangular plates consist of matrix material, fiber, and CNT as reinforcement material. The grading of fiber material in the thickness direction ensured using a power–law distribution. The material characteristics of the hybrid FG plates predicted using the Halpin-Tsai equation and the rule of mixing technique. No shear correction factor is required due to realistic parabolic behavior considered in the present work. The comparison study results of the present model are in good agreement with the published work. After confirming the accuracy of the present model a parametric study was carried outd to check the influence of different parameters. [ABSTRACT FROM AUTHOR]

In this article, the static response of a functionally graded material (FGM) plate is studied via hybrid higher-order shear deformation theory which uses hyperbolic and polynomial shape functions and includes the effect of thickness stretching. The composition of the plate comprises metallic and ceramic phases. The ceramic volume fraction varies gradually along with the thickness following the power law. The mechanical properties of the FGM plate are determined by the rule of mixtures and the Mori–Tanaka homogenization scheme. The displacement fields are defined to satisfy the requirement of traction-free boundary conditions at the bottom and top surfaces of the plate surface removing the need for determination of shear correction factor. A C0 continuity FE model is developed for the present mathematical model. Nine-node isoparametric elements with eight nodal unknowns at each node are developed. The present model comparison with existing literature is completed and found to be coherent. Inhouse MATLAB code is developed for the present work. Sinusoidal and uniformly distributed loading is analyzed in the present work. The parametric study is undertaken to explore the effect of the side-to-thickness ratio, aspect ratio, thickness, and volume fraction index on stresses and transverse displacements. [ABSTRACT FROM AUTHOR]

The present paper investigates the axial and shear buckling analysis of a carbon nanotube (CNT)-reinforced multiscale functionally graded material (FGM) plate. Modified third-order deformation theory (MTSDT) with transverse displacement variation is used. CNT materials are assumed to be uniformly distributed, and ceramic fibers are graded according to a power-law distribution of the volume fraction of the constituents. The effective material properties are obtained using the Halpin–Tsai equation and Voigt rule of the mixture approach. A MATLAB code is developed using nine noded iso-parametric elements containing 13 nodal unknowns at each node. The shear correction factor is eliminated in the present model, and top and bottom transverse shear stresses are imposed null to derive higher-order unknowns. Comparisons of the present results with those available in the literature confirm the accuracy of the existing model. The effects of material components, plate sizes, loading types, and boundary conditions on the critical buckling load are investigated. For the first time, the critical buckling loads of CNT-reinforced multiscale FGM rectangular plates with diverse boundary conditions are given, and they can be used as future references. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to attempt the buckling analysis of a laminated composite skew plate using the C0 finite element (FE) model based on higher-order shear deformation theory (HSDT) in conjunction with minimax probability machine regression (MPMR) and multivariate adaptive regression spline (MARS). Design/methodology/approach: HSDT considers the third-order variation of in-plane displacements which eliminates the use of shear correction factor owing to realistic parabolic transverse shear stresses across the thickness coordinate. At the top and bottom of the plate, zero transverse shear stress condition is imposed. C0 FE model based on HSDT is developed and coded in formula translation (FORTRAN). FE model is validated and found efficient to create new results. MPMR and MARS models are coded in MATLAB. Using skew angle (α), stacking sequence (Ai) and buckling strength (Y) as input parameters, a regression problem is formulated using MPMR and MARS to predict the buckling strength of laminated composite skew plates. Findings: The results of the MPMR and MARS models are in good agreement with the FE model result. MPMR is a better tool than MARS to analyze the buckling problem. Research limitations/implications: The present work considers the linear behavior of the laminated composite skew plate. Originality/value: To the authors' best of knowledge, there is no work in the literature on the buckling analysis of a laminated composite skew plate using C0 FE formulation based on third-order shear deformation theory in conjunction with MPMR and MARS. These machine-learning techniques increase efficiency, reduce the computational time and reduce the cost of analysis. Further, an equation is generated with the MARS model via which the buckling strength of the laminated composite skew plate can be predicted with ease and simplicity. [ABSTRACT FROM AUTHOR]

Failure mode prediction of laminated composite sandwich plates is presented using improved higher order shear deformation theory (IHSDT) mathematical model and its C0 finite element (FE) implementation in FORTRAN. The proposed 2D IHSDT satisfies the inter-laminar shear stress continuity at each adjacent layer and nil transverse shear stress conditions at top and bottom of the plate are imposed. The parabolic shear stress variation is piecewise across thickness of each layer; hence no need of shear correction factors. The possible modes of failures are transverse matrix cracking, fiber breakage and inter-fiber shear failure of the matrix. The failure mode along with its location for laminated composite sandwich plates are obtained and are found in good agreement with the available 3D elasticity results. • Failure analysis of laminated composite sandwich plate is done first time by IHSDT. • The efficient C0 finite element modeling based on IHSDT is coded in FORTRAN. • Present 2D IHSDT results are quite close to 3D elasticity results. • Present model predicts better transverse shear stresses than HSDT/FSDT. • Failure results laminated composite sandwich plates may be useful for designers. [ABSTRACT FROM AUTHOR]

In the presented paper, a study of bi-axial buckling of the laminated composite plate with mass variation through the cutout and additional mass is carried out using the improved shear deformation theory (ISDT). The ISDT mathematical model employs a cubic variation of thickness co-ordinates in the displacement field. A realistic parabolic distribution of transverse shear strains through the plate thickness is assumed and the use of shear correction factor is avoided. A C° finite element formulation of the mathematical model is developed to analyze the buckling behavior of laminated composite plate with cutout and additional mass. As no results based on ISDT for the considered problem of bi-axial buckling of the laminated composite plate with mass variation are available in the literature, the obtained results are validated with the data available for a laminated composite plate without cutout and additional mass. Novel results are obtained by varying geometry, boundary conditions and ply orientations. [ABSTRACT FROM AUTHOR]