Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.

Smart damping of skew composite plates using Murakami zig-zag function

The present work is aimed at deriving a finite element model for active constraining layer damping treatment (ACLD) of layered skew plates by incorporating zig-zag behaviour using a Murakami zig-zag function (MZZF). The ACLD in skew patch form comprises of 1–3 PZC material and viscoelastic material in the layer form placed on substrate skew plate. The overall skew substrate ACLD system deformation kinematics are derived using MZZF and the equations of motion for the same are derived by virtual work method. A MATLAB subroutine for the overall skew plate ACLD system has been developed to present the closed loop frequency responses by successful implementation of closed-loop feedback system. The substrate skew plates with different lamination schemes namely symmetric/antisymmetric cross-ply and antisymmetric angle-ply are considered to assess the damping behavior of the skew plates undergoing ACLD. Also, the piezo-fiber angle (obliquely reinforced) variation of the PZC layer on the damping responses of the skew plates have been thoroughly examined.

Buckling of laminated composite skew plate using FEM and machine learning methods

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.

Vibration of Skew Plate with Circular Variation in Thickness and Poisson’s Ratio

The present study analyzes the natural vibration of non homogeneous visco elastic skew plate (parallelogram plate) with non uniform thickness under temperature field. Here non homogeneity in the plate’s material arises due to circular variation in Poisson’s ratio. Also the circular variation in thickness causes non uniformity in the shape of the plate. Bi linear temperature variation on the plate along both the axes is being viewed. The equation of motion related to frequency modes are solved by Rayleigh Ritz method. The findings of the present analysis are presented with the help of tables.