BITS Faculty Publications

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Author: search.filters.author.Kumar, RajeshSubject: search.filters.subject.Civil Engineering

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    Tunable thermal postbuckling response of imperfect skew sandwich plates with auxetic core and FGCNTRC facings using isogeometric approach
    (Elsevier, 2024-04) Watts, Gaurav; Kumar, Rajesh; Patel, Shuvendu Narayan
    The present work investigates the stability characteristics of skew sandwich plates with functionally graded (FG) facings reinforced with carbon nanotubes having temperature-dependent properties and a re-entrant auxetic core with tunable material properties using isogeometric analysis. The continuous function for material properties of the CNTs is obtained by interpolating the parameters at different temperature values using the fourth-degree polynomial, and resultant properties for the facings are determined using the modified rule of mixtures with the efficiency parameters. The mechanical and thermal properties of the reentrant auxetic core are based on modified Gibson’s relations. The equations of equilibrium are derived using the principle of virtual displacements, which are discretised through the approximation of solution and geometrical variables using B-spline basis functions. Several parametric studies are conducted to study the influence of type and magnitude of initial geometric imperfection, CNT distribution pattern in facings, cell angle of the auxetic core, rib length to thickness ratio, skew angle and boundary conditions on linear and nonlinear thermal post-buckling characteristics of the sandwich plate. New findings on the influence of geometric imperfection and auxetic core parameters on the thermal postbuckling behaviour of sandwich plates are presented for the first time, which may contribute towards a better understanding of the stability behaviour of lightweight structures.
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    Buckling of Laminated Composite Plate with Imperfections Subjected to In-Plane Pulse Loads
    (Springer, 2021-06) Kumar, Rajesh; Patel, Shuvendu Narayan
    In this article, the stability of a laminated composite plate when subjected to in-plane compressive pulse load is investigated in the finite element method framework. Convergence and validation studies are carried out using the current mathematical formulation and compared with the results from the existing literatures. The effects of loading duration, imperfection and ply orientation on the dynamic buckling behavior of the plate with irregular imperfection are studied in detail and the results are reported. It is observed that the plate having irregular imperfection of the order of 20% of the plate thickness has a lower non-linear dynamic buckling load than the plate with 15% irregular imperfection.
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    Parametric Instability Analysis of Functionally Graded CNT-Reinforced Composite (FG-CNTRC) Plate Subjected to Different Types of Non-uniform In-Plane Loading
    (Springer, 2021-06) Kumar, Rajesh; Patel, Shuvendu Narayan
    Carbon nanotube has attracted many researchers from last two decades due to its exceptional mechanical and multiuse properties. In this article, a semi-analytical study is performed to determine the dynamic instability of a Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) plate exposed to uniform and various non-uniform in-plane loadings. The efficient mechanical properties for the plate are estimated using rule of mixture where CNTs are distributed aligned and distributed across the plates’ thickness such as Uniformly distributed (UD) and Functionally Graded (FG-X and FG-O). Here, The FG-CNTRC plate is modeled by means of higher order shear deformation theory (HSDT) and the stress distributions (σxx, σyy, τxy) within the plate because of non-uniform loadings are calculated using Airy’s stress method. Then, the Hamilton’s principle is applied to obtain the governing partial differential equations of the FG-CNTRC plate, and which is later solved with the help of Galerkin’s method to convert it to ordinary (Mathieu type) differential equations. Next, these Mathieu type equations are solved employing Bolotin’s method to trace the instability boundaries corresponding to period 2T. At last, the consequence of different parameters like volume fraction of CNT, types of non-uniform loading, static load factor, types of CNTs distribution on instability of the FG-CNTRC plate are examined.
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    Analytical and Numerical Study of Fractured Isotropic and Composite Plates Under Mode-I Crack Extension
    (Springer, 2022-04) Patel, Shuvendu Narayan; Kumar, Rajesh
    This paper deals with the study of fracture characteristics through the analytical method and FE (Finite Element) based methods of isotropic and anisotropic plates containing a central crack under uniform in-plane tensile load. In this study, mode I (opening mode) of fracture is considered. A governing differential equation is established for the plates and complex theory in terms of complex variables is employed to find stress functions to satisfy the equilibrium equation, compatibility equation and boundary condition at infinite distance and crack surfaces. An analytical solution which follows the Cauchy-Riemann conditions in the form of is introduced to study the stress characteristics at different positions of the plate. The effect of the uniform in-plane tensile load on the near field and far-field crack tip stress characteristics for mode-I crack is studied. ABAQUS/Standard software is used to carry out numerical analysis. The FEM results are compared with those of the analytical results. The damage parameters for composite plate is also studied.
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    Nonlinear Vibration of Functionally Graded CNT-Reinforced Composite Plate Under Nonuniform In-Plane Loading
    (Springer, 2022-04) Kumar, Rajesh
    In this study, a functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plate exposed to uniform and different forms of nonuniform in-plane loadings is analyzed for the determination of plate’s nonlinear vibration behavior (frequency-amplitude curve). Firstly, to guesstimate the effective mechanical properties of the FG-CNTRC plate, the extended rule-of-mixture technique is implemented when CNTs are aligned and distributed throughout the thickness of the plate. The different forms of CNTs distributions are considered, like - uniformly distributed (UD) and functionally Graded (FG-X type and FG-O type). Secondly, the FG-CNTRC is modeled based on higher order shear deformation theory (HSDT) including von-Kármán nonlinearity. Then, the distribution of stresses (σxx, σyy, τxy) within the plate because of nonuniform in-plane loading is estimated by resolving the in-plane elasticity problem using Airy’s stress approach. Thirdly, the governing partial differential equations (PDEs) of the FG-CNTRC plate are derived by employing Hamilton’s principle and solved using Galerkin’s method to convert these PDEs to the nonlinear ordinary differential equations (ODEs). Lastly, the Incremental Harmonic Balance (IHB) method are used to solve these nonlinear ODEs to trace the non-linear vibration behavior (frequency-amplitude curve) of the FG-CNTRC plate. The effect of different parameters like volume fraction of CNT, types of nonuniform loadings, types of CNTs distribution, and dynamic load factors on nonlinear vibration behavior of the FG-CNTRC plate are examined.
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    Nonlinear Vibration of Functionally Graded Porous-Cellular Timoshenko Beam Subjected to In-Plane Periodic Loading
    (Springer, 2022-07) Kumar, Rajesh
    The present study deals with an open cell shear deformable functionally graded porous beam subjected to in-plane periodic loading to analyze its nonlinear vibration behaviour. The porous beam in this study is modelled based on Timoshenko beam theory i.e., first-order shear deformation theory (FSDT). The porosities are dispersed throughout the thickness of the beam considering uniform and non-uniform symmetric distribution models. For the two distribution systems, the mass density and elasticity moduli of porous beams are considered to vary in the thickness direction. Using Hamilton’s principle, the partial differential equations (PDEs) governing the behaviour of porous beams are derived for the simply supported boundary condition. Then, Galerkin’s method is employed to convert the PDEs to nonlinear ordinary differential equations (ODEs). Further to trace the non-linear vibration behaviour (frequency-amplitude curve) of the porous beam, these ODEs are solved by Incremental Harmonic Balance (IHB) method. A parametric study is presented to assess the influence of porosity, static and dynamic load factors on the vibrational characteristics of the porous beams. As anticipated, the porous beam with non-uniformly symmetric distribution exhibited a higher critical buckling load compared to the uniform distribution of porosity
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    Postbuckling Study of the Laminated Composite Stiffened Plates Subjected to Parabolic In-Plane Loading
    (Springer, 2022-07) Patel, Shuvendu Narayan; Kumar, Rajesh
    This work is focused on the study of postbuckling aspect of laminated composite stiffened plates subjected to parabolic in-plane loading, using finite element method. The eight-noded degenerated shell element and the three-noded degenerated curved beam element with isoparametric formulation with C0 continuity (FSDT) of the primary variables are used to model the plate skin and stiffeners, respectively. The postbuckling analysis is carried out by solving the nonlinear load-deformation equation by Crisfield arc-length method. The results obtained from the present formulation are compared with available results to ensure accuracy of the formulation. The linear eigen-value buckling analysis is also performed to compare the results. The Green–Lagrange strain displacement relationship in total Lagrangian coordinate system is adopted in the formulation. The effect of different parameters like lamination scheme, number of layers, aspect ratio, stiffener depth and boundary condition, on the postbuckling response of the plates is considered in the present study.
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    Stability of Plates and Shell Panels Under Non-uniform In-Plane Loadings
    (Springer, 2022) Kumar, Rajesh
    In this chapter, the linear and non-linear stability analyses of plates and shell panels subjected to various types of non-uniform edge in-plane loadings are presented. Kinematics of the plates and panels are formulated based on higher-order shear deformation theory (HSDT) and incorporating von Kármán type of non-linearity. As the applied edge load is non-uniform, the pre-buckling stress distributions within the plates and shell panels are not known a priori. These stress distributions are obtained by solving in-plane elasticity problems. Using these stresses, the non-linear partial differential equations (PDEs) of the cylindrical shell panels and plates are developed by minimization of the total potential energy. These PDEs are reduced into a set of non-linear algebraic equations via Galerkin’s method when the plates and panels are reinforced with constant fibers orientation, and via the Ritz method when the plates and panels are reinforced with variable fibers orientation. After dropping the nonlinear terms, the buckling load of the plate/panel is computed via the associated eigenvalue problem. The post-buckling equilibrium path is traced by solving non-linear algebraic equations via the Newton–Raphson method in conjunction with Rik's approach. In the end, the influence of various types of non-uniform edge loadings, constant and variable fibers orientations and porosity distributions, and their magnitude on the buckling load and post-buckling equilibrium path are investigated in detail.
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    Stability and Failure Study of Suddenly Loaded Laminated Composite Cylindrical Panel
    (World Scientific, 2019) Patel, Shuvendu Narayan; Kumar, Rajesh
    In this paper, nonlinear dynamic buckling of laminated composite cylindrical panels subjected to in-plane impulsive compressive load is studied along with the failure analysis. Balanced and symmetric angle-ply laminated composite curved panels are considered. Convergence study is performed, and results are validated with the results from the existing literature, and then the dynamic buckling loads are calculated. The failure index of laminated composite curved panel is also calculated to check the precedence of first ply failure load over nonlinear dynamic buckling load. The effect of aspect ratio, loading function, and radius of curvature is studied. The analysis is carried out using finite element method. It is observed that the first ply failure for balanced and symmetric angle-ply laminated composite curved panels occurs after the panel has buckled due to dynamic impulse loads.
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    Forced nonlinear vibrations of circular cylindrical sandwich shells with cellular core using higher-order shear and thickness deformation theory
    (Elsevier, 2021-10) Kumar, Rajesh
    A geometrically nonlinear forced vibration analysis of circular cylindrical sandwich shells with open/closed cellular core using higher-order thickness and shear deformation theory is presented. The proposed sandwich shell comprises two thin face-sheets perfectly bonded to a functionally graded porous core. The face-sheets are made of carbon nanotubes (CNTs) reinforced composites. Three different types of porosity distribution, including two non-uniform and a uniform variation through the thickness, are considered. The effective mechanical properties of the core material, having open cells or closed cells, are determined using the Gibson and Ashby model. The rule-of-mixture, which includes efficiency parameters to account for scale-dependent properties of nanocomposite media, is adopted to obtain the mechanical properties of the face-sheets. The in-plane and transverse displacements of a generic point are assumed as a third and fourth-order polynomials of the through-the-thickness coordinate. The model is derived within the framework of an equivalent single layer (ESL) theory. Hamilton's principle is employed to obtain the nonlinear governing differential equations and further discretised by adopting the Galerkin method. Finally, the incremental harmonic balance (IHB) method, in conjunction with the arc-length continuation method, is used to solve the nonlinear system of coupled ordinary differential equations and compute the frequency-amplitude response. An extensive numerical study is carried out to examine the effects of the porosity coefficient, porosity distribution, core-to-face ratio and the volume fraction of CNTs in the face-sheets on the frequency-amplitude response of circular cylindrical sandwich shells.