BITS Faculty Publications

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Author: search.filters.author.Patel, Shuvendu Narayan

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    Geometric nonlinear buckling behaviour of randomly distributed carbon nanotube and fibre reinforced hybrid stiffened composite plates: Effect of CNT agglomeration
    (Elsevier, 2025-10) Patel, Shuvendu Narayan; Kumar, Rajesh; Watts, Gaurav
    This article investigates buckling and geometric nonlinear buckling response of stiffened composite plates reinforced with randomly distributed carbon nanotubes and hybrid composites embedded with carbon nanotubes and carbon fibres, using the finite element method. Carbon nanotubes (CNTs) tend to agglomerate into spherical inclusions within matrix due to weak Van der Waals force of attraction between them, which reduces mechanical properties and affects the structural performance. Eshelby-Mori-Tanaka homogenisation method, which incorporates CNT agglomeration, is employed to determine mechanical properties of randomly distributed carbon nanotube reinforced composite (RD-CNTRC) plates, which are further used in mixture rule to estimate mechanical properties of carbon nanotube and fibre reinforced hybrid composite (CNT-FRHC) plates. The plate and stiffener are modelled by isoparametric formulation based on first-order shear deformation theory (FSDT). The plate is modelled by eight-nodded degenerated shell element, and stiffener is modelled by 3-nodded curved beam element. Buckling analysis is performed by solving eigenvalue equation, and postbuckling behaviour is traced by Crisfield's arc-length method. Accuracy of present finite element formulation is validated with different examples from literature, followed by buckling and postbuckling analysis of RD-CNTRC and CNT-FRHC plates under different non-uniform loads. A distinct behaviour is observed in RD-CNTRC plates, where the transverse displacement reduces at the plate's centre due to increased stresses. A parametric investigation includes the influence of CNT volume fraction, agglomeration types, agglomeration parameters, loads, and stiffener parameters on buckling and postbuckling behaviour of RD-CNTRC and CNT-FRHC plates.
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    Postbuckling behaviour of functionally graded carbon nanotube reinforced stiffened composite plate under non-uniform loadings
    (Elsevier, 2025-11) Patel, Shuvendu Narayan; Watts, Gaurav; Kumar, Rajesh
    Understanding buckling and postbuckling characteristics of composite plates is essential to ensure lightweight, safe and optimized design of aerospace, marine and civil structures under in-plane loads. The main contribution of the study is investigation of buckling and postbuckling behaviour of functionally graded carbon nanotube (FG-CNT) reinforced stiffened composite plates under various non-uniform in-plane loading conditions. Carbon nanotubes (CNTs) are embedded through the plate thickness in both uniform distribution (UD) and functional gradation (FG) patterns including FG-X, FG-O and FG-V. Finite element method based on first order shear deformation theory (FSDT) is employed in isoparametric formulation of the plate and stiffener. The plate is modelled with eight-noded degenerated shell element, while the stiffener is modelled by three-noded degenerated curved beam element. Layer-wise effective mechanical properties of FG-CNTRC plate are estimated by extended rule of mixture. Buckling loads are determined by solving eigenvalue equation, while postbuckling behaviour is studied by solving nonlinear equilibrium equation using arc-length method. Accuracy of the present formulation is verified with existing analytical, experimental, and finite element results. Results show that adopting functional gradation approach can enhance buckling and postbuckling performance for constant CNT volume fraction. The addition of stiffeners further improves structural stability of FG-CNTRC plates. A detailed parametric study examines the influence of CNT volume fraction, CNT configuration, number of stiffeners, and unidirectional and bidirectional non-uniform in-plane loading types on buckling and postbuckling performance of FG-CNTRC plates.
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    A meshfree formulation for size-dependent thermal buckling and post-buckling behaviour of porous microplates on elastic foundation subjected to localized heating
    (Springer, 2025-01) Kumar, Rajesh; Patel, Shuvendu Narayan; Watts, Gaurav
    This article introduces a novel semi-analytical solution for the aggregation equation utilizing the Temimi–Ansari Method in conjunction with Pade approximants. The methodology is further adapted to address coupled aggregation–fragmentation equations, owing to the demonstrated accuracy and efficiency in handling aggregation equations. The study conducts a comprehensive convergence analysis and establishes error bounds for the proposed method. Various test cases are examined to demonstrate the efficacy of the methodology. Comparative assessments between approximated and exact solutions reveal a noteworthy concordance over an extended temporal domain, thereby addressing a substantial void in the existing literature. In the study conducted by Arora et al. (J Comput Sci 67:101973, 2023), it is noteworthy to highlight that the variational iteration method demonstrates superior quantitative accuracy in comparison to both Adomian decomposition and homotopy perturbation methods. Additionally, it is observed that the Temimi–Ansari Method yields comparable accuracy to the variational iteration method but requires less computational time. Simultaneously, the Temimi–Ansari Method, when coupled with Pade approximants, exhibits superior quantitative accuracy compared to the variational iteration method. As a result, the presented article showcases a notable advancement in solutions, surpassing the accuracy of prevailing semi-analytical solutions documented in the literature. The discrepancies between the exact and the derived series solutions are presented through graphical plots and tables, affirming the applicability and precision of the proposed approach.
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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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    Nonlinear dynamic instability and dynamic response of stiffened laminated composite plates subjected to in-plane pulsating patch loading
    (Taylor & Francis, 2023-11) Patel, Shuvendu Narayan
    In this article, the nonlinear dynamic instability of stiffened laminated composite plates is studied in the finite element (FE) framework subjected to uniform in-plane harmonic patch loading. The harmonic load is applied to the two opposite sides of the stiffened plate. The linear and nonlinear time-history response analysis is also studied. The skin and the stiffener are modeled using an eight-node isoparametric degenerated shell element and a three-node curved beam element, respectively. A system of matrices is developed by considering the Green–Langrange strain–displacement relationship. In the linear case, the Bolotin method is used to analyze the dynamic instability region (DIR). The nonlinear instability behavior of the laminated composite stiffened plate is studied by applying the Incremental Harmonic Balance Method (IHB). The Newmark-β method is used to solve the linear and nonlinear time-history response equations to understand the instability behavior of the stiffened plates. The effect of the parameters such as the length of the in-plane loading patch, varying number of stiffeners in x-direction and the position of the patch on the nonlinear vibrations and nonlinear dynamic response is examined.
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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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    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 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.