BITS Faculty Publications

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Author: search.filters.author.Watts, Gaurav

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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 vibration and instability of a randomly distributed CNT-reinforced composite plate subjected to localized in-plane parametric excitation
    (Elsevier, 2022-01) Kumar, Rajesh; Patel, Shuvendu Narayan; Watts, Gaurav
    This study presents a semi-analytical formulation for the nonlinear vibration and dynamic instability of a randomly distributed carbon nanotube-reinforced composite (RD-CNTRC) plate. Three cases of localized in-plane periodic loadings are studied. The analytical stress fields within the RD-CNTRC plate for all the in-plane stress components (σij, (i, j = x, y)) are developed by solving the in-plane elastic problem using Airy's stress approach. The effective mechanical properties of the RD-CNTRC plate are evaluated by the Eshelby-Mori-Tanaka technique. The plate is modeled based on higher-order shear deformation theory (HSDT) in conjunction with the von-Kármán nonlinearity. Using Hamilton's principle, the governing partial differential equations (PDEs) are derived, whose approximate solution is sought, referring to the Galerkin method. The resulting nonlinear ODEs are solved using the Incremental Harmonic Balance (IHB) Method to compute the nonlinear vibration response of the RD-CNTRC plate. Further dropping the nonlinear terms, these ODEs are solved by Bolotin's method to trace the instability region. The proposed semi-analytical method is an effective strategy for studying the influence of different parameters such as agglomeration models, CNT mass fraction, pre-loading, and boundary conditions on the nonlinear vibration and dynamic instability characteristics of the RD-CNTRC plates. The reduced computational effort allows the design phase to be supported in selecting parameters when designing RD-CNTRC plates with stability and vibration requirements.
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    Effect of Cutout on the Stability and Failure of Laminated Composite Cylindrical Panels Subjected to In-Plane Pulse Loads
    (World Scientific, 2022) Watts, Gaurav; Kumar, Rajesh; Patel, Shuvendu Narayan
    In this investigation, the nonlinear dynamic buckling analysis and the failure analysis of laminated composite cylindrical (LCC) panel with different shapes of cutouts under the action of rectangular in-plane pulse loads are performed in the finite element framework. Cross-ply laminates which are balanced symmetric are considered in the investigation. The first ply failure load (FPFL) of the panel is evaluated and checked whether it occurs before the nonlinear dynamic buckling phenomenon considering Tsai–Wu failure criterion. Convergence and validation studies are undertaken, and the results are compared with those from the existing literature. The effects of loading duration, cutout area and cutout geometry on the panel are investigated in detail and results are reported. The results indicate that for the panel with cutout, its dynamic buckling load (DBL), in certain cases, compared to the static buckling load (SBL), can be lower even if the loading duration is half of its first natural period. Additionally, the vibration and the static buckling analyses of the panels are carried out as and when required.
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    Postbuckling and postbuckled vibration behaviour of imperfect trapezoidal sandwich plates with FG-CNTRC face sheets under nonuniform loadings
    (Elsevier, 2022-08) Watts, Gaurav; Kumar, Rajesh; Patel, Shuvendu Narayan
    The present work investigates the postbuckling, and postbuckled vibration behaviour of initially imperfect trapezoidal sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets and FG porous metal foam core under the influence of non-uniform edge compression. The plate's kinematic assumptions are based on a refined higher order theory and the strain-displacement relations include von Karman assumptions for geometrical nonlinearity. The weak form of governing equations derived using Hamilton's principle is transformed into a discretized form of algebraic equations using the element free Galerkin (EFG) method in conjunction with moving kriging (MK) interpolation functions. The pre-buckling stresses are determined using static analysis to evaluate accurate critical buckling loads. Modified Riks technique is used to trace nonlinear equilibrium paths. Parametric studies include the effect of CNT distribution in face sheets, porosity distribution in the core layer and edge loading conditions on the nonlinear stability and vibration behaviour of sandwich plates. New results on trapezoidal sandwich plates with initial imperfections, hitherto not found in the literature, are presented for the first time, which can be used as benchmark solutions for further research.
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    Effect of Cutout on the Stability and Failure of Laminated Composite Cylindrical Panels Subjected to In-Plane Pulse Loads
    (World Scientific, 2022) Patel, S. N.; Kumar, Rajesh; Watts, Gaurav
    In this investigation, the nonlinear dynamic buckling analysis and the failure analysis of laminated composite cylindrical (LCC) panel with different shapes of cutouts under the action of rectangular in-plane pulse loads are performed in the finite element framework. Cross-ply laminates which are balanced symmetric are considered in the investigation. The first ply failure load (FPFL) of the panel is evaluated and checked whether it occurs before the nonlinear dynamic buckling phenomenon considering Tsai–Wu failure criterion. Convergence and validation studies are undertaken, and the results are compared with those from the existing literature. The effects of loading duration, cutout area and cutout geometry on the panel are investigated in detail and results are reported. The results indicate that for the panel with cutout, its dynamic buckling load (DBL), in certain cases, compared to the static buckling load (SBL), can be lower even if the loading duration is half of its first natural period. Additionally, the vibration and the static buckling analyses of the panels are carried out as and when required.
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    Nonlinear dynamic instability of laminated composite stiffened plates subjected to in-plane pulsating loading
    (Taylor & Francis, 2023-06) Patel, Shuvendu Narayan; Watts, Gaurav; Kumar, Rajesh
    A nonlinear finite element dynamic instability analysis of laminated composite stiffened plates subjected to in-plane harmonic edge loading is presented in this article along with the linear and nonlinear dynamic response study. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the stiffened plates. Bolotin method is applied to analyze the dynamic instability regions in linear case. Incremental Harmonic Balance (IHB) method is applied to solve the nonlinear frequency response equations and Newmark-β method is used to solve the linear and nonlinear time history response equations.
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    Size-Dependent Nonlinear Free and Forced Vibration Analyses of a Functionally Graded Microplate Subjected to Transverse Patch Loading
    (ASCE, 2023) Kumar, Rajesh; Watts, Gaurav
    This paper presents a semianalytical methodology for the nonlinear vibration of a functionally graded microplate under transverse patch loadings. The higher-order shear deformation theory (HSDT) is combined with the modified strain gradient theory (MSGT) to model the microplate. The power-law function is used to model the functionally graded material. Hamilton’s principle is used to obtain the governing partial differential equations of motion, which are then solved using Galerkin’s method. The nonlinear free and forced vibration responses are obtained using the incremental harmonic balance (IHB) method, where the incremental part is performed using the arc-length continuation methods. The dependence of the steady-state amplitude on the amplitude of initial perturbation is studied using time history plots. These are plotted using the Newmark-β method. The effects of various parameters such as the power-law index, thickness of plate, thickness to material length scale parameter ratio, damping coefficient, different boundary conditions, and different positions of patch loading and its concentrations on the nonlinear free and forced vibration characteristics are examined in detail.