BITS Faculty Publications

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Author: search.filters.author.Kumar, RajeshSubject: search.filters.subject.Buckling

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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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    Buckling and free vibration analysis of randomly distributed CNT reinforced composite beam under thermomechanical loading
    (Elsevier, 2022-12) Kumar, Rajesh
    In this study, the buckling and free vibration characteristics of three-phase randomly distributed carbon nanotube (CNT) reinforced fiber composite (RD-CNTRFC) beams subjected to in-plane compressive loadings and thermal environment are discussed in-depth through a semi-analytical approach. Displacement-based governing equations of motion are derived using Lagrange equation considering higher-order shear deformation theory (HSDT). The effective material properties of RD-CNTRFC are determined in two stages; firstly, effective properties of hybrid matrix (CNTs + Polymer) are evaluated using the Eshelbhy-Mori-Tanaka approach. Finally, overall effective properties of CNTRFC are estimated by implementing different homogenization techniques. The influences of temperature-dependent material properties and CNT-agglomeration are included in the derived formulation. The buckling loads and natural frequencies of RD-CNTRFC beams are computed using a typical eigenvalue solution. The influence of various boundary conditions, CNT mass fraction, CNT-agglomeration, length-to-thickness ratio, and various ply sequences are also addressed.
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    Buckling behaviour of laminated composite skew plates with various boundary conditions subjected to linearly varying in-plane edge loading
    (Elsevier, 2015-09) Kumar, Rajesh
    In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle.
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    Vibration and buckling of skew plates under linearly varying edge Compression
    (International Journal of Acoustics and Vibration, 2019-06) Kumar, Rajesh
    Pre-buckling vibration and buckling behaviour of composite skew plates subjected to linearly varying in-plane edge loading with different boundary conditions are studied. The total energy functional of the skew plate mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram-Schmidt orthogonalization process. Using Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total energy functional is converted into sets of algebraic equations for static stability problems and ordinary differential equation for free vibration problem. Pre-buckling vibration frequencies of the stressed skew plate are obtained by solving associated linear eigen value problem for free vibration and solution of the eigen value problem for static case results critical buckling load. From different parametric study, it is observed that the pre-buckling vibration frequency and critical buckling load increase with the increase of skew angle and edge restraint.