BITS Faculty Publications

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Author: search.filters.author.Kumar, RajeshStart date: 2020

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    A comprehensive review on mechanical performance and environmental resilience of fiber-reinforced polymer composites
    (Taylor & Francis, 2026-03) Kumar, Rajesh; Shrivastava, Sharad
    This review provides a comprehensive analysis of fiber-reinforced polymer composites (FRPCs), focusing on the enhancement of their mechanical properties and environmental resilience. This paper classifies key fiber types, such as glass, carbon, aramid, and basalt, and discusses their contributions to composite strength, stiffness, and durability. he paper highlights how manufacturing route and curing quality (e.g. hand lay-up, VARTM/RTM, pultrusion, prepreg/autoclave, and optimized compression molding) govern void content, fiber volume fraction, interlaminar consolidation, and interphase integrity, thereby strongly influencing tensile, flexural, interlaminar shear, fatigue, and impact responses. The critical role of the fiber-matrix interface is examined, with surface modification techniques and nanofillers, such as carbon nanotubes and graphene, highlighted for their impact on tensile, flexural, and shear properties. Environmental challenges, such as moisture absorption, chemical degradation, thermal aging, and UV exposure, are also addressed, with mitigation strategies such as surface coatings and modified resin systems. By integrating advanced interfacial engineering with environmental resilience techniques, this review outlines pathways for developing next-generation FRPCs for aerospace, automotive, marine, and civil infrastructure applications, while aligning with global sustainability goals.
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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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    Mathematical study of BLUES function method for KdV Burgers’ and BBM-Burgers’ equations
    (Elsevier, 2025-10) Kumar, Rajesh
    The Korteweg–De Vries (KdV) Burgers’ and Benjamin–Bona–Mohoney (BBM) Burgers’ equations are crucial in understanding wave dynamics, heat transfer, and plasma waves. It is essential to solve these models over a long time domain to study how energy will transmit and dissipate, or whether waves will remain coherent or disperse due to dissipation effects. Researchers study various semi-analytical and numerical methods to solve these models. However, numerical methods come with the drawback of discretizing the domain, which leads to some errors in the solutions. In a recent paper (Berx and Indekeu, 2021), the authors introduced a new semi-analytical technique, namely the beyond linear use of the superposition (BLUES) function method for partial differential equations, and showed that the proposed method provides better accuracy compared to existing methods. Therefore, the purpose of this article is to describe the BLUES function method for the KdV and BBM Burgers’ equations. The absence of assumptions, convergence control parameters, linearization, and discretization demonstrates the method’s superiority over conventional numerical and semi-analytical techniques. The article mainly focuses on the stability and convergence analysis of the method. Additionally, the numerical validation of the results includes two instances of KdV-Burgers equations and two instances of BBM-Burgers equations. The efficacy and precision of the suggested methodology are illustrated through the utilization of graphical representations and tabular data.
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    An iterative scheme for nonlinear collision-induced breakage equation and convergence analysis
    (Elsevier, 2025-07) Kumar, Rajesh
    The particulate process (Population balance equation (PBE)) has significant applications in milling processes, astrophysics, and the formation of raindrops. A novel PBE is presented, where particle collisions result in one particle fragmenting into multiple pieces (two or more) due to the impact of elastic collisions. This article aspires to offer a semi-analytical solution of a nonlinear collision-induced breakage equation (CBE) using the Temimi and Ansari method (TAM). Firstly, we describe the contraction mapping theorem for the local existence of the solution to CBE. Then, the convergence analysis of the TAM iterative solution is exhibited under some physical assumptions on the collision kernels. In addition to this, the maximum error bound is calculated for the finite term truncated solution. In order to show the accuracy and efficiency of the proposed method, we have numerically simulated the finite-term approximate density functions and moments with the available analytical results at various time stages considering several numerical examples. In all numerical cases, TAM yields closed-form solutions for the zeroth and first moments. Furthermore, it is noted that the TAM consumes less computing time despite producing results with precision comparable to the Homotopy Perturbation method [1]. Finally, it has been shown that the proposed method provides the first-order convergence rate.
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    Weak convergence analysis for non-linear collisional induced breakage equation with singular kernel
    (2024-12) Kumar, Rajesh
    The phenomenon of collisional breakage in particulate processes has garnered significant interest due to its wide-ranging applications in fields such as milling, astrophysics, and disk formation. This study investigates the analysis of the pure collisional breakage equation (CBE), characterized by its nonlinear nature with presence of locally bounded collision kernels and singular breakage kernels. Employing a finite volume scheme (FVS), we discretize the continuous equation and investigate the weak convergence of the approximated solution of the conservative scheme towards the continuous solution of CBE. A weight function is introduced to ensure the conservation of the scheme. The non-negativity of the approximated solutions is also shown with the assistance of the mathematical induction approach. Our approach relies on the weak compactness argument, complemented by introducing a stable condition on the time step.
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    Study on bending characteristics of CNT-reinforced metal Timoshenko composite porous beam exposed to transverse patch loading
    (Sage, 2025-03) Kumar, Rajesh
    Bending characteristics of porous composite beams reinforced by carbon nanotubes (CNTs) under localized transverse loading is examined in the current study. Initially, single-walled carbon nanotubes (SW-CNTs) are utilized as nanofillers within a metal matrix to enhance the beam’s mechanical properties. The effective mechanical properties of the beam are assessed using the Eshelby-Mori-Tanaka method. Next, the porosity of the beam is modeled as being distributed layer-by-layer through the beam’s thickness, either uniformly or in a non-uniform manner, with three distinct distribution types considered: uniform, symmetric non-uniform, and asymmetric non-uniform. The beam is mathematically modeled using theory of Timoshenko beam combining nonlinearity of von-Kármán. The governing nonlinear algebraic equations are derived from the principle of minimizing total potential energy. These equations are then simplified using the Galerkin method and solved implementing Newton-Raphson technique to determine the load-deformation path. Finally, the study is performed using different parameters to analyze their impact on the bending behavior of CNT-metal reinforced porous composite beams. This includes the mass fraction of SW-CNTs, porosity distribution types, agglomeration effects of CNTs, porosity coefficients, aspect ratio, types of transverse loading, and different metal matrices.
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    A semi-analytical method for non-linear instability analysis of variable stiffness laminated composite beams under thermo-mechanical loading
    (Elsevier, 2025-03) Kumar, Rajesh
    This investigation explores the non-linear instability phenomena of variable stiffness laminated composite (VSLC) beams subjected to thermo-mechanical loading. A semi-analytical model is developed to determine the post-buckling and post-buckled vibration behavior of VSLC beams based on trigonometric shear deformation theory. Non-linear strain equations are formulated based on von-Karman’s geometric non-linearity assumptions. Constitutive relations are modified for VSLC beam to account for various coupling effects that arise due to varying fiber orientation and Poisson effects that arise due to the development of zero-stress conditions in the width direction of beams. Using Gram-Schmidt orthogonalization process, an orthogonal basis for the displacement field is constructed to enhance accuracy and ease. The model employs a displacement-based Ritz approach to derive the matrix representation of the governing equations. The present model is developed assuming equivalent single-layer theory, and material properties and temperature variations are assumed to be constant across the thickness of the beam. Moreover, arc-length method is employed to obtain the non-linear response curves of VSLC beam. Pre-buckled and post-buckled vibration responses are obtained using a standard eigenvalue approach. A parametric analysis is conducted to investigate the effect of slenderness ratio, boundary conditions, and ply-sequence on post-buckling and post-buckled vibration characteristics of VSLC beam.
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    Nonlinear dynamics of axially functionally graded, porous sandwich panel subjected to periodic non-uniform in-plane excitation
    (Elsevier, 2025-06) Kumar, Rajesh
    The dynamic response of axially functionally graded (AFG) porous core sandwich panels under periodic non-uniform in-plane axial loads is investigated. The panel is a circular cylindrical shell with a rectangular base with simply supported, in-plane movable edges. The material properties of the face sheet are obtained using the rule of mixture, and porosity in the core is assumed to be randomly distributed. The core is modelled for compressibility with fourth and fifth-order expansions by neglecting the tangential displacement due to large rotations. Non-uniform in-plane stresses are obtained using the Airy stress function. The equations of motion are derived by using variational principles and multi-term Galerkin's approach. The region of dynamic instability is obtained using Bolotin's method; the novelty is that a proportional damping model of the panel is retained in this study. The Newmark-Beta technique is applied to calculate time-histories and phase-plane responses. Results show that damping plays a significant role in dynamic responses. Different from most of the semi-analytical solutions published in the literature, the present study satisfies both natural and essential boundary conditions. The functional gradation of material shows that by increasing the power law constant (k), the material properties present a softening character. Non-uniform in-plane loads are studied, which is another significant novelty for the problem under investigation. Porosity can play an important role in structural performance; it can be due to manufacturing defects or desired for the development of lightweight structures. Therefore, the influence of porosity is studied in detail by considering a random void distribution for both open and closed-type cellular structures.
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    Convergence and error estimation of weighted finite volume scheme for coagulation-fragmentation equation
    (Wiley, 2022-12) Kumar, Rajesh
    This article is dedicated to analyze a finite volume scheme for solving coagulation and multiple fragmentation equation. The rates of coagulation and fragmentation are chosen locally bounded and unbounded (singularity near the origin), respectively. It is shown that using weak compactness method, the numerically approximated solution tends to the weak solution of the continuous problem under a stability condition on the time step for non-uniform mesh. Further, considering a uniform mesh, first order error approximation is demonstrated when kernels are in space. The accuracy of the scheme is also authenticated numerically for several test problems.