Department of Civil Engineering
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Item 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 NarayanThe 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.Item Nonlinear dynamic instability and dynamic response of stiffened laminated composite plates subjected to in-plane pulsating patch loading(Taylor & Francis, 2023-11) Patel, Shuvendu NarayanIn 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.Item Buckling of Laminated Composite Plate with Imperfections Subjected to In-Plane Pulse Loads(Springer, 2021-06) Kumar, Rajesh; Patel, Shuvendu NarayanIn 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.Item 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 NarayanCarbon 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.Item Analytical and Numerical Study of Fractured Isotropic and Composite Plates Under Mode-I Crack Extension(Springer, 2022-04) Patel, Shuvendu Narayan; Kumar, RajeshThis 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.Item Postbuckling Study of the Laminated Composite Stiffened Plates Subjected to Parabolic In-Plane Loading(Springer, 2022-07) Patel, Shuvendu Narayan; Kumar, RajeshThis 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.Item Stability and Failure Study of Suddenly Loaded Laminated Composite Cylindrical Panel(World Scientific, 2019) Patel, Shuvendu Narayan; Kumar, RajeshIn 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.Item Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces(Sage, 2021-05) Kumar, Rajesh; Patel, Shuvendu NarayanThis study presents a semi-analytical solution of the non-linear dynamic response, shock spectrum, and dynamic buckling of an imperfect angle-ply laminated composite plate under various types of in-plane pulse forces. The laminated composite plate is modeled using a higher-order shear deformation theory and von-Kármán geometric nonlinearity. The non-linear governing partial differential equations (PDEs) of imperfect laminated composite plates are derived via Hamilton’s principle. Using Galerkin’s method, the non-linear PDEs are transformed into non-linear algebraic equations for the static stability problems and non-linear ordinary differential equations for the dynamic problem such as dynamic response, shock spectrum, and dynamic buckling. The buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the composite plate is evaluated using the post-buckling analysis based on the Tsai-Wu failure criterion. The dynamic response and shock spectrum of the composite plate are determined via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the Tsai-Wu failure criterion. Dynamic buckling is to be characterized by dynamic load factor (DLF), which is represented as the ratio of the dynamic failure load to the static failure load. Based on the pulse/shock duration time, the pulse forces are divided into three loading regimes known as impulsive, dynamic, and quasi-static. The study revealed that the DLF values are > 1, < 1, and 1 respectively for the case of impulsive, dynamic, and quasi-static loading regimes of pulse force. The influences of various types of in-plane pulse forces, amplitude and time duration of pulse forces, and amplitude of initial geometric imperfections on the non-linear dynamic response, shock spectrum, and dynamic buckling behavior of the laminated composite plate are addressed in detail. The results will help in the appropriate design of the laminated composite plate against dynamic buckling.Item Semianalytical Development of Dynamic Instability and Response of a Multiscale Laminated Hybrid Composite Plate(ASCE, 2021-01) Patel, Shuvendu Narayan; Kumar, RajeshThe use of carbon nanotubes (CNTs) in augmenting the mechanical properties of fiber-reinforced laminated composites is a fact. In this paper, the semianalytical studies on the dynamic instability behavior and linear and nonlinear responses of a randomly distributed CNT and fiber-reinforced interlamina hybrid composite (CNTFRHC) plate with and without damping under time-dependent in-plane uniaxial uniform compression loading are presented. Each lamina of the laminate is made of multiscale materials such as CNT/polymer/fiber. The effective mechanical properties of the lamina are estimated in two steps. First, the Eshelby–Mori–Tanaka technique is used to compute the effective mechanical properties of randomly distributed CNTs in a polymer matrix (i.e., CNT-embedded matrix). Second, the effective mechanical properties of the CNT-embedded matrix reinforced with fiber (either carbon or glass) are estimated by using various homogenization techniques. The plate is modeled by using higher-order shear deformation theory (HSDT) and von Kármán nonlinearity. Governing partial differential equations of the CNTFRHC plate are obtained by Hamilton’s principle and reduced to Mathieu–Hill equations by using the Galerkin method. Mathieu–Hill equations are solved by the Bolotin method to trace the boundaries of the instability region corresponding periods and . Finally, the influence of different parameters such as CNT agglomerations, CNT mass fraction, edge-to-thickness ratio, compression preloading, boundary conditions, and damping on the dynamic instability region of the CNTFRHC plates are studied in detail. Numerical results provide useful insights into the selection of parameters with different combinations for the desired design of the CNTFRHC plate against instability. Furthermore, to know the characteristics of the instability region of a CNTFRHC plate such as the existence of beats, dependence on geometric nonlinearity, and forcing frequency for which the linear and nonlinear responses with and without damping in both stable and unstable regions are presented.Item Non-linear stability and failure of laminated composite stiffened cylindrical panels subjected to in-plane impulse loading(Elsevier, 2021-02) Patel, Shuvendu Narayan; Kumar, RajeshIn this article, the non-linear dynamic buckling behavior and failure of laminated composite stiffened cylindrical (LCSC) panel is performed in the finite element framework when subjected to sinusoidal and rectangular in-plane pulse loading. Balanced symmetric cross-ply laminates and balanced symmetric angle ply laminates are considered in this study. The first ply failure load (FPFL) of the panel is evaluated and checked whether it occurs before the non-linear dynamic buckling phenomenon considering four different failure theories. Convergence and validation studies are carried out using the present mathematical formulation and compared with the results from the existing literatures. The effect of loading duration, loading function, aspect ratio of stiffener and the ply orientation of the skin and stiffener on the non-linear dynamic buckling of LCSC panel is studied in detail and the results are reported. It is observed that the non-linear dynamic buckling load (DBL) of balanced and symmetric angle ply (45°/−45°/−45°/45°) stiffened panel is lower than those of unstiffened composite cylindrical panel upto aspect ratio of the stiffener (ds/bs) equal to 8 when subjected to rectangular pulse load. In case of balanced and symmetric cross ply (0°/90°/90°/0°) stiffened panel the DBL of stiffened panel is lower than those of unstiffened panel when the aspect ratio of the stiffener is less than 4 with rectangular pulse load. Further, the free vibration, static buckling and static post-buckling analyses of the panels are carried out as and when required.