Department of Civil Engineering

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Author: search.filters.author.Patel, S. N.

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    Nonlinear stability analysis of multi-stiffened laminated composite plates under uniform in-plane harmonic loading
    (Springer, 2025-04) Patel, S. N.
    When an in-plane harmonic loading is applied to a plate, the linear dynamic instability region (DIR) formed, gives only the range of frequencies where the plate becomes unstable, however, it doesn’t give any information about the transverse deformations. Hence, a nonlinear time history analysis is required to capture the actual time-varying deformations along with the nonlinear frequency response analyses to capture the actual frequency-varying deformations in the dynamic instability zone.
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    Harmonic in-plane patch loading induced nonlinear dynamic instability of unidirectional and bidirectional stiffened composite plates
    (Sage, 2024-02) Patel, S. N.
    A finite element framework is established to study the nonlinear dynamic instability of stiffened plates subjected to in-plane harmonic patch loading. An eight-noded isoparametric degenerated shell element and a three-noded curved beam element are used to model the skin and the stiffener, respectively. The Green–Lagrange strain displacement relationship is adopted to formulate the system matrices for the plate and the stiffener, adopting the total Lagrangian approach. The Bolotin method is adopted to trace the boundaries of linear dynamic instability region. The Incremental Harmonic Balance (IHB) method is used to investigate the nonlinear instability behavior of stiffened plates. The effect of varying loading patches along with the number of stiffeners in unidirectional (x-directional and y-directional) and bidirectional (x as well as y-directional) stiffened plates on the nonlinear frequency response is studied. It is observed that the cross-stiffened plates with the higher number of stiffeners are dynamically more stable than the unidirectional stiffened plates. Moreover, the stiffened plates with smaller loading patches are dynamically more stable than those with larger loading patches.
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    Nonlinear Finite Element Bending Analysis of Composite Shell Panels
    (2014-12) Patel, S. N.
    This paper deals with the geometric nonlinear bending response of laminated composite shell panels subjected to transverse loading. The eight-noded degenerated shell element with five degrees of freedom per node is adopted in the present analysis to model the composite shell panels. The Green-Lagrange strain displacement relationship is adopted to formulate the matrices. The total Lagrangian approach is taken in the formulation. The arc-length method of solution is adopted in tracing the equilibrium path. The results by this method are compared with the available results and the conclusions are made.
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    Nonlinear Dynamic Buckling and Failure Study of Laminated Composite Plates Subjected to Axial Impulse Loads
    (Springer, 2020-03) Patel, S. N.; Kumar, Rajesh
    In this paper, the nonlinear dynamic buckling of laminated composite plate is studied along with the failure of the plates. The balanced and symmetric cross-ply laminated composite plates are subjected to in-plane impulse compressive loads. The dynamic buckling load is calculated using Volmir’s criterion. The nonlinear dynamic equations are solved using the finite element method. Imperfections are incorporated in the plate in order to simulate the actual behavior. The effect of imperfection, loading function, and duration of loading is studied. The first ply failure load for the plate is calculated to check the precedence of dynamic buckling and first ply failure. It is observed that the first ply failure for balanced and symmetric cross-ply laminated composite plates occurs after the plate has buckled due to dynamic impulse loads.
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    Dynamic Instability of CNT-Reinforced Composite Plate Under Non-uniform In-plane Loading
    (Springer, 2022) Patel, S. N.; Kumar, Rajesh
    An analytical study is conducted to define the dynamic instability of the carbon nanotubes-reinforced composite (CNTRC) plate under the action of different kinds of non-uniform loadings. The efficient mechanical properties of the lamina are calculated using the Eshelby–Mori–Tanaka scheme, where CNTs are distributed randomly within the epoxy. Hence, the CNT-embedded matrix is considered isotropic. The CNTRC plate is modeled as per higher-order shear deformation theory (HSDT). Due to the non-uniform nature of loading, the distribution of stresses (σxx, σyy, τxy) within the CNTRC plate is derived by solving the in-plane elasticity problem using Airy's stress method. Hamilton's principle is implemented to derive the partial differential equations (PDEs) of the CNTRC plate using the derived stresses. These PDEs are solved to obtain the ordinary differential (Mathieu type) equations using the Galerkin method. Subsequently, Mathieu type equations are solved using the Bolotin method to find the boundaries of instability corresponding to periods T and 2 T. Finally, the effect of changed parameters such as the mass fraction of CNT, CNT agglomeration, static and dynamic load factors, and various non-uniform in-plane loadings on the dynamic instability of the CNTRC plates is examined.
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    Dynamic instability analysis of laminated composite stiffened shell panels subjected to in-plane harmonic edge loading
    (Korea Science, 2006) Patel, S. N.
    The dynamic instability characteristics of laminated composite stiffened shell panels subjected to in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented to demonstrate the effects of various parameters like shell geometry, lamination scheme, stiffening scheme, static and dynamic load factors and boundary conditions, on the dynamic instability behaviour of laminated composite stiffened panels subjected to in-plane harmonic loads along the boundaries. The results of free vibration and buckling of the laminated composite stiffened curved panels are also presented.
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    Buckling and dynamic instability analysis of stiffened shell panels
    (Elsevier, 2006-03) Patel, S. N.
    The static and dynamic instability characteristics of stiffened shell panels subjected to uniform in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effect of various parameters like shell geometry, stiffening scheme, static and dynamic load factors, stiffener size and position, and boundary conditions are considered in buckling and dynamic instability analysis of stiffened panels subjected to uniform in-plane harmonic loads along the boundaries.
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    Dynamic stability analysis of stiffened shell panels with cutouts
    (ASCE, 2009-04) Patel, S. N.
    A finite element dynamic instability analysis of stiffened shell panels with cutout subjected to uniform in-plane harmonic edge loading along the two opposite edges is presented in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover the new formulation for the beam element requires five degrees of freedom per node as that of shell element. Bolotin method is applied to analyze the dynamic instability regions. Numerical results of convergence studies are presented and comparison is made with the published results from literature. The effects of various parameters such as shell geometry, radius of curvature, cutout size, stiffening scheme, and dynamic load factors are considered in dynamic instability analysis of stiffened shell panels with cutout. The free vibration and static stability (buckling) results are also presented. With the consideration of radius of curvatures the panels reduce from deep shell case to shallow shell case and finally become flat plate.
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    Parametric study on the dynamic instability behaviour of laminated composite stiffened plate
    (ASCE, 2009-11) Patel, S. N.
    This paper deals with the study of dynamic or parametric instability behavior of laminated composite stiffened plates with step-uniform and concentrated in-plane harmonic edge loading. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the plate and the stiffeners, respectively. The method of Hill’s infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effects of parameters like loading type, stiffening scheme, lamination scheme, dynamic load factor, and boundary conditions are considered in the dynamic instability analysis of laminated composite stiffened plate. It has been shown that the type of loading and the width of loading have remarkable effect on the dynamic instability characteristics of the stiffened plate.
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    Effect of harmonic in-plane edge loading on dynamic stability of stiffened shell panels with cutouts
    (World Scientific, 2010) Patel, S. N.
    The effect of non-uniform in-plane pulsating edge loading on dynamic instability behavior of perforated stiffened shell panels is presented in this paper using finite element method. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. Bolotin method is applied to analyze the dynamic instability regions. Numerical results of convergence studies are presented and comparison is made with the published results from the literature. The effects of various parameters like shell geometry, loading type, cutout size and dynamic load factors are considered in dynamic instability analysis of stiffened shell panels with cutout. The buckling results of the cutout stiffened panels are also presented.