Browsing by Author "Patel, S. N."

Now showing 1 - 20 of 21

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.
Buckling response of laminated composite stiffened plates subjected to partial in-plane edge loading
(Taylor & Francis, 2016-09) Patel, S. N.
This article presents the buckling analysis of laminated composite stiffened plates subjected to partial in-plane edge loading. The finite element method is used to carry out the analysis. The eight-noded isoparametric degenerated shell element with C0 continuity and first-order shear deformation and a compatible three-noded curved beam element are used to model the plate skin and the stiffeners, respectively. The eigen value analysis is carried out to track the buckling load. The convergence study is performed for some specific problems and the results are compared with the available results in the literature. It is observed that the convergence of results is very fast for this finite element model. Effect of different parameters like orientation of fibers, number of layers, and loading types are considered in the present investigation. It is also observed that all these parameters have significant effect on the buckling response of the composite stiffened plate.
Dynamic buckling analysis of a composite stiffened cylindrical shell
(Korea Science, 2011) Patel, S. N.
The paper investigates the dynamic buckling behaviour of a laminated composite stiffened cylindrical shell using the commercial finite element code ABAQUS. The numerical model of the composite shell is validated by static tests. In particular, the experimental collapse test is numerically simulated by a quasi static analysis carried out by both ABAQUS/Standard and ABAQUS/Explicit. The behaviour in the post-buckling field and the collapse load obtained by the analyses are close to the experimental data. The validated model is then used to study the dynamic buckling behaviour with ABAQUS/Explicit. The effects of the loading magnitude and of the loading duration are investigated, implementing in the analysis also first-ply failure criteria. It is observed that the dynamic buckling load is highly affected by the loading duration.
Dynamic Buckling of Laminated Composite Curved Panels Subjected to In-plane Compression
(Springer, 2018-08) Patel, S. N.
This paper deals with dynamic buckling of laminated composite curved panels subjected to in-plane dynamic compressive loads. Results from the available literature are used to validate the static buckling load of curved panels, and the dynamic buckling loads of the same panel are predicted using finite element software ABAQUS/Explicit. Volmir’s criterion is used to find the dynamic buckling load. Dynamic load of various magnitudes in the form of pulse load is applied on the panel for various duration. The effect of aspect ratio and radius of curvature are studied. It is observed that smaller loads require longer duration of loading and vice versa for dynamic buckling to occur. The dynamic buckling load is observed to be lesser than static buckling load for longer duration of loading which is an important aspect to be considered in designing.
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.
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.
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.
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.
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
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.
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.
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.
Non-Linear dynamic pulse buckling of laminated composite curved panels
(TechnoPress, 2020-01) Patel, S. N.
In this paper, non-linear dynamic buckling behaviour of laminated composite curved panels subjected to dynamic in-plane axial compressive loads is studied using finite element methods. The work is carried out using the finite element software ABAQUS. The curved panels are modelled with S4R element and the nonlinear dynamic equilibrium equations are solved using the ABAQUS/Explicit algorithm. The effect of aspect ratio, radius of curvature and thickness are studied. The importance of orientation of plies in the direction of loading is also reiterated in this study. Vol\'mir\'s criterion is used to calculate the dynamic buckling loads. The panels are subjected to rectangular pulse load of various amplitude and durations and the responses are observed. For particular loading amplitude, a critical value of loading duration is observed beyond which the variation of dynamic buckling load is insignificant. It is also observed that, the value of dynamic bucking load reduces as the loading duration is increased though the reduction is not much after a particular loading duration.
Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces
(Sage, 2021-05) Patel, S. N.; Kumar, Rajesh; Roy, Nishant
This 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.
Non-Linear Stability and Failure of Laminated Composite Stiffened Cylindrical Panels Subjected to In-Plane Impulse Loading
(Elsevier, 2021-02) Patel, S. N.; Kumar, Rajesh
In 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.
Nonlinear bending analysis of laminated composite stiffened plates
(Korea Science, 2014) Patel, S. N.
This paper deals with the geometric nonlinear bending analysis of laminated composite stiffened plates subjected to uniform transverse loading. The eight-noded degenerated shell element and three-noded degenerated curved beam element with five degrees of freedom per node are adopted in the present analysis to model the plate and stiffeners respectively. The Green-Lagrange strain displacement relationship is adopted and the total Lagrangian approach is taken in the formulation. The convergence study of the present formulation is carried out first and the results are compared with the results published in the literature. The stiffener element is reformulated taking the torsional rigidity in an efficient manner. The effects of lamination angle, depth of stiffener and number of layers, on the bending response of the composite stiffened plates are considered and the results are discussed.
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.
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.
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.
Nonlinear vibration and instability of a randomly distributed CNT-reinforced composite plate subjected to localized in-plane parametric excitation
(Elsevier, 2022-01) Patel, S. N.; Kumar, Rajesh
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.
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.