Browsing by Author "Patel, Shuvendu Narayan"

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Analytical and Numerical Study of Fractured Isotropic and Composite Plates Under Mode-I Crack Extension
(Springer, 2022-04) Patel, Shuvendu Narayan; Kumar, Rajesh
This 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.
Buckling of Laminated Composite Plate with Imperfections Subjected to In-Plane Pulse Loads
(Springer, 2021-06) Kumar, Rajesh; Patel, Shuvendu Narayan
In 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.
Dynamic instability of trapezoidal composite plates under non-uniform compression using moving kriging based meshfree method
(Elsevier, 2021-07) Watts, Gaurav; Patel, Shuvendu Narayan; Kumar, Rajesh
Meshfree formulation based on the element free Galerkin method (EFGM) in conjunction with moving kriging (MK) shape function is employed to investigate buckling and parametric instability behaviour of shear deformable isotropic and laminated composite trapezoidal plates subjected to different types of non-uniform periodic edge compressive loads. Hamilton’s principle is used to derive the governing equations, which are transformed into the discretized form using the EFG method. The actual pre-buckling stresses are determined from static analysis to evaluate the accurate buckling loads of isotropic and laminated composite trapezoidal plates under non-uniform edge compression. The ordinary differential equations of Mathieu–Hill type are solved using Bolotin’s method to determine regions of dynamic instability. The accuracy of the present formulation is examined first by comparing results with those available in the literature. Thereafter, the influence of geometric parameters, lamination scheme, boundary conditions, static pre-load, and various types of non-uniform edge compression on the critical buckling loads and dynamic instability behaviour of both isotropic and laminated composite trapezoidal plate is investigated. The new results on dynamic stability behaviour of trapezoidal plates under non-uniform edge loads are presented for the first time, which may serve as benchmark results for future research. Furthermore, the time history response and corresponding phase plots are also presented for a better understanding of the dynamic behaviour of the trapezoidal plates.
Effect of Cutout on the Stability and Failure of Laminated Composite Cylindrical Panels Subjected to In-Plane Pulse Loads
(World Scientific, 2022) Watts, Gaurav; Kumar, Rajesh; Patel, Shuvendu Narayan
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.
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.
Geometrically nonlinear dynamic analysis of a damped porous microplate resting on elastic foundations under in-plane nonuniform excitation
(Taylor & Francis, 2023-07) Kumar, Rajesh; Patel, Shuvendu Narayan
This article uses the semi-analytical approach to study the combined nonlinear vibration and nonlinear response of a damped porous microplate under nonuniform periodic parametric excitation to understand the complete nonlinear dynamic behavior of the plate. The plate is supported by a Winkler-Pasternak elastic foundation and modeled using modified strain gradient and third-order shear deformation theories to simulate the small-scale effects and shear deformation, respectively. Using Hamilton’s principle, the governing partial differential equations of motion are derived and solved using Galerkin’s method to convert them into ordinary differential equations (ODEs). These ODEs are solved using a combined incremental harmonic balance (IHB) and arc-length continuation approaches to get the nonlinear vibration (frequency–amplitude curves). The same ODEs are solved using the Newmark-β technique to obtain the nonlinear response (time–amplitude curves). The effect of elastic foundation parameters and aspect ratio on mode shape is presented. The effect of parameters such as the porosity coefficient, type of porosity, Winkler-Pasternak elastic foundation parameters, different size-dependent theories, plate thickness, size of plate, damping coefficient, different loading profiles, and loading concentrations on the nonlinear vibration and nonlinear response is examined. Also, the dependence of initial displacements on the frequency–amplitude curves with respect to the excitation frequency is demonstrated with the help of time-amplitude curves.
Instability and Vibration Analyses of Functionally Graded Carbon Nanotube–Reinforced Laminated Composite Plate Subjected to Localized In-Plane Periodic Loading
(ASCE, 2021-11) Kumar, Rajesh; Patel, Shuvendu Narayan
Carbon nanotubes (CNTs) have attracted many researchers during the last three decades due to their versatile nature and excep-tional mechanical properties. In this study, a functionally graded CNT-reinforced laminated composite (FG-CNTRLC) plate subjected todifferent types of localized in-plane loadings was analyzed semianalytically to determine its dynamic instability and nonlinear vibrationcharacteristics. The effective mechanical properties of the FG-CNTRLC plate were estimated using the extended rule-of-mixture technique.The FG-CNTRLC plate was modeled based on higher-order shear deformation theory (HSDT) in conjunction with von Kármán nonlinearity.The distribution of prebuckling stresses within the plate due to localized in-plane loading was estimated by solving the in-plane elasticityproblem using Airy’s stress approach. The nonlinear governing partial differential equations (PDEs) of the FG-CNTRLC plate were derivedusing Hamilton’s principle. The Galerkin method was used to convert these nonlinear PDEs to the nonlinear ordinary differential equations(ODEs). The nonlinear ODEs were solved using the incremental harmonic balance (IHB) method to obtain the nonlinear vibration responseof the FG-CNTRLC plate. After dropping the nonlinear terms, the linear ODEs were solved by the Bolotin method to trace the dynamicinstability regions. The effect of different parameters such as volume fraction of CNTs, different types of localized in-plane loadings, typesof CNTs distribution, the static and dynamic load factor on the dynamic instability regions, and the nonlinear vibration characteristics of theFG-CNTRLC plate, were examined
A meshfree formulation for size-dependent thermal buckling and post-buckling behaviour of porous microplates on elastic foundation subjected to localized heating
(Springer, 2025-01) Kumar, Rajesh; Patel, Shuvendu Narayan; Watts, Gaurav
This article introduces a novel semi-analytical solution for the aggregation equation utilizing the Temimi–Ansari Method in conjunction with Pade approximants. The methodology is further adapted to address coupled aggregation–fragmentation equations, owing to the demonstrated accuracy and efficiency in handling aggregation equations. The study conducts a comprehensive convergence analysis and establishes error bounds for the proposed method. Various test cases are examined to demonstrate the efficacy of the methodology. Comparative assessments between approximated and exact solutions reveal a noteworthy concordance over an extended temporal domain, thereby addressing a substantial void in the existing literature. In the study conducted by Arora et al. (J Comput Sci 67:101973, 2023), it is noteworthy to highlight that the variational iteration method demonstrates superior quantitative accuracy in comparison to both Adomian decomposition and homotopy perturbation methods. Additionally, it is observed that the Temimi–Ansari Method yields comparable accuracy to the variational iteration method but requires less computational time. Simultaneously, the Temimi–Ansari Method, when coupled with Pade approximants, exhibits superior quantitative accuracy compared to the variational iteration method. As a result, the presented article showcases a notable advancement in solutions, surpassing the accuracy of prevailing semi-analytical solutions documented in the literature. The discrepancies between the exact and the derived series solutions are presented through graphical plots and tables, affirming the applicability and precision of the proposed approach.
Non-linear response and buckling of imperfect laminated composite plates under in-plane pulse forces
(Sage, 2021-05) Kumar, Rajesh; Patel, Shuvendu Narayan
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, Shuvendu Narayan; 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.
Non-linear vibration and instability of multi-phase composite plate subjected to non-uniform in-plane parametric excitation: Semi-analytical investigation
(Elsevier, 2021-05) Patel, Shuvendu Narayan; Kumar, Rajesh
Non-linear vibration and instability of a randomly distributed carbon nanotube fiber-reinforced composite (CNTFRC) plate under the action of different types of non-uniform in-plane periodic loadings are presented in this study. The composite plates are modeled considering von Kàrmàn non-linearity and Higher-order shear deformation theory (HSDT). The analytical expression for stresses ( ) distribution within the CNTFRC plate due to non-uniform loads is developed by solving the in-plane elasticity problem using Airy’s stress approach. Using these stresses, Hamilton’s principle is applied to derive the non-linear partial differential equations for dynamic instability and non-linear vibration of CNTFRC plates. Employing the Galerkin method, the non-linear partial differential equations are transformed into a set of non-linear ordinary differential (Mathieu type) equations. After dropping the nonlinearity terms, the linear ordinary differential equations are solved by using Bolotin’s method to trace the boundaries of the dynamic instability region corresponding to periods 2T and T. In the end, the non-linear ordinary differential equations are solved by using the Incremental Harmonic Balance method (IHB) for analyzing the non-linear vibration behavior of the CNTFRC plate. The result obtained from the current work will help in the appropriate design of the CNTFRC plate against stability and vibration in presence of non-uniform in-plane loadings.
Nonlinear analysis of sandwich plate with FG porous core and RD-CNTCFRC face sheets under transverse patch loading
(Springer, 2022-09) Kumar, Rajesh; Bhunia, Dipendu; Patel, Shuvendu Narayan
Nonlinear bending analysis of a sandwich plate with randomly distributed carbon nanotube and carbon fiber-reinforced composite (RD-CNTCFRC) face sheets and functionally graded (FG) porous core subjected to transverse patch loading is performed in the present work. The mechanical properties of the hybrid matrix, which is formed after mixing of single-walled carbon nanotubes and polymer epoxy, are estimated using Eshelby–Mori–Tanaka techniques. Subsequently, the rule of mixture technique is employed to compute the mechanical properties of RD-CNTCFRC face sheets. The mechanical properties of a functionally graded porous core are determined considering both the open-cell and closed-cell metal foam. Utilizing the mechanical properties of RD-CNTCFRC face sheets and FG porous core, the effective properties of RD-CNTCFRC porous sandwich plate are estimated. The sandwich plate is modeled based on higher-order shear deformation theory in conjunction with von Kármán geometric nonlinearity, and subsequently minimization of potential energy is employed to obtain the partial differential equations (PDEs). PDEs are solved using Galerkin’s method and reduced to nonlinear algebraic equations (NAEs). Later, these NAEs are solved via Newton–Raphson method to analyze the nonlinear bending behavior of the RD-CNTCFRC porous sandwich plate using various parameters which can help in suitable design of sandwich plates.
Nonlinear dynamic instability and dynamic response of stiffened laminated composite plates subjected to in-plane pulsating patch loading
(Taylor & Francis, 2023-11) Patel, Shuvendu Narayan
In 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.
Nonlinear dynamic instability of laminated composite stiffened plates subjected to in-plane pulsating loading
(Taylor & Francis, 2023-06) Patel, Shuvendu Narayan; Watts, Gaurav; Kumar, Rajesh
A nonlinear finite element dynamic instability analysis of laminated composite stiffened plates subjected to in-plane harmonic edge loading is presented in this article along with the linear and nonlinear dynamic response study. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the stiffened plates. Bolotin method is applied to analyze the dynamic instability regions in linear case. Incremental Harmonic Balance (IHB) method is applied to solve the nonlinear frequency response equations and Newmark-β method is used to solve the linear and nonlinear time history response equations.
Nonlinear Response and Buckling of Imperfect Plates Under In-Plane Pulse Forces: A Semi-analytical Investigation
(Springer, 2022) Kumar, Rajesh; Patel, Shuvendu Narayan
This study presents a semi-analytical solution of the nonlinear dynamic response, shock spectrum, and dynamic buckling of a simply supported imperfect plate under various types of in-plane pulse forces. Here, the plate is modelled based on higher-order shear deformation theory (HSDT) considering the von-Kármán geometric nonlinearity. The governing nonlinear partial differential equations (NLPDEs) of the imperfect plates are developed via Hamilton’s principle. Using Galerkin’s method, the NLPDEs are converted into sets of nonlinear algebraic equations (NLAEs) for static stability problems and nonlinear ordinary differential equations (NLODEs) for dynamic problems. The critical buckling load of the plate is obtained through the associated eigenvalue problem. The static failure load of the plate is evaluated using nonlinear static stability analysis based on the yield stress failure criterion. The dynamic response and shock spectrum of the plates are plotted via Newmark’s method. The dynamic failure load of the plate is evaluated using Newmark’s method based on the yield stress failure criterion. Dynamic load factor (DLF) is the ratio of dynamic failure load to static failure load. Based on the pulse duration time, the pulse forces are divided into three categories known as impulsive, dynamic, and quasi-static. In the case of impulsive, dynamic, and quasi-static loading regimes, DLF > 1, DLF < 1, and DLF 1, respectively. The results obtained from the current works will help in the appropriate design of the imperfect plates against dynamic buckling.
Nonlinear vibration and instability of a randomly distributed CNT-reinforced composite plate subjected to localized in-plane parametric excitation
(Elsevier, 2022-01) Kumar, Rajesh; Patel, Shuvendu Narayan; Watts, Gaurav
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 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 Narayan
Carbon 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.
Postbuckling and postbuckled vibration behaviour of imperfect trapezoidal sandwich plates with FG-CNTRC face sheets under nonuniform loadings
(Elsevier, 2022-08) Watts, Gaurav; Kumar, Rajesh; Patel, Shuvendu Narayan
The present work investigates the postbuckling, and postbuckled vibration behaviour of initially imperfect trapezoidal sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets and FG porous metal foam core under the influence of non-uniform edge compression. The plate's kinematic assumptions are based on a refined higher order theory and the strain-displacement relations include von Karman assumptions for geometrical nonlinearity. The weak form of governing equations derived using Hamilton's principle is transformed into a discretized form of algebraic equations using the element free Galerkin (EFG) method in conjunction with moving kriging (MK) interpolation functions. The pre-buckling stresses are determined using static analysis to evaluate accurate critical buckling loads. Modified Riks technique is used to trace nonlinear equilibrium paths. Parametric studies include the effect of CNT distribution in face sheets, porosity distribution in the core layer and edge loading conditions on the nonlinear stability and vibration behaviour of sandwich plates. New results on trapezoidal sandwich plates with initial imperfections, hitherto not found in the literature, are presented for the first time, which can be used as benchmark solutions for further research.
Postbuckling and postbuckled vibration behaviour of imperfect trapezoidal sandwich plates with FG-CNTRC face sheets under nonuniform loadings
(Elsevier, 2022-08) Kumar, Rajesh; Watts, Gaurav; Patel, Shuvendu Narayan
The present work investigates the postbuckling, and postbuckled vibration behaviour of initially imperfect trapezoidal sandwich plates with functionally graded carbon nanotube reinforced composite (FG-CNTRC) face sheets and FG porous metal foam core under the influence of non-uniform edge compression. The plate's kinematic assumptions are based on a refined higher order theory and the strain-displacement relations include von Karman assumptions for geometrical nonlinearity. The weak form of governing equations derived using Hamilton's principle is transformed into a discretized form of algebraic equations using the element free Galerkin (EFG) method in conjunction with moving kriging (MK) interpolation functions. The pre-buckling stresses are determined using static analysis to evaluate accurate critical buckling loads. Modified Riks technique is used to trace nonlinear equilibrium paths. Parametric studies include the effect of CNT distribution in face sheets, porosity distribution in the core layer and edge loading conditions on the nonlinear stability and vibration behaviour of sandwich plates. New results on trapezoidal sandwich plates with initial imperfections, hitherto not found in the literature, are presented for the first time, which can be used as benchmark solutions for further research.
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.