Browsing by Author "Watts, Gaurav"

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An analytical solution for the static bending of smart laminated composite and functionally graded plates with and without porosity
(Springer, 2022-02) Watts, Gaurav
In this paper, an analytical solution for smart laminated composite and functionally graded material plates with and without through-thickness porosity is presented. The kinematics of the deformation in smart structures is modelled through the newly proposed five non-polynomial higher-order shear deformation theories. The relative performance and accuracy of the different theories are assessed for the static bending response of the smart structures under a combined electromechanical loading. The proposed theories assume a nonlinear variation of the transverse shear strain through the thickness of the plate with transverse shear stress-free top and bottom surfaces. The governing differential equations of the plate derived through Hamilton’s principle are solved by Navier’s solution technique with simply supported boundary conditions. To demonstrate the accuracy and applicability of the proposed higher-order shear deformation theories, a wide range of numerical examples for static bending under mechanical and electrostatics loads are considered. The accuracy of the present theories is compared against the three-dimensional elasticity solution, and thereafter, several benchmark solutions for the functionally graded plates with and without porosity are reported.
Ductile Fracture Simulation in a Compact Tension Specimen Using a Triaxiality Dependent Cohesive Zone Model
(Elsevier, 2018-01) Watts, Gaurav
The nonlinear bending and snap-though instability phenomenon of isotropic and composite conical shell panels are investigated here using the element free Galerkin (EFG) method with moving kriging (MK) shape function. Sanders’ shell theory along with von Kármán strain-displacement assumptions are employed to derive the nonlinear equations of equilibrium, which are solved by modified Riks technique in conjunction with Newton-Raphson method. The convergence and accuracy of the EFG method are examined for the linear and nonlinear bending behavior of conical shell panels. Thereafter, the effect of geometrical parameters on the nonlinear stability characteristics of conical panels is investigated under different loading conditions. New results for linear as well as nonlinear bending behavior of isotropic and laminated conical shell panels, hitherto not found in the literature, are presented for future reference.
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) 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) 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.
Elastic Properties and Nonlinear Elasticity of the Noncarbon Hexagonal Lattice Nanomaterials Based on the Multiscale Modeling
(ASME, 2021-04) Watts, Gaurav
This study presents the elastic properties and nonlinear elasticity of the two-dimensional noncarbon nanomaterials of hexagonal lattice structures having molecular structure XY. Four nitride-based and two phosphide-based two-dimensional nanomaterials, having graphene-like hexagonal lattice structure, are considered in the present study. The four empirical parameters associated with the attractive and repulsive terms of the Tersoff–Brenner potential are calibrated for noncarbon nanomaterials and tested for elastic properties, nonlinear constitutive behavior, bending modulus, bending and torsional energy. The mathematical identities for the tangent constitutive matrix in terms of the interatomic potential function are derived through an atomistic–continuum coupled multiscale framework of the extended version of Cauchy–Born rule. The results obtained using newly calibrated empirical parameters for cohesive energy, bond length, elastic properties, and bending rigidity are compared with those reported in the literature through experimental investigations and quantum mechanical calculations. The continuum approximation is attained through the finite element method. Multiscale evaluations for elastic properties and nonlinear stretching of the nanosheets under in-plane loads are also compared with those obtained from atomistic simulations.
Free vibration analysis of non-rectangular plates in contact with bounded fluid using element free Galerkin method
(Elsevier, 2018-07) Watts, Gaurav
Free vibration characteristics of a flexible non-rectangular bottom of a fluid-filled rectangular tank are investigated using a semi-analytical technique. Element free Galerkin method (EFG) based on moving kriging (MK) shape functions is used along with the Mindlin plate theory to model the flexible plate. Two different types of non-rectangular structural domains, viz., skew and trapezoidal configurations are considered in the present study. The fluid is assumed to be incompressible, inviscid and the effect of surface waves is ignored. Potential flow theory is assumed and the velocity potential is used to calculate the kinetic energy of the fluid. The results obtained are first validated with available solutions in the literature for elastic rectangular plates in contact with the fluid. Thereafter, the effects of various structural and fluid domain parameters on natural frequencies of thin isotropic and laminated composite skew/trapezoidal bottom of a rectangular tank filled with fluid are investigated in detail. New results on the vibration of non-rectangular plates in contact with the fluid, hitherto not found in the literature are presented here for the first time.
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.
Meshfree analysis of non-rectangular sandwich plates based on refined C0 higher order shear deformation theories
(Elsevier, 2020-11) Watts, Gaurav
In the present work, bending and free vibration characteristics of non-rectangular laminated composite and sandwich plates are investigated using C0 meshfree formulation based on element free Galerkin (EFG) method with moving kriging (MK) shape function and newly proposed higher-order shear deformation theories. The five new refined higher-order theories with non-polynomial transverse shear stress functions are proposed, which automatically satisfy traction free conditions on top and the bottom surfaces of the plate. The governing differential equations of motion for the continuum system are derived through the minimization of Lagrange functional and are discretized into the algebraic form using MK based meshfree method. The accuracy and applicability of the proposed models are examined first for benchmark problems on the bending and vibration analysis of thin and thick laminated composite and sandwich square plates. Thereafter, several new results on the flexural and free vibration behaviour of sandwich skew, trapezoidal and L-shaped plates, hitherto not found in the literature, are presented for various geometrical parameters and boundary conditions. The presented results for the sandwich plates may serve as the benchmark solutions for the other numerical methods employed for structural analysis of complicated geometry.
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.
Nonlinear analysis of quadrilateral composite plates using moving kriging based element free Galerkin method
(Elsevier, 2017-01) Watts, Gaurav
Element free Galerkin (EFG) method with moving kriging (MK) shape functions is employed here to investigate geometrically nonlinear bending behavior of shear deformable isotropic and laminated composite straight-sided quadrilateral plates. Nonlinear governing equations derived based on the first order shear deformation theory and von Karman strains are solved using Newton-Raphson iterative technique. The applicability and accuracy of the EFG method for the linear and nonlinear bending analyses of isotropic arbitrary quadrilateral plates are examined. Thereafter, geometrically nonlinear analyses of trapezoidal and arbitrary straight-sided quadrilateral thin and moderately thick composite plates are presented for the first time, which may serve as benchmark results for future research purposes.
Nonlinear bending analysis of isotropic plates supported on Winkler foundation using element free Galerkin method
(Elsevier, 2014) Watts, Gaurav
In the present work, constraint effects on growth curves of a mode-I crack are determined using a triaxiality dependent cohesive model. Plane strain elastic-plastic analysis based on the modified boundary layer formulation is performed and for modeling the fracture process, the cohesive parameters and the mechanical properties for a mild steel are taken from literature. From the analysis, the resistance curves for a range of constraint parameter are obtained. A discussion is developed on the effectiveness of the triaxiality dependent model in capturing the well-known effect of constraint and also on the effect of the two model parameters on the resistance curves.
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 vibration and instability of a randomly distributed CNT-reinforced composite plate subjected to localized in-plane parametric excitation
(Elsevier, 2022-01) 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.
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.
A numerical study on the nonlinear behavior of corner supported flat and curved panels
(Springer, 2017-11) Watts, Gaurav
The nonlinear behavior of corner supported plates and curved shell panels is investigated here using the first-order shear deformation theory based on Marguerre’s membrane strains for shallow shells and von Kármán’s nonlinearity. The nonlinear differential equations are transformed into a set of nonlinear algebraic equations by using the element-free Galerkin method. The moving kriging shape function with two different types of correlation formulae (Gaussian and quartic spline) is employed here. After studying the effectiveness of the method, a detailed parametric study is conducted to examine the effect of support size on the displacements and bending moments of corner supported rectangular plates. Thereafter, the numerical study is extended to the nonlinear bending and stability behaviors of corner supported shallow cylindrical and spherical shell panels.
Postbuckled vibration behaviour of skew sandwich plates with metal foam core under arbitrary edge compressive loads using isogeometric approach
(Elsevier, 2023-03) Watts, Gaurav; Kumar, Rajesh
In the present work, nonuniform rational B-spline (NURBS) based isogeometric formulation in conjunction with refined higher-order theory is used to investigate the linear buckling, post-buckling, and post-buckled vibration behaviour of initially imperfect skew sandwich plates. The face sheets are functionally graded carbon nanotube-reinforced composite (FGCNTRC), and the core layer is made up of aluminium foam. The effects of three types of CNT distributions (uniform, FGX and FGO) in the face sheets, two types (uniform, symmetric) of porosity distribution functions for the core layer and five types of in-plane compressive loads are examined in the present investigation. The pre-buckling stresses are calculated using static analysis to evaluate accurate, critical loads. The post-buckling paths are traced using the modified Riks method. The accuracy of the present results is ascertained by comparing the results for critical loads and post-buckling paths with those available in the literature. Subsequently, the influence of CNT distribution functions, porosity functions, compressive loads, skew angle and the side-to-thickness ratio is studied on the nonlinear stability and free vibration behaviour of the post-buckled skew sandwich plates. The obtained results highlight that the buckling strength can be improved by increasing the skew angle, increasing the concentration of CNTs towards the surface of the face sheets and by using a metal foam core with nonuniform porosity distribution.
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.