BITS Faculty Publications

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Author: search.filters.author.Watts, GauravSubject: search.filters.subject.Element free Galerkin method

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    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.
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    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.
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    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.
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    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.
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    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.
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    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.