In the present work, the nonlinear free flexural vibration of thick curvilinear fiber composite laminates is investigated using a higher-order shear flexible eight-noded quadrilateral element devel...

Nonlinear Free Flexural Vibration of Curvilinear Fibre Composite Laminates Using a Higher-Order Element

The nonlinear static responses of the skew sandwich flat/curved shell panel including the corresponding stress values are examined in this article under the influence of the unvarying transverse mechanical load. To evaluate the said responses of the sandwich panel, the physical structure model turned to a mathematical form via a higher-order kinematic theory including the stretching term effect in the displacement field variable. The effect of geometrical nonlinearity has been included via Green–Lagrange strain–displacement kinematics. The governing equation has been derived from the variational principle and is solved via direct iterative technique including the finite element procedure. Further, a customized finite element computer code has been developed in MATLAB environment based on the current mathematical model for the computational purpose. To check the comprehensive behavior of the proposed model, the bending responses are obtained for different mesh sizes and compared with the published data (numerical and 3D elasticity solution). Subsequently, a wide range of numerical examples have been solved for the different geometrical configurations (side-to-thickness ratio, curvature ratio, core-to-face thickness ratio, skew angle and support conditions) and the influence of the same on deflection and stress behavior has been shown and discussed in detail.

Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory

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 Karman 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.

Nonlinear bending and snap-through instability analyses of conical shell panels using element free Galerkin method

Free vibration analysis of non-rectangular plates in contact with bounded fluid using element free Galerkin method

This paper investigates the nonlinear bending behaviours of functionally graded trapezoidal nanocomposite plates reinforced with graphene platelets (GPLs) under thermo-mechanical loading by employing finite element method. The modified Halpin–Tsai model and rule of mixtures are adopted to determine the Young’s modulus, Poisson’s ratio and the thermal expansion coefficient of the nanocomposites. The influences of a number of factors, including the distribution pattern, concentration and size of GPLs, plate geometry and temperature, on the nonlinear bending of the nanocomposite plates are comprehensively investigated. Numerical results demonstrate that dispersing a small amount of GPLs into nanocomposites can significantly enhance the nonlinear bending performance of the trapezoidal plates. The trapezoidal plates with more GPLs dispersing close to the top and bottom surfaces has the minimum bending deflection and are less sensitive to the temperature increases. GPLs with fewer layers and larger surface area are better reinforcing fillers than their counterparts. Moreover, the plates with bigger bottom angles are found to have better bending performances. However, when the bottom angles are greater than 75°, the variation of the bottom angles will have limited effects on the bending behaviours of the trapezoidal plates.

Geometrically nonlinear bending of functionally graded nanocomposite trapezoidal plates reinforced with graphene platelets (GPLs)

Linear and nonlinear analyses of shear deformable thin and thick arbitrary straight-sided quadrilateral plates are reported here using smoothed finite element technique. The Reissner-Mindlin plates are discretized with quadrilateral background cells. Then membrane and bending stiffness matrices of background quadrilateral cells are evaluated using edge-based smoothed finite element method(ES-FEM). The shear stiffness matrix is calculated based on "smoothed shear strain approach" and the performance is compared with "edge-consistent four-node quadrilateral finite element". The convergence, accuracy and sensitivity to mesh distortion of the present quadrilateral element is examined. Thereafter, the nonlinear bending and vibration analyses of trapezoidal and arbitrary straight-sided quadrilateral composite plates are presented for which only limited analytical results are available in the literature.

Nonlinear bending and vibration analyses of quadrilateral composite plates

Series of experiments and a detailed computational analysis has been performed to investi-
gate the high strain rate behaviour of homostacked Al 6063-T6 and IS 1570 alloys Split
Hopkinson pressure bar technique was utilized to study the effect of high rate loading on the
stress strain relationship of single, double, tri and quad layered/stacked specimens Three
different specimen aspect ratios 1, 075 and 05 were also evaluated for different strain rates
A 2mm thick pulse shaper was employed in achieving dynamic stress equilibrium, a near
constant strain rate and a high rise time as per requirements After analyzing the results
from the experiments it was observed that single and halved specimens showed a close match
in both the elastic and plastic regions for aluminium alloy as well as for steel In the case of
Al 6063-T6, a nearly bi-linear nature of the constitutive curve was observed for single and
halved specimens, which transformed into near tri-linear nature for tri and quad stacked
specimens The dynamic numerical analysis showed a good agreement between the nume-
rical and experimental results for a single and halved specimen in the case of Al alloy For
steel, a close correlation was observed for all the four cases

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Structural response of multilayered aluminum and steel specimens subjected to high strain rate loading conditions

Structural response of metal sheets under combined shear and tension

The stability characteristics of shear deformable trapezoidal composite plates are studied here. Thestrain smoothing technique is employed to approximate the membrane strains and curvatures of the ...

Stability Analysis of Shear Deformable Trapezoidal Composite Plates

Post-failure observation based analysis of a structure can reveal the information like residual deformations, type, and location of the fracture. But it does not provide the required information completely. Factors like boundary conditions at the impact zone and failure mechanisms remain unresolved. This article presents a combined experimental and numerical approach as an effective tool to examine the transient and post-impact three dimensional full-field response of thin steel plates, when subjected to moderate velocity (100–250 m/s) projectile impact. Experiments were conducted with the help of a single stage gas gun and different projectile shapes in conjunction with 3D DIC (digital image correlation). Finite element (FEM) simulations were also performed to correlate both the transient data and post-impact parameters. Important parameters like the failure modes, plug geometry, out of plane deformations of the steel target plates of two different thicknesses were analysed in detail and reported. Also a comprehensive error measure criterion incorporating both the magnitude error and the phase error was employed to accurately quantify the temporal response. Excellent correlation was observed between the experiments and simulations.

Vikrant Tiwari

Papers

Nonlinear bending and vibration analyses of quadrilateral composite plates

Structural response of multilayered aluminum and steel specimens subjected to high strain rate loading conditions

Structural response of metal sheets under combined shear and tension

Stability Analysis of Shear Deformable Trapezoidal Composite Plates

Investigations on the influence of projectile shape on the transient and post impact response of thin sheet structures