NURBS-augmented finite element method for stability analysis of arbitrary thin plates

Mishra, Biraja Prasad; Barik, Manoranjan

doi:10.1007/s00366-018-0603-9

Cited by 21 publications

(1 citation statement)

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“…But the exact solutions of those deflection problems are very difficult to be solve.So, many methods have been used to solve those problems such as Yun et al [1] used the homotopy perturbation method to solve a problem of large deflection of circular plate; Wang et al [2] used the modified iteration method for a problem of large deflection of circular plate. Duan [3] used least-squares finite element method for the thin plate problem under clamped, simply supported and free boundary conditions; Abd Elhady et al [4] analyzed stress and strain concentration factors for plate with small notch subjected to biaxial loading by using three dimensional finite element method; Sladek [5] used mesh-free methods for simple boundary value problems for circular plate; Alkhayal [6] considered the von Karman equations in the case of a simply supported thin plate via nonlinear Gauss-Seidel fixed point scheme; Man et al [7] analysed high-order plate bending based on the scaled boundary finite element method; Mishra and Barik [8] used augmented finite element method for stability problem of arbitrary thin plates augmented finite element method for stability problem of thin plates; Assari et al [9,10] proposed the local thin plate splines for solving logarithmic Fredholm integral equation and Vol terra integral equation; Kosmodamianskii [11] used small parameter method for problems of the strain of thin plates and so on. In this paper, we will use the Adomian decomposition method to consider circular plates of variable thickness with fixed edge under uniform load as Fig.…”

Section: Introductionmentioning

confidence: 99%

Deflection problem of circular plates of variable thickness with fixed edges under uniform loaded

Yun,

2024

Preprint

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The deflection problem of circular plates of variable thickness with fixed edges under uniform loaded is considered in this paper. When the thickness of the thin plate along the diameter section follows an exponential function curve, new approximate decomposition solution of the kind of deflection problems is constructed by the Adomian decomposition method. Based on the approximate decomposition solution, the influence of different design of the thickness change for the thin circular plate of variable thickness on the deflection, the radial bending stress and the tangential stress of the thin plate is discussed. The radial bending stress and the tangential stress of the plate of variable thickness at the center and the edge are analyzed with the parameters of thickness change of the plates through its 2-dimensional graphs. The center deflection of the plates of variable thickness is discussed with the parameters of thickness change of the plates through its 2-dimensional graph. From those discussions, one can see the radial bending stress and the tangential stress of the plate at the center tend to decrease after increasing to a certain level with the increase of the parameter. The center deflection and the absolute values of the radial bending stress and the tangential stress of the plate at the edge are increase along a curve as exponential curve with the increase of the parameter.

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