The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

黄家寅,; 秦圣立,; Huang, Jiayin; Sheng-li, Qin

doi:10.1007/bf00193619

Cited by 4 publications

(1 citation statement)

References 7 publications

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“…Zhao-Ping et al (1994) used the incompatible bending elements with internal shear strain for the geometrically nonlinear analysis of rectangular Mindlin plate without any shear locking and with simply supported, clamped and combination of simply supported and clamped boundary conditions. Jiayin and Shengli (1996) solved the problems of nonlinear bending for thin orthotropic rectangular plates with four clamped edges by using the methods of two variables and mixing perturbation. Sheikh and Mukhopadhyay (2000) presented the geometric nonlinear analysis of stiffened plates by the spline finite strip method based on Von Karman nonlinear plate theory and total Lagrangian (TL) coordinate system.…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Jafari

Azhari

2016

Engineering Computations

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Purpose – The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates. Design/methodology/approach – Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function. Findings – The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered. Originality/value – This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

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Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Jafari

Azhari

2016

Engineering Computations

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Basic equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness

Huang¹

2004

Appl Math Mech

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Under the case of ignoring the body forces and considering components caused by diversion of membrane in vertical direction (z-direction), the constitutive equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness are given; then introducing the dimensionless variables and three small parameters, the dimensionaless governing equations of the deflection function and stress function are given.

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Uniformly valid asymptotic solutions of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate of four clamped edges with variable thickness

Huang¹

2004

Appl Math Mech

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By using " the method of modified two-variable ", " the method of mixing perturbation" and introducing four small parameters, the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied. And the uniformly valid asymptotic solution of Nth-order for e l and Mth-order for e 2 of the deflection functions and stress function are obtained.

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The problems of nonlinear bending for orthotropic rectangular plate with four clamped edges

Cited by 4 publications

References 7 publications

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Geometrically nonlinear analysis of thick orthotropic plates with various geometries using simple HP-cloud method

Basic equations of the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with variable thickness

Uniformly valid asymptotic solutions of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate of four clamped edges with variable thickness

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