A Simplified Approach to the Analysis of Large Deflections of Plates

This paper uses the method of constant deflection contour lines [1–3] to analyze the nonlinear large deflections of thin elastic plates of arbitrary shape in a new fashion. As an illustration the case of an elliptical plate with edges constrained against motion in the horizontal direction is discussed.

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Buckling analysis of plates of arbitrary shape

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000004343 ◽

1984 ◽

Vol 26 (1) ◽

pp. 77-91 ◽

Cited By ~ 2

Author(s):

D. Bucco ◽

J. Mazumdar

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Arbitrary Shape ◽

Numerical Technique ◽

Buckling Analysis ◽

Contour Method ◽

Elastic Plates ◽

Standard Finite Element Method ◽

Thin Elastic Plates ◽

Element Method

AbstractA simple and efficient numerical technique for the buckling analysis of thin elastic plates of arbitrary shape is proposed. The approach is based upon the combination of the standard Finite Element Method with the constant deflection contour method. Several representative plate problems of irregular boundaries are treated and where possible, the obtained results are validated against corresponding results in the literature.

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THIN ELASTIC PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

10.31224/osf.io/hr79j ◽

2021 ◽

Author(s):

Sergey Selyugin

Keyword(s):

Virtual Work ◽

Plate Thickness ◽

Geometrically Nonlinear ◽

Large Deflections ◽

Elastic Plates ◽

Equilibrium Equations ◽

Virtual Work Principle ◽

Von Karman ◽

Von Kármán ◽

Thin Elastic Plates

Thin elastic plates (homogeneous or composite) experiencing large deflections are considered. The deflections are much larger than the plate thickness. The geometrically nonlinear elasticity theory and the Kirchhoff assumptions are employed. Small elongations and shears are assumed. Following Novozhilov, the strain expressions are derived. Then, under a small in-plane rotation assumption and using the virtual work principle, the equilibrium equations and the boundary conditions are obtained. The equations/conditions become the known von Karman ones for the case of moderate deflections. The solutions of the obtained equations may be used as benchmarks for the nonlinear structural analysis (e.g., FEM) software in the case of large deflections.

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Buckling of elastic plates by the method of constant deflection lines

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700010636 ◽

1972 ◽

Vol 13 (1) ◽

pp. 91-103 ◽

Cited By ~ 8

Author(s):

J. Mazumdar

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Large Class ◽

Arbitrary Shape ◽

Elastic Stability ◽

Buckling Analysis ◽

Mathematical Treatment ◽

Elastic Plates ◽

Bent Plate ◽

Thin Elastic Plates

In a previous paper of this series – hereinafter to be referred to as [1] – the author introduced a new method for a large class of boundary value problems connected with the flexure analysis of elastic plates of arbitrary shape where the concept of ‘Lines of Equal Deflection’, i.e. lines which are obtained by intersecting the bent plate by planes parallel to the original plane of the plate, was introduced. The present paper extends this analysis to the buckling analysis of thin elastic plates with various forms of boundary conditions. It is shown that the proposed method appears to be a powerful tool for the investigation of those problems of elastic stability which could not be solved by conventional methods because of the difficulty of the mathematical treatment.

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A new approach to an analysis of large deflections of thin elastic plates

International Journal of Non-Linear Mechanics ◽

10.1016/0020-7462(81)90031-7 ◽

1981 ◽

Vol 16 (1) ◽

pp. 47-52 ◽

Cited By ~ 35

Author(s):

B. Banerjee ◽

S. Datta

Keyword(s):

Large Deflections ◽

Elastic Plates ◽

New Approach ◽

Thin Elastic Plates

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Application of the charge simulation method to analysis of large deflections of elastic plates

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247jsa26 ◽

2007 ◽

Vol 42 (7) ◽

pp. 543-550 ◽

Cited By ~ 8

Author(s):

K Kimura

Keyword(s):

General Solution ◽

Boundary Conditions ◽

Simulation Method ◽

Numerical Results ◽

Graphical Form ◽

Large Deflections ◽

Elastic Plates ◽

Charge Simulation Method ◽

Collocation Points ◽

Thin Elastic Plates

The non-linear Berger equation is used to obtain solutions for deformation of thin elastic plates, and is solved by applying the charge simulation method. The general solution for the deflection is first obtained by a combination of two kinds of series of Green's functions. Satisfying the boundary conditions at the collocation points, the unknown constants in the general solution are determined, and the deflection of the plate is calculated. Numerical results are presented in dimensionless graphical form for rectangular and isosceles triangular plates.

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A KINEMATIC VARIATIONAL PRINCIPLE FOR THIN METALLIC AND COMPOSITE PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

10.31224/osf.io/e2vgj ◽

2021 ◽

Author(s):

Sergey Selyugin

Keyword(s):

Variational Principle ◽

Plate Thickness ◽

Composite Plates ◽

Geometrically Nonlinear ◽

Large Deflections ◽

Elastic Plates ◽

Equilibrium Equations ◽

Von Karman ◽

Von Kármán ◽

Thin Elastic Plates

Thin elastic plates (metallic or composite) experiencing large deflections are considered. The plate deflections are much larger than the plate thickness. The geometrically nonlinear elasticity theory and the Kirchhoff assumptions are employed. The elongations, the shears and the in-plane rotations are assumed to be small. A kinematic variational principle leading to a boundary value problem for the plate is derived. It is shown that the principle gives proper equilibrium equations and boundary conditions. For moderate plate deflections the principle is transformed to the case of the von Karman plate.

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