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

2007 ◽  
Vol 42 (7) ◽  
pp. 543-550 ◽  
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.

Stability of Thin Elastic Plates Covering an Arbitrary Simply Connected Region and Subject to any Admissible Boundary Conditions

1953 ◽  
Vol 20 (1) ◽  
pp. 23-29
Author(s):  
G. A. Zizicas
Keyword(s):  
Boundary Conditions ◽  
Direct Method ◽  
Elastic Plates ◽  
Simple Manner ◽  
Particular Solutions ◽  
Isotropic Plates ◽  
Simply Connected Region ◽  
Simply Connected ◽  
A Direct Method ◽  
Thin Elastic Plates

Abstract The Bergman method of solving boundary-value problems by means of particular solutions of the differential equation, which are constructed without reference to the boundary conditions, is applied to the problem of stability of thin elastic plates of an arbitrary simply connected shape and subject to any admissible boundary conditions. A direct method is presented for the construction of particular solutions that is applicable to both anisotropic and isotropic plates. Previous results of M. Z. Krzywoblocki for isotropic plates are obtained in a simple manner.

scholarly journals THIN ELASTIC PLATES EXPERIENCING LARGE DEFLECTIONS ABOVE THE VON KARMAN LIMITS

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.

scholarly journals Enhanced Single-Degree-of-Freedom Analysis of Thin Elastic Plates Subjected to Blast Loading Using an Energy-Based Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-29
Author(s):  
M. D. Goel ◽  
T. Thimmesh ◽  
P. Shirbhate ◽  
C. Bedon
Keyword(s):  
Boundary Conditions ◽  
Blast Waves ◽  
Degree Of Freedom ◽  
Elastic Plates ◽  
Nonlinear Parameters ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impulsive Loads ◽  
Technical Interest ◽  
Thin Elastic Plates

Single-degree-of-freedom (SDOF) models are known to represent a valid tool in support of design. Key assumptions of these models, on the other hand, can strongly affect the expected predictions, hence resulting in possible overconservative or misleading estimates for the response of real structural systems under extreme actions. Among others, the description of the input loads can be responsible for major design issues, thus requiring the use of more refined approaches. In this paper, a SDOF model is developed for thin elastic plates under large displacements. Based on the energy approach, careful attention is given for the derivation of the governing linear and nonlinear parameters, under different boundary conditions of technical interest. In doing so, the efforts are dedicated to the description of the incoming blast waves. In place of simplified sinusoidal pressures, the input impulsive loads are described with the support of infinite trigonometric series that are more accurate. The so-developed SDOF model is therefore validated, based on selected literature results, by analyzing the large displacement response of thin elastic plates, under several boundary conditions and real blast pressures. Major advantage for the validation of the proposed SDOF model is obtained from experimental finite element (FE) and finite difference (FD) models of literature, giving evidence of a rather good correlation and confirming the validity of the presented formulation.

A Simplified Approach to the Analysis of Large Deflections of Plates

1974 ◽  
Vol 41 (2) ◽  
pp. 523-524 ◽  
Author(s):  
J. Mazumdar ◽  
R. Jones
Keyword(s):  
Arbitrary Shape ◽  
Horizontal Direction ◽  
Large Deflections ◽  
Elastic Plates ◽  
Elliptical Plate ◽  
Simplified Approach ◽  
Contour Lines ◽  
Thin Elastic 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.

Buckling of elastic plates by the method of constant deflection lines

1972 ◽  
Vol 13 (1) ◽  
pp. 91-103 ◽  
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.

scholarly journals Ray analysis and punching problems for stretched elastic plates

1982 ◽  
Vol 24 (1) ◽  
pp. 98-119 ◽  
Author(s):  
T. Bryant Moodie ◽  
R. J. Tait ◽  
D. W. Barclay
Keyword(s):  
Uniaxial Tension ◽  
Circular Hole ◽  
Transversely Isotropic ◽  
Simple Algebra ◽  
Numerical Results ◽  
Graphical Form ◽  
Elastic Plates ◽  
Ray Method ◽  
Propagation Process ◽  
Isotropic Plates

AbstractThe present paper presents a ray analysis for a problem of technical importance in fragmentation studies. The problem is that of suddenly punching a circular hole in either isotropic or transversely isotropic plates subjected to a uniaxial tension field. The ray method, which involves only differentiation, integration, and simple algebra, is shown to be particularly useful in clarifying the propagation process of the resulting unloading waves and obtaining the attendant discontinuities of the various quantities involved. Numerical results obtained from the ray analysis are presented in graphical form and compared with those obtained by more elaborate schemes.

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