Large Deflections of Rectangular Plates

1971 ◽  
Vol 15 (02) ◽  
pp. 164-171
Author(s):  
Norman Jones ◽  
R. M. Walters
Keyword(s):  
Approximate Method ◽  
Rectangular Plate ◽  
Large Deflections ◽  
Rectangular Plates ◽  
Finite Deflections ◽  
Perfectly Plastic ◽  
Aspect Ratios ◽  
Plastic Analysis ◽  
Theoretical Procedure

An approximate rigid, perfectly plastic analysis which retains the influence of finite deflections is presented herein for a uniformly loaded, fully clamped rectangular plate. This theoretical procedure provides reasonable engineering estimates of the permanent deflections of rectangular plates according to the recent experiments of Hooke and Rawlings on plates with aspect ratios in the range 1/3 ≤ β ≤ 1. The approximate method also predicts values which agree fairly well with the tests of Young on long rectangular plates β = 1/3), and for large permanent deflections gives similar values to the analysis by Greenspon when β = 1.

The Influence of Large Deflections on the Behavior of Rigid-Plastic Cylindrical Shells Loaded Impulsively

1970 ◽  
Vol 37 (2) ◽  
pp. 416-425 ◽  
Author(s):  
Norman Jones
Keyword(s):  
Cylindrical Shells ◽  
Dynamic Loads ◽  
Large Deflections ◽  
Finite Deflections ◽  
Shell Material ◽  
Governing Equations ◽  
Rigid Plastic ◽  
Perfectly Plastic ◽  
Dynamic Analyses ◽  
Circular Cylindrical Shells

A theoretical investigation is herein undertaken in order to examine the response of circular cylindrical shells subjected to dynamic loads of an intensity sufficient to cause large permanent deformations. The shell material is assumed to be rigid, perfectly plastic and the influence of finite deflections is retained in the governing equations. It emerges clearly from the study that geometry changes influence markedly the shell behavior even for quite small deflections and, therefore, they should be retained in any dynamic analyses of cylindrical shells with axial restraints.

scholarly journals Analysis of inelastic buckling of rectangular plates with a free edge using polynomial deflection functions

2020 ◽  
Vol 11 (1) ◽  
pp. 15-21
Author(s):  
Uchechi G. Eziefula
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Polynomial Function ◽  
Free Edge ◽  
Rectangular Plates ◽  
Maclaurin Series ◽  
Inelastic Buckling ◽  
Aspect Ratios ◽  
Isotropic Plates ◽  
Deformation Plasticity

AbstractThe inelastic buckling behaviour of different rectangular thin isotropic plates having a free edge is studied. Various combinations of boundary conditions are subject to in-plane uniaxial compression and each rectangular plate is bounded by an unloaded free edge. The characteristic deflection function of each plate is formulated using a polynomial function in form of Taylor–Maclaurin series. A deformation plasticity approach is adopted and the buckling load equation is modified using a work principle technique. Buckling coefficients of the plates are calculated for various aspect ratios and moduli ratios. Findings obtained from the investigation are found to reasonably agree with data published in the literature.

Loss Factor for a Rectangular Plate of Parabolic Thickness Variation

1977 ◽  
Vol 99 (3) ◽  
pp. 799-801
Author(s):  
S. P. Nigam ◽  
G. K. Grover ◽  
S. Lal
Keyword(s):  
Rectangular Plate ◽  
Variable Thickness ◽  
Fundamental Mode ◽  
Loss Factor ◽  
Thickness Variation ◽  
Stress System ◽  
Rectangular Plates ◽  
Uniform Thickness ◽  
Aspect Ratios ◽  
Mode Loss

The importance of the internal damping and of the evaluation of the fundamental mode loss factor of structural members subjected to multiaxial stress system is well known. A good amount of work is available on the elastic vibrations of ectangular plates of uniform thickness but it appears that little work has been done on vibrations of rectangular plates of variable thickness, though such cases are of interest in the aeronautical field since they approximate to wing sections. In the present work, the fundamental mode loss factors for a simply supported rectangular plate with parabolic thickness variation in X direction have been evaluated for different combinations of the aspect ratios and the taper parameters. An approximate relationship has been obtained which correlates the loss factor for the plate of variable thickness with that of a plate of uniform thickness.

Simulation of Planarization of Rectangular Glass Plate Using Tool-Path-Control-Type Polishing

2009 ◽  
Vol 76-78 ◽  
pp. 313-318
Author(s):  
Kenichiro Yoshitomi ◽  
Atsunobu Une ◽  
Masaaki Mochida
Keyword(s):  
Rectangular Plate ◽  
Tool Path ◽  
Liquid Crystal Display ◽  
Glass Plate ◽  
Rectangular Plates ◽  
Short Side ◽  
Aspect Ratios ◽  
Path Control ◽  
Rotary Type ◽  
Rectangular Glass

The size of the photo mask and mother glass used in liquid crystal display production has increased yearly. Large rectangular glass plates are difficult to planarize using rotary-type polishing machines. We have developed a rotary-type polishing machine with tool path control that is optimized by polishing simulation for a rectangular wafer. The present paper describes the planarization of a rectangular plate by simulation. The influence of tool size and the aspect ratio of the rectangular plate on the flatness are clarified. For a square plate, the flatness obtained under optimized oscillation speed is less than a quarter of that obtained under uniform oscillation speed. For rectangular plates with aspect ratios of 1:1.25 and 1:1.5, planarization using a tool having a diameter equal to half the diagonal length of the plate is shown to be difficult because the stock removal distributions in diagonal and short side of the workpiece become the different shape.

Dynamic Plastic Analysis of Impulsively Loaded Viscoplastic Rectangular Plates With Finite Deflections

1986 ◽  
Vol 53 (3) ◽  
pp. 667-674 ◽  
Author(s):  
David Hui ◽  
J. G. de Oliveira
Keyword(s):  
Pressure Pulse ◽  
Dynamic Pressure ◽  
Rectangular Plates ◽  
Finite Deflections ◽  
Equilibrium Equations ◽  
Dynamic Nature ◽  
Sensitive Material ◽  
Energy Balance Method ◽  
Runge Kutta Method ◽  
Plastic Analysis

An energy balance method for the dynamic plastic analysis of thin rectangular plates made of a strain-rate sensitive material, taking into account the influence of finite-deflections, is proposed. The particular case of a fully clamped plate under uniformly distributed dynamic pressure pulse or blast loading is studied in some detail. In addition to the nonaxisymmetric and dynamic nature of the problem, the analysis considers important nonlinearities in the strains, equilibrium equations, and constitutive equations. Nonlinear ordinary differential equations in various regimes of plate deflections and loading histories are derived and solved using a Runge–Kutta method. Comparisons are made with existing experimental data.

Buckling of Rectangular Plates With Built-In Edges

1942 ◽  
Vol 9 (4) ◽  
pp. A171-A174
Author(s):  
Samuel Levy
Keyword(s):  
Exact Solution ◽  
Rectangular Plate ◽  
Infinite Series ◽  
Numerical Results ◽  
Buckling Load ◽  
Rectangular Plates

Abstract This paper presents an exact solution in terms of infinite series of the problem of buckling by compressive forces in one direction of a rectangular plate with built-in edges (zero slope, zero displacement in the direction normal to the plane of the plate). The buckling load is calculated for 14 ratios of length to width, ranging in steps of 0.25 from 0.75 to 4. On the basis of convergence, as the number of terms used in the infinite series is increased, it is estimated that the possible error in the numerical results presented is of the order of 0.1 per cent. A comparison is given with the work of other authors.

Wavelet Multi-Scale Solution for Deflection of Thin Rectangular Plates under Temperature

2012 ◽  
Vol 166-169 ◽  
pp. 2871-2875
Author(s):  
Yan Chang Wang ◽  
Ke Liang Ren ◽  
Yan Dong ◽  
Ming Guang Wu
Keyword(s):  
Differential Equations ◽  
Rectangular Plate ◽  
Thermal Environment ◽  
Operational Matrix ◽  
Rectangular Plates ◽  
Thin Rectangular Plate ◽  
Multi Scale ◽  
Scale Method ◽  
The Matrix ◽  
Operational Matrix Of Integration

To consider the deformation of thin rectangular plate under temperature. In this paper, the wavelet multi-scale method was used to solve the thin plate governing differential equations with four different initial or boundary conditions. An operational matrix of integration based on the wavelet was established and the procedure for applying the matrix to solve the differential equations was formulated, and got the deflection of thin rectangular plates under temperature. The result provides a theoretical reference for solving thin rectangular plate deflection in thermal environment using multi-scale approach.

The Influence of Rotatory Inertia and Transverse Shear on the Dynamic Plastic Behavior of Beams

1979 ◽  
Vol 46 (2) ◽  
pp. 303-310 ◽  
Author(s):  
Norman Jones ◽  
J. Gomes de Oliveira
Keyword(s):  
Transverse Shear ◽  
Shear Force ◽  
Yield Criterion ◽  
Yield Condition ◽  
Bending Moment ◽  
Plastic Behavior ◽  
Plastic Response ◽  
Rotatory Inertia ◽  
Perfectly Plastic ◽  
Theoretical Procedure

The theoretical procedure presented herein examines the influence of retaining the transverse shear force in the yield criterion and rotatory inertia on the dynamic plastic response of beams. Exact theoretical rigid perfectly plastic solutions are presented for a long beam impacted by a mass and a simply supported beam loaded impulsively. It transpires that rotatory inertia might play a small, but not negligible, role on the response of these beams. The results in the various figures indicate that the greatest departure from an analysis which neglects rotatory inertia but retains the influence of the bending moment and transverse shear force in the yield condition is approximately 11 percent for the particular range of parameters considered.

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