Rectangular Plates on Unilateral Edge Supports: Part 2—Implementation; Concentrated and Uniform Loading

1986 ◽  
Vol 53 (1) ◽  
pp. 151-156 ◽  
Author(s):  
J. P. Dempsey ◽  
Hui Li
Keyword(s):  
Unilateral Contact ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Computer Implementation ◽  
Concentrated Loads ◽  
Uniform Loading ◽  
Loss Of Contact ◽  
Implementation Aspects ◽  
Laterally Loaded ◽  
Support Reactions

Rectangular plates in unilateral contact with sagged and unsagged supports laterally loaded by centrally concentrated loads and uniform pressure are examined. The loss of contact and the redistribution of deflections, moments, and support reactions are presented. Computer implementation aspects are discussed.

Rectangular Plates on Unilateral Edge Supports: Part 1—Theory and Numerical Analysis

1986 ◽  
Vol 53 (1) ◽  
pp. 146-150 ◽  
Author(s):  
J. P. Dempsey ◽  
Hui Li
Keyword(s):  
Singular Integral Equations ◽  
Integral Transforms ◽  
Rectangular Plates ◽  
Centrally Symmetric ◽  
Solution Methods ◽  
Dual Series Equations ◽  
Finite Integral ◽  
Loss Of Contact ◽  
Laterally Loaded ◽  
Numerical Approaches

The corners of a simply supported, laterally loaded rectangular plate must be anchored to prevent them from lifting off the supports. If no such anchors are provided, and the supports are unilateral or capable of exerting forces in one direction only, parts of the plate will bend away from the supports upon loading. The loss of contact when uplift of laterally loaded rectangular plates is not prevented is examined in this paper. Arbitrary centrally symmetric loading is considered. Finite integral transforms convert the coupled dual-series equations that result from the Levy-Nadai approach to two coupled singular integral equations. Different solution methods are applicable for sagged and unsagged supports; these two numerical approaches are discussed in detail.

Loss of Contact in the Vicinity of a Right-Angle Corner for a Simply Supported, Laterally Loaded Plate

1981 ◽  
Vol 48 (3) ◽  
pp. 597-600 ◽  
Author(s):  
L. M. Keer ◽  
A. F. Mak
Keyword(s):  
Integral Transform ◽  
Space Region ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Concentrated Force ◽  
Simply Supported ◽  
Quarter Space ◽  
Loss Of Contact ◽  
Restraining Force ◽  
Laterally Loaded

The solutions to problems of laterally loaded, simply supported rectangular plates are classical ones that can be found in standard textbooks. It is found that forces directed downward must be present to prevent the corners of the plate from rising up during bending. The objective of the present analysis is to determine the extent to which such a plate will rise if the corner force is not present and the plate is unilaterally constrained. Rather than determine the solution for a rectangular plate, we consider a laterally loaded, simply supported plate which occupies a quarter space region. The plate is unilaterally constrained and may rise at the corner due to an absence of restraining force there. Using integral transform techniques appropriate to the quarter space for elastic plates, the region of lost contact is determined for a general loading. The special loading due to a concentrated force is given as an example.

Design of Long Rectangular Elasto-Plastic Plates

1961 ◽  
Vol 5 (04) ◽  
pp. 16-33
Author(s):  
Thein Wah
Keyword(s):  
Strengthening Effect ◽  
Rectangular Plates ◽  
Uniform Pressure ◽  
Analysis And Design ◽  
Elastic Range ◽  
Salient Features

In a previous paper3 a theory was derived for the analysis of rectangular plates loaded with a uniform pressure and beyond the elastic range of the material. The theory took into account the strengthening effect of membrane tensions in the plane of the plate, the effects of edge displacements and of initial deflections and locked-in moments which might exist in the plate. In the present paper the salient features of the theory are put in the form of charts and tables for convenience in analysis and design.

Plastic Reserve Strength of Rectangular Plates

1984 ◽  
Vol 28 (03) ◽  
pp. 173-185
Author(s):  
Ching-Yuan Chu ◽  
William S. Vorus
Keyword(s):  
Upper Bound ◽  
Load Capacity ◽  
Programming Algorithm ◽  
Rectangular Plates ◽  
Unknown Parameters ◽  
Various Boundary Conditions ◽  
Elastic Load ◽  
Minimization Procedure ◽  
Laterally Loaded ◽  
Reserve Strength

An upper-bound functional which attains its minima at collapse of thin laterally loaded plates is formulated. A general collapse pattern for various thin plate problems is constructed in terms of a set of unknown parameters. An appropriate mathematical programming algorithm is applied to search for the correct parameters in the minimization procedure. Rectangular plates under uniform load are treated specifically. The least upper-bound solutions for rectangular plates with various boundary conditions are calculated. The corresponding elastic solutions are also calculated. From these elastic and plastic solutions the reserve strength of the plate beyond its elastic load capacity is predicted.

Design of Laterally Loaded Plating—Concentrated Loads

1983 ◽  
Vol 27 (04) ◽  
pp. 252-264
Author(s):  
Owen Hughes
Keyword(s):  
Experimental Data ◽  
Load Parameter ◽  
Uniform Pressure ◽  
Concentrated Loads ◽  
Rigid Plastic ◽  
Concentrated Load ◽  
Load Effect ◽  
Permanent Set ◽  
Multiple Location ◽  
Single Location

In the design of plating subject to lateral loading, the principal load effect to be considered is the amount of permanent set, that is, the maximum permanent deflection in the center of each panel of plating bounded by the stiffeners and the crossbeams. The present paper is complementary to a previous paper [1]2 which dealt with uniform pressure loads. It first shows that for design purposes there are two types of concentrated loads, depending on the number of different locations in which they can occur; single location or multiple location. The hypothesis is then made that for multiple-location loads the eventual and stationary pattern of plasticity which is developed in the plating is very similar to that for uniform pressure loads, and hence the value of permanent set may be obtained by using the same formula as for uniform pressure loads, with a load parameter Q that is some multiple r of the load parameter for the concentrated load: 0 = rQP. The value of r is a function of the degree of concentration of the load and is almost independent of plate slenderness and aspect ratio. The general mathematical character of this function is established from first principles and from an analysis of the permanent set caused by a multiple-location point load acting on a long plate. The results of this theoretical analysis provide good support for the hypothesis, as do also the relatively limited experimental data which are available. The theory and the experimental data are combined to obtain a simple mathematical expression for r. A more precise expression can be obtained after further experiments have been performed with more highly concentrated loads. Single-location loads produce a different pattern of plasticity and require a different approach. A suitable design formula is developed herein by performing regression analysis on the data from a set of experiments performed with such loads. Both methods presented herein, one for multiple-location loads and the other for single-location loads, are valid for small and moderate values of permanent set and can be used for all static and quasistatic loads. Dynamic loads and applications involving large amounts of permanent set require formulas based on rigid-plastic theory. Such formulas are available for uniform pressure loads and were quoted in reference [1]. A formula for single-location loads has recently been derived by Kling [4] and is quoted herein.

Bifurcation of Circular Rings Under Normal Concentrated Loads

1973 ◽  
Vol 40 (1) ◽  
pp. 233-238 ◽  
Author(s):  
P. Seide ◽  
E. D. Albano
Keyword(s):  
Bifurcation Point ◽  
Circular Ring ◽  
Average Pressure ◽  
Uniform Pressure ◽  
Concentrated Loads ◽  
Finite Distortion ◽  
Circular Rings ◽  
Concentrated Forces

The deformation in bending of a circular ring loaded in its plane by concentrated forces is studied. The ring is assumed to be an elastica. The loads are of equal magnitudes and are equally spaced about the ring. Values of loading at which bifurcation of the symmetrical finite distortion shape occurs are determined for forces which remain normal to the ring. It is found that no bifurcation point exists for a ring under three loads. Buckling of a ring under two loads can occur only when the prebuckling configuration is an extremely distorted one. If the number of loads is five or greater, the critical average pressure does not differ greatly from the result for the ring under uniform pressure.

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