Bending of Circular Plates Under a Variable Symmetrical Load

Bending of Circular Plates Under a Variable Symmetrical Load
Author: J. C. Heap
Publisher:
Total Pages: 36
Release: 1964
Genre: Bending
ISBN:

The basic equations of deflection, slope, and moment for a thin, flat, circular plate, under a symmetrical variable load, for a constant force divided by the square of the radial distance, have been developed. Six cases have been derived. The first four cases cover the variable load acting over the entire plate., (1) fixed, supported, outer edge and fixed, inner edge, 92) simply supported, outer edge and free, inner edge, (3) simply supported, outer edge and free, inner edge, (4) fixed, supported outer edge and free, inner edge; and the final two cases are for a solid plate having the acting variable load bounded by circles of an inner radius and the outer support-load radius; i.e., (5) fixed, supported, outer edge and (6) simply supported, outer edge.

The Bending and Stretching of Plates

The Bending and Stretching of Plates
Author: E. H. Mansfield
Publisher: Elsevier
Total Pages: 161
Release: 2014-05-12
Genre: Technology & Engineering
ISBN: 1483222667

The Bending and Stretching of Plates deals with elastic plate theory, particularly on small- and large-deflexion theory. Small-deflexion theory concerns derivation of basic equations, rectangular plates, plates of various shapes, plates whose boundaries are amenable to conformal transformation, plates with variable rigidity, and approximate methods. Large-deflexion theory includes general equations and some exact solutions, approximate methods in large-deflexion theory, asymptotic large-deflexion theories for very thin plates. Asymptotic theories covers membrane theory, tension field theory, and inextensional theory. The book explains stress-strain relations, effect of forces in the plane of the plate, and rectangular plates that have all edges simply supported, or where plates that have all edges clamped. The text also considers plates of constant thickness whose boundaries are circular, sector-shaped, elliptical, or triangular. Muskhelishvili (1933) addresses boundary value problems of plane stress using analytical methods of the biharmonic equation. The book also investigates some approximate methods of analysis of large-deflexion behavior of plates of constant thickness where there is either a uniformly distributed load, or a compressive load in the plane of the plate in excess of that necessary to cause initial buckling. The book explains that the engineer can use the principle of minimum potential energy to investigate large deflexion of plates. The text is suitable for structural engineers in civil, mechanical or marine engineering, as well as to structural research workers and students.

Technical Report

Technical Report
Author: University of Illinois (Urbana-Champaign campus). Engineering Experiment Station
Publisher:
Total Pages: 236
Release: 1964
Genre: Engineering
ISBN:

Bending of Circular Plates Under a Uniform Load on a Concentric Circle

Bending of Circular Plates Under a Uniform Load on a Concentric Circle
Author: J. C. Heap
Publisher:
Total Pages: 46
Release: 1964
Genre: Bending
ISBN:

The basic equations of deflection, slope, and moments for thin, flat, circular plate subjected to a uniform load on a concentric circle were derived for four generalized cases. From these generalized cases, six simplified cases were deduced.