Recent Approaches in the Theory of Plates and Plate-Like Structures

2022 ◽  
Keyword(s):  
Theory Of Plates

The Method of Finite Differences in Solutions Concerning Circular Plate

2011 ◽  
Vol 490 ◽  
pp. 305-311
Author(s):  
Henryk G. Sabiniak
Keyword(s):  
Circular Plate ◽  
Finite Differences ◽  
Machine Building ◽  
Polar Coordinates ◽  
Circular Plates ◽  
Technical Problems ◽  
Theory Of Plates ◽  
Worm Gearing ◽  
Mixed Derivatives ◽  
Plate Deflection

Finite difference method in solving classic problems in theory of plates is considered a standard one [1], [2], [3], [4]. The above refers mainly to solutions in right-angle coordinates. For circular plates, for which the use of polar coordinates is the best option, the question of classic plate deflection gets complicated. In accordance with mathematical rules the passage from partial differentials to final differences seems firm. Still final formulas both for the equation (1), as well as for border conditions of circular plate obtained in this study and in the study [3] differ considerably. The paper describes in detail necessary mathematical calculations. The final results are presented in identical form as in the study [3]. Difference of results as well as the length of arm in passage from partial differentials to finite differences for mixed derivatives are discussed. Generalizations resulting from these discussions are presented. This preliminary proceeding has the purpose of searching for solutions to technical problems in machine building and construction, in particular finding a solution to the question of distribution of load along contact line in worm gearing.

Flexure of a Circular Plate With a Ring of Holes

1962 ◽  
Vol 29 (3) ◽  
pp. 489-496 ◽  
Author(s):  
H. Kraus
Keyword(s):  
Circular Plate ◽  
Shear Force ◽  
General Boundary Condition ◽  
Uniform Pressure ◽  
Simply Supported ◽  
Moment Distribution ◽  
Theory Of Plates ◽  
Circular Holes ◽  
The Moment ◽  
Kirchhoff Theory

The problem of the moment distribution resulting from a uniform pressure load acting over the surface of a circular plate containing a ring of equally spaced circular holes with, and without, a central circular hole is solved within the framework of the Poisson-Kirchhoff theory of plates. A general boundary condition is applied at the outer rim of the plate to make the solution valid for a range of conditions from the simply supported case to the clamped case. The edges of the perforations are allowed to be either free or to have a net shear force acting. Numerical results in the form of curves are given for typical cases, and the results of a photoelastic test are also presented.

Elementary Theory of Plates

2000 ◽  
pp. 297-315
Author(s):  
Teodor M. Atanackovic ◽  
Ardéshir Guran
Keyword(s):  
Elementary Theory ◽  
Theory Of Plates

TRANSVERSE BENDING AND FREE VIBRATIONS OF ELASTIC ISOTROPIC PLATES IN THE FORM OF ISOSCELES TRIANGLES

2021 ◽  
Vol 98 (6) ◽  
pp. 20-27
Author(s):  
А.V. KOROBKO ◽  
◽  
N.G. KALASHNIKOVA ◽  
Е.G. ABASHIN ◽  
◽  
...  
Keyword(s):  
Form Factor ◽  
Free Vibrations ◽  
Arbitrary Form ◽  
Maximum Deflection ◽  
Isotropic Plates ◽  
Unloaded State ◽  
Theory Of Plates ◽  
Technical Theory ◽  
Hinged Support ◽  
Isosceles Triangles

This paper considers elastic isotropic plates in the form of isosceles triangles with combined boundary conditions (a combination of hinged support and rigid restraint conditions along the sides of the contour). Calculations were performed using FEM to determine the integral physical characteristics in the considered problems F (the maximum deflection of uniformly loaded plates w0 and the fundamental frequency of oscillations in the unloaded state ω). On the basis of the obtained numerical results, approximating functions have been constructed: "maximum deflection - form factor of plates", "basic frequency of oscillations - form factor of plates", the structure of which corresponds to the structure of similar formulas obtained when presenting known exact solutions in the corresponding problems of technical theory of plates in isoperimetric form. Based on the properties of the form factor of plates, these approximating functions limit the whole set of considered integral physical quantities and therefore can be used as reference solutions for the calculation of triangular plates of arbitrary form applying the method of interpolation by form factor (MIFF). We consider an example of calculation of a plate in the form of a rectangular triangle with hinged support of the sides.

Bending of Circular and Ring-Shaped Plates on an Elastic Foundation

1954 ◽  
Vol 21 (1) ◽  
pp. 45-51
Author(s):  
Herbert Reismann
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Series Solution ◽  
Circular Disk ◽  
Symmetric Problem ◽  
Concentrated Load ◽  
Transverse Loads ◽  
Infinite Extent ◽  
Theory Of Plates ◽  
Pure Moment

Abstract This paper develops a method for the evaluation of deflections, moments, shears, and stresses of a circular or ring-shaped plate on an elastic foundation under transverse loads. A series solution is derived for plates subjected to edge and/or concentrated loads and is given in terms of tabulated functions. It is exact within the assumptions underlying the classical theory of plates and includes, as a particular case, the known solution of the corresponding radially symmetric problem. Two examples displaying radial asymmetry are worked. A solution is given for (a) a circular plate resting on an elastic foundation, clamped at the boundary and subjected to an arbitrarily placed concentrated load, and (b) a plate of infinite extent, resting on an elastic foundation and clamped to the boundary of a rigid circular disk to which a pure moment is applied.

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