Large Deflection of a Circular Plate on Elastic Foundation Under a Concentrated Load at the Center

1975 ◽  
Vol 42 (2) ◽  
pp. 503-505 ◽  
Author(s):  
S. Datta
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Large Deflection ◽  
Concentrated Load ◽  
Plate On Elastic Foundation

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.

Dynamic Analysis of Circular Plate on Elastic Foundation by EFHT Method

2003 ◽  
Vol 19 (3) ◽  
pp. 337-347
Author(s):  
Lai-Yun Wu ◽  
Wen-Haur Lee
Keyword(s):  
Differential Equation ◽  
Dynamic Response ◽  
Circular Plate ◽  
Elastic Foundation ◽  
Bending Moment ◽  
Hankel Transform ◽  
Elastic Circular Plate ◽  
Internal Forces ◽  
Plate On Elastic Foundation ◽  
Element Method

AbstractThe dynamic response of a homogeneous, isotropic and elastic circular plate on an elastic foundation subjected to axisymmetric time dependent loads is investigated both analytically and numerically in thisv paper. First, the Extended Finite Hankel Transform (EFHT) is derived. After applying the technique of the EFHT to the governing equation of the vibrating circular plate, the governing partial differential equation (PDE) is transformed into the governing ordinary differential equation (ODE). Therefore, the analytical solution of the plate problem can be found completely. Once the dynamic response of the plate is solved, the internal forces of the plate, including shear force, bending moment and torsion, can be obtained subsequently. Under the particular case that elastic springs do not exist under the foundation, the dynamic response of the circular plate by the method of EFHT matches exactly with that by the method of modal analysis. By comparing the methods of EFHT, Boundary Element Method (BEM) and Finite Element Method (FEM), the results indicate that the proposed method of EFHT is accurate, systematic and convenient.

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