Bending of a thin cantilevered orthotropic plate with a concentrated load at the free edge

1972 ◽  
Vol 4 (4-6) ◽  
pp. 582-584
Author(s):  
V. M. Aranovich ◽  
A. V. Pescherov
Keyword(s):  
Orthotropic Plate ◽  
Free Edge ◽  
Concentrated Load

Deflections and Moments Due to a Concentrated Load on a Cantilever Plate of Infinite Length

1950 ◽  
Vol 17 (1) ◽  
pp. 67-72 ◽  
Author(s):  
T. J. Jaramillo
Keyword(s):  
Constant Width ◽  
Arbitrary Point ◽  
Free Edge ◽  
Practical Significance ◽  
Infinite Length ◽  
Cantilever Plate ◽  
Concentrated Load ◽  
Numerical Examples ◽  
Improper Integrals ◽  
Special Case

Abstract This paper contains an exact solution in terms of improper integrals for the deflections and moments due to a transverse concentrated load acting at an arbitrary point of an infinitely long cantilever plate of constant width and thickness. The solution is transformed into series form by means of contour integration, and is illustrated by numerical examples. In particular, comparisons are made with the known solution (1) for the special case where the load is applied at the free edge of the plate. The results obtained are of practical significance in connection with the design of certain types of monorail cranes.

Cantilever Plate With Concentrated Edge Load

1937 ◽  
Vol 4 (1) ◽  
pp. A8-A10 ◽  
Author(s):  
D. L. Holl
Keyword(s):  
Approximate Solution ◽  
Boundary Conditions ◽  
Finite Length ◽  
Finite Differences ◽  
Free Edge ◽  
Cantilever Plate ◽  
Transverse Stress ◽  
Longitudinal Stress ◽  
Concentrated Load ◽  
Clamped Edge

Abstract The author gives, by the method of finite differences, an approximate solution of the problem of a finite length of a cantilever plate which bears a concentrated load at the longitudinal free edge. All the boundary conditions are taken into account, and the plate action is determined approximately at all points of the plate. The author points out that a secondary maximum transverse stress occurs at the clamped edge nearest the loading point, and that the longitudinal stress is greatest directly under the loading point.

Nonlinear Theory for Flexural Motions of Thin Elastic Plate, Part 3: Numerical Evaluation of Boundary Layer Solutions

1982 ◽  
Vol 49 (2) ◽  
pp. 409-416
Author(s):  
N. Sugimoto
Keyword(s):  
Boundary Layer ◽  
Stress Singularity ◽  
Free Edge ◽  
Thin Elastic Plate ◽  
Normal Stresses ◽  
Interior Region ◽  
First Order ◽  
Plausible Values ◽  
Bending Stresses ◽  
Order Stress

The boundary layer solutions previoulsy obtained in Part 2 of this series for the cases of the built-in edge and the free edge are evaluated numerically. For the built-in edge, a characteristic penetration depth of the boundary layer toward the interior region is given by 0.13 εh, εh being the normalized thickness of the plate, while for the free edge, it is given by 0.32 εh. Thus the boundary layer for the free edge penetrates more deeply toward the interior region than that for the built-in edge. The first-order stress distribution in each boundary layer is displayed. For the built-in edge, the stress singularity appears on the edge. It is shown that, in the boundary layer, the shearing and normal stresses become comparable with the bending stresses. Similarly for the free edge, the shearing stress also becomes comparable with the twisting stress. It should be remarked that, in the boundary layer, the shearing or the normal stress plays a primarily important role as the bending or the twisting stress. But the former decays toward the interior region and remains higher order than the latter. Finally owing to these numerical results, the coefficients involved in the “reduced” boundary conditions for the built-in edge are evaluated for the various plausible values of Poisson’s ratio.

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