Circular Plate w/ Hole: Boundary Conditions

In summary: Its like a mystery to me.In summary, the boundary conditions for a circular plate with a central hole are as follows: there is a zero bending moment at the free end, a zero shear force at the fixed end, and a zero displacement at the center.
  • #1
harpreet singh
40
0
Hey people can u please tell me what will be the boundary conditions for a circular plate with a central hole clamped at the circumference... Plate is axis symmetric and is under uniform load..
 
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  • #2
You'll obviously have no displacements at the outer edge. There should also be a zero slope at the edge. At the center there are similarities for the conditions of a beam's free end. Can you think of what those would be?
 
  • #3
These two were known to me.. I was encountring problem with the inner edge only..
 
  • #4
Well, if you have a cantilevered beam, what can you say about the moment at the free end?
 
  • #5
I guess moment will b zero there
 
  • #6
But then also i will be needing 1 more condition coz i have 4 constants to be determined in my equation..
 
  • #7
Is the shear force defined at the fixed edge of the plate, perhaps by calculating the resultant reaction at that edge?
 
  • #8
Will there be any shear force at the fixed edge??
 
  • #9
On a uniformly loaded a cantilever beam, the shear force will be maximum at the fixed end of the beam, and equal to the reaction force at that end. Additionally, since the beam is only supported by one end, the shear force is zero at the free end of the beam.
 
  • #10
According to Roark's Table 11.2 Case 2e (Annular plate, outer edge fixed, inned edge free), the following boundary conditions apply:

  • Bending moment at the free end is zero.
  • Shear force at the free end is zero.
  • Displacement at the fixed end is zero.
  • Slope at the fixed end is zero.

They also have a definition of the shear force at the fixed edge (enge "a") that is basically a calculation of the reaction force along that edge.

[tex]Q_{a}=\frac{-q}{2a}(a^2-r_{o}^2)[/tex]
 
  • #11
Thanx a lot.. can u please send me that link??
 
  • #13
Ok.. Do u have ebook or hard copy??
 
  • #14
Can u please check wat r d conditions if inner edge is simply supported and outer edge clamped..
 
  • #15
Mech_Engineer said:
According to Roark's Table 11.2 Case 2e (Annular plate, outer edge fixed, inned edge free), the following boundary conditions apply:

  • Bending moment at the free end is zero.
  • Shear force at the free end is zero.
  • Displacement at the fixed end is zero.
  • Slope at the fixed end is zero.

They also have a definition of the shear force at the fixed edge (enge "a") that is basically a calculation of the reaction force along that edge.

[tex]Q_{a}=\frac{-q}{2a}(a^2-r_{o}^2)[/tex]
I was trying to not directly quote that to get the OP to think about the conditions on his own...Make him work!
 
  • #16
Thanx a lot sir for helping me that way..
 
  • #17
FredGarvin said:
I was trying to not directly quote that to get the OP to think about the conditions on his own...Make him work!

Sorry about that Fred, I just get so excited!

harpreet singh said:
Can u please check wat r d conditions if inner edge is simply supported and outer edge clamped..

Its quite easy to interpolate what you've "learned" on the case above to the simply supported case. Perhaps trying to sketch a rough shear force and bending moment diagram could help you... specifically looking at what a simple support's effect looks like on those diagrams.
 
  • #18
sorry but i got stuck once more.. I am not being able to integrate dw/rdr w.r.t dr
 
  • #19
Mech_Engineer said:
Sorry about that Fred, I just get so excited!
I just can't touch that one...
 

What is a circular plate with a hole?

A circular plate with a hole is a simple structure often used in engineering and mechanics to demonstrate the principles of stress and strain. It is a circular-shaped plate that has a hole in its center, which creates a stress concentration point.

What are boundary conditions?

Boundary conditions are the constraints or limitations imposed on a physical system, such as a circular plate with a hole. They define the behavior of the system by specifying the values of certain variables, such as displacement, stress, or strain, at the boundaries of the system.

Why are boundary conditions important in analyzing a circular plate with a hole?

Boundary conditions are essential in analyzing a circular plate with a hole because they help us understand how the plate will behave under different loading conditions. They provide us with information about stress and strain distribution, deformation, and failure of the plate.

What are the different types of boundary conditions for a circular plate with a hole?

There are three main types of boundary conditions for a circular plate with a hole: fixed, simply supported, and free. In a fixed condition, the edges of the plate are fixed and cannot move. In a simply supported condition, the edges are allowed to rotate and move vertically, but not horizontally. In a free condition, the edges are free to move and rotate in all directions.

How do boundary conditions affect the stress and strain distribution in a circular plate with a hole?

The type of boundary condition applied to a circular plate with a hole greatly affects the stress and strain distribution in the plate. Fixed boundary conditions result in high stress concentrations near the edges, while simply supported and free boundary conditions distribute the stress more evenly across the plate.

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