Formula for a non-uniform distributed load on a flat plate

In summary: Your Name]In summary, the user is struggling with representing a distributed load for a flat plate using the rayleigh-ritz method. They have tried using a heaviside function, but it only works for the bottom half of the plate. They are looking for suggestions on how to accurately represent the load for the entire plate, and some possible approaches include using nested if statements or a combination of the heaviside and sign functions.
  • #1
psuaero
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Homework Statement


I am writing a MATLAB code to predict plate displacement for multiple load conditions using the rayleigh-ritz method. I have gotten the first three loads but I am struggling with the last load case.

I need to represent a distributed load for a flat plate that is piecewise defined as follows:

p(z)=
c 0<=x<=[tex]\frac{L}{2}[/tex] , 0<=y<=[tex]\frac{L}{2}[/tex]
-c 0<=x<=[tex]\frac{L}{2}[/tex] , [tex]\frac{L}{2}[/tex]<=y<=L
c [tex]\frac{L}{2}[/tex]<=x<=L , [tex]\frac{L}{2}[/tex]<=y<=L
-c [tex]\frac{L}{2}[/tex]<=x<=L , 0<=y<=[tex]\frac{L}{2}[/tex]

Homework Equations


The Attempt at a Solution



I've tried to represent this loading case using a heaviside function and this load case looks correct from the bottom of the plate to the middle of the plate but is not correct for the top half of the plate. as shown in the figure below.

[PLAIN]http://www.personal.psu.edu/kwm140/Loadcase.jpg [Broken]

this is the function that I used to create this load case:
p=10*heaviside(12 -x)-10*heaviside(-12+x)-10*heaviside(-12+y);
I used the value of 10 in place of c

Any ideas on how to represent this loading in a way that would allow the load to be integrated over the area of the plate.
 
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  • #2

Thank you for sharing your progress on your MATLAB code. Representing a distributed load using a piecewise function can be challenging, but there are a few approaches you can try.

One option is to use a nested if statement to define the load in different regions of the plate. For example, your first condition could be if x is between 0 and L/2 and y is between 0 and L/2, then the load is c. Then, you can add additional conditions for each of the remaining regions of the plate.

Another approach is to use a combination of the heaviside and sign functions. The sign function returns -1 for negative values and 1 for positive values, so you can use it to alternate between positive and negative values for your load. You can then use the heaviside function to define the boundaries of each region.

I would also recommend checking your units and making sure they are consistent throughout your code. It's possible that the incorrect values for the top half of the plate are due to a unit conversion error.

I hope this helps and good luck with your code! Let me know if you have any further questions.


 

1. What is a non-uniform distributed load on a flat plate?

A non-uniform distributed load on a flat plate is a type of load that is applied to a flat surface in varying magnitudes and locations. This means that the load is not evenly distributed across the entire surface, but rather is concentrated in certain areas.

2. How is the formula for a non-uniform distributed load on a flat plate calculated?

The formula for a non-uniform distributed load on a flat plate is calculated by multiplying the load intensity (force per unit area) by the differential area and integrating over the entire surface. This takes into account the varying magnitudes and locations of the load.

3. What factors affect the distribution of the load on a flat plate?

The distribution of the load on a flat plate is affected by several factors, including the shape and size of the plate, the location and magnitude of the applied load, and the material properties of the plate.

4. How does a non-uniform distributed load affect the structural integrity of a flat plate?

A non-uniform distributed load can significantly affect the structural integrity of a flat plate by creating areas of high stress and strain. This can lead to deformation, buckling, and potential failure of the plate if it is unable to withstand the load.

5. Are there any limitations to using the formula for a non-uniform distributed load on a flat plate?

Yes, there are limitations to using the formula for a non-uniform distributed load on a flat plate. It is based on several assumptions, such as the plate being thin and flat, and the load being applied in a perpendicular direction to the surface. It may not accurately predict the behavior of more complex structures or non-linear material properties.

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