I am wondering if anyone can give me an idea of what the transformation of the constant pressure load function is and for which values of n and m must be taken into account?
I do not understand what you mean by 'transformation of the constant pressure load function'.
Suppose you wish to find the analytical solution of a simply-supported rectangular plate under a uniform pressure load. The solution is Sigma(i=1,n; j=1,m) [ A_ij*sin(i*pi*x/a)*sin(j*pi*y/b) ], where a and b are dimensions of the plate in the x and y directions; A_ij are series coefficients to be determined from the exteral load.
If the pressure is uniform, only odd sines in the series solutions are present. 2 sine terms in x and in y are good enough.
The key is the integration of cos(n*pi*y/b) over [0, b] at n = 0, 1, 2, ...
The integration has two results (branches): (1) the branch at n 0, which is what you have already got; (2) the branch at n = 0, which is b.
You error is that you have ignored the 2nd branch, whcih happens to be the right answer to the integral for a uniform pressure.
Got it?
There is a good reason why only n = 0 term is present when the external load is uniform.
In other special types of loads, only certain n terms occur.
When n = 0, shape function cos is 1. This means that if any function to be decomposed into cos series has a constant component, the series must involve n = 0 term, for example, if the exteral distributed load is p_0 + p_1*y, where p_0 and p_1 are constants.
In general, n = 0 term should be kept, on the safe side.
- Badges
- Science topic