Material Minds HELP: Entering Non-Uniform Pressure Distributions

The input field used to enter pressure is typically used to enter a scalar value for uniform pressure. However, the system can accept pressure that is a function of the normalized x and y coordinates. The trick is to use x and y as symbols. x and y each have the range of -1 to 1. This means that the normalized x is equivalent to /a in the global coodinate system, where the tilde is being used to indicate global coordinates.

The system can accept any "simple" function defined in Mathematica. Note that adding a functional distribution can increase the computation time. There is a potential that the server may isse a "time out" error before the solution can be returned.

Examples

Linear variation of pressure in x coordinate

If the pressure is p1 at the =0a/2 boundary of the plate, and p2 at =+a/2, then the following interpolation equation can be used.

(1/2)*(p1 + p2 - p1*x + p2*x)

For example, if p1 =0, and p2 = 10, then the following formula would be entered directly into the field labled "Enter Pressure Magnitude".

Sinusoidal Pressure Distribution

Consider a pressure distribution which has the value of 1 at the center of the plate, and falls to zero at all the edges, following a Cos function distribution. The following formula would be entered.

Pressure Over a Patch

Consider a pressure that is applied only over a limited area of the plate. The following formula applies a pressure of 10 units for x between -0.5 and +0.5 (in normalized coordinates) and zero elsewhere. && is the And operator in Mathematica.

Created by Mathematica  (July 9, 2004)