# Material Differential-Equation

1. Sep 28, 2004

### Mathman23

Hi

I have the following problem:

A wall has a size of X square-feet.

Is has been build by a material called Y which can withstand Z amounts of pressure.
A storm which produces winds of N Miles/hour (Equivalent to Z) blows onto the wall.

My question is:

Is it possible to express the above as a differential equation ?

So I can calculate how much pressure a wall of a certain size and material can withstand

Sincerely
Fred
Denmark

2. Sep 28, 2004

### Clausius2

If I understood you well, Fred, in my opinion no differential form is needed, unless you want to do an accurate stress analysis inside the wall.

You have two ways:

i) establishing equilibrium in the wall considering the laws of the Resistance of Materials. Given the pressure exerted, you will have to solve for finding the bending stress that is bearing the wall. Once you have this bending stress you will employ a withstand criterion, (i.e. the material starts to have a plastic behaviour). All of that can be done with one-dimensional analysis at one of the lines of symmetry of your wall, where surely are concentred the maximum stresses.

ii) If you want to do a three-dimensional analysis, you will have to employ the complete Navier-Bresse equations of the Elastic Theory. They will report you the stress an deformation in each point of the wall. Surely you will have to employ FEM methods.

To be honest, you ought to clarify yourself if you want an "engineering" solution, or you want a full detail solution.

Anyway, there exists ODE's for one dimensional and narrow girders bearing a lot of variety of force distributions.

3. Sep 28, 2004