i´m searching for the displacement of the surface of a elastic rectangle for a given x and y and a force at a position.

like a bowling ball on a trampoline

the equation should include a var for the elasticity of the surface and the position and strength of the point-shaped force. the return should be a delta-z to any given xy-pair.

I tried a lot of sin cos stuff but could not figure it out. One of the problems is the surface should be fixed at the edges (like a trampoline). so the influence of the force is getting weaker (or the surface is getting stiffer) near the edge.

the is no need for a physically correct model. A function that gives me a roughly such a curve would help me alot

Any suggestions???