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Analytical solution for this geotechnical problem

Analytical solution for this geotechnical problem

(OP)
This is a geotechnical problem that I am seeking an analytical solution to.

A soil layer of depth H and width L is loaded in plane-strain by a periodic load of F=sin t, where F is in units of Force/Length^2. The soil layer is perfectly linear elastic, fixed at the bottom in horizontal and vertical directions. At either side it is fixed only in the horizontal direction.

I would like a physical/mathematical model that can come up with resulting stresses, strains, displacements, accelerations and velocities at any point (x0,y0)(x0,y0) as a function of time. All material parameters are readily available, including Poisson's Ratio and Shear Modulus.

PLease see attachment for a graphic of the problem...

RE: Analytical solution for this geotechnical problem

Looks a lot like a homework problem I had in grad school

RE: Analytical solution for this geotechnical problem

The prof had a rough party last nite last nite lasting until daylight.

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