Consider an elastic half-space loaded over its entire free surface with a sinusoidal pressure as shown. Using a portion of the general solution (8.2.6), show that an Airy stress function of the form ∅ = cos βx [Be–^βy + Dye–^βy] will satisfy the appropriate boundary and far-field conditions and thus solve this problem. Next determine the x-location where the horizontal shear stress is a maximum and plot the distribution of this component versus depth into the medium. Such solutions have been used in geomechanics problems to simulate seafloor loading from surface water waves.

Equation 8.2.6

Transcribed Image Text:

X y p=p.cos(x/L)