Pressure on circular area of a semi-infinite plane: typos in textbooks "contact mechanics" "surface mechanics" "elasticity"

This is supposed to be a very classic analytical solution in applied elasticity. Forgive me if this is a repost or some correction has been made before. I had a hard time with it.

Problem statement:  uniform pressure is applied on cirular area (radius=r) on top of a semi-infinite plane. Find the vertical deflection.

We got discrepancy between FEA solution and analytical solution which I found from different textbooks (famous and non-famous): Deflection within the circle is good, however, no good outside the circle.

We found the correct solution is attached.

[img_assist|nid=4181|title=contact mechanics|desc=|link=node|align=left|width=640|height=295]

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The following refs have typos in the solution of displacement (Uz) out of the circle.

Ref 1: Feriderich Ling, “Fundamentals of Surface Mechanics”, Springer, 2002

Ref 2: Anthony Fischer-Cripps, "Introduction to Contact Mechanics", Springer, 2000

Ref 3: K.L. Johnson, “Contact Mechanics” , Cambridge University Press, 1985

Ref 4: •Z.L. Xu, “Applied Elasticity”, Wiley, 1992

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