I'm referring to the paper:
Mindlin, R.D. (1936) "Force at a Point in the Interior of a Semi-Infinite Solid", Physics 7, 195-202 (1936).
By plotting "w" from Eq. 18 as a function of x for y=z=0, I'm unable to reproduce Fig. 6 in his paper. I get the red curve instead of the black in the attached file. Has anyone tried this? Are there known inconsistencies in this very important paper, from so long ago?
I've double checked very carefully my evaluation of w, but have not checked that the displacements (u,v,w) in Eq. satisfy all the required conditions (which would take quite a lot of algebra).
This is only a partial answer:
1) By using Maxima to calculate the vertical displacement due to a horizontal point load with Mindlin's Eq. 1 and 17 instead of Eq. 18, I get a horrenduously complicated expression for the displacements, but what I plot it, I get something that agrees with Mindlin's Fig. 6, as shown by the green plot in the attached.
2) By subtituting Mindlin's displacements from Eq. 18 into the equilibrium equations (in Maxima) and evaluating it numerically for a particular case, it appears that the equilibrium equations are not satisfied, but if the same calculation is done using displacements derived from Eqs. 1 and 7, they are.
These two points suggest the problem is more likely to be in Mindlins expression for w in Eq. 18 than in his Fig. 6, though the possibility that I've not correctly evaluated the expression for w from Eq. 18 with Maxima can also not be excluded.
The difficulty I'm having with Maxima is that it gives horrenduously complicated expressions, that only readily simplify by evaluating them numerically for a particular case.
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