2. Benchmark solution#
2.1. Calculation method used for the reference solution#
The value of the axial displacement at the center of the disk (point A) is given by:
\({W}_{a}=-\frac{P{\phi }^{2}}{64\pi D}\times \frac{3+\nu }{1+\nu }\)
Where \(D=\frac{E{h}^{3}}{12(1-{\nu }^{2})}\)
The value of potential energy (at equilibrium) is given by:
\({E}_{p}=-\frac{1}{2}P{W}_{a}\)
The absolute value of potential energy per radian is:
\({e}_{p}=\frac{1}{2}\frac{P{W}_{a}}{2\pi }\)
2.2. Benchmark results#
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\({W}_{a}=–0.4596\times {10}^{-3}m\) |
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\({e}_{p}=0.012799\mathrm{Nm}/\mathrm{rd}\) |
2.3. Uncertainty about the solution#
Analytical solution.
2.4. Bibliographical references#
R.J. ROARK and W.C. YOUNG Formulas for stress and strain, 5th edition, New York, McGraw-Hill, 1975