2. Benchmark solution

2.1. Calculation method used for the reference solution

The reference solution is the one given in sheet SSLV07 /89 of the guide VPCS, which presents the calculation method as follows:

Travel:

\(\begin{array}{c}u\mathrm{=}\mathrm{-}\frac{\nu \rho gxz}{E}\\ v\mathrm{=}\mathrm{-}\frac{\nu \rho gyz}{E}\\ w\mathrm{=}\frac{\rho g{z}^{2}}{2E}+\frac{\nu \rho g}{2E}({x}^{2}+{y}^{2})\mathrm{-}\frac{\rho g{L}^{2}}{2E}\end{array}\)

Constraints:

\(\begin{array}{c}{\sigma }_{\mathit{zz}}\mathrm{=}\rho gz\\ {\sigma }_{\mathit{xx}}\mathrm{=}{\sigma }_{\mathit{yy}}\mathrm{=}{\sigma }_{\mathit{xy}}\mathrm{=}{\sigma }_{\mathit{yz}}\mathrm{=}{\sigma }_{\mathit{zx}}\mathrm{=}0\end{array}\)

2.2. Benchmark results

Move points \(B\), \(C\), \(D\), and \(E\).

Constraints \({\sigma }_{\mathrm{zz}}\) in \(A\) and \(E\).

2.3. Uncertainty about the solution

Analytical solution.

2.4. Bibliographical references

1. S.P. TIMOSHENKO. Theory of elasticity. Paris. Polytechnic bookstore. Ch.Béranger, p.279 to 282 (1961).