2. Benchmark solution

2.1. Calculation method used for the reference solution

The reference solution comes from the one given in sheet SSLV07 /89 of the guide VPCS (by also considering an orthotropic elastic matrix). The analytical expression for the solution is as follows:

Travel:

\(u=-\frac{{\nu }_{\text{NL}}\rho gxz}{{E}_{N}}\)

\(v=-\frac{{\nu }_{\text{NT}}\rho gyz}{{E}_{N}}\)

\(w=\frac{\rho g{z}^{2}}{2{E}_{N}}+\frac{\rho g}{2{E}_{N}}({\nu }_{\text{NL}}{x}^{2}+{\nu }_{\text{NT}}{y}^{2})-\frac{\rho g{L}^{2}}{2{E}_{N}}\)

Constraints:

\({\sigma }_{\mathrm{zz}}=\rho gz\) \({\sigma }_{\mathrm{zz}}={\sigma }_{\mathrm{yy}}={\sigma }_{\mathrm{xy}}={\sigma }_{\mathrm{yz}}={\sigma }_{\mathrm{zx}}=0\)

2.2. Benchmark results

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

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

2.3. Uncertainty about the solution

Exact analytical results.

2.4. Bibliographical references

• TIMOSHENKO (S.P) Theory of elasticity - Paris - Librairie Polytechnique Ch. Béranger, p.279 to 282 (1961)

• S.W. TSAI, H.T. HAHN - Introduction to composite materials. Technomic Publishing Company (1980).