1. Reference problem#
1.1. Geometry#
Coordinates of points (in meters):
\(A\) |
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\(x\) |
0.5 |
0.5 |
0.5 |
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\(y\) |
0.5 |
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\(z\) |
1.5 |
1.2. Material properties#
Young’s modules in directions \(x\), \(y\), and \(z\):
\({E}_{L}=5.{10}^{11}\mathrm{Pa}\), \({E}_{T}=5.{10}^{11}\mathrm{Pa}\), \({E}_{N}=2.{10}^{11}\mathrm{Pa}\).
Coefficient of POISSON in the \(\mathrm{xy}\), \(\mathrm{xz}\), and \(\mathrm{yz}\) planes:
\({\nu }_{\text{LT}}=0.1\), \({\nu }_{\text{LN}}=0.3\), \({\nu }_{\text{TN}}=0.1\).
Shear modules in planes \(\mathit{xy}\), \(\mathit{xz}\), and \(\mathit{yz}\):
\({G}_{\text{LT}}=7.69231{10}^{10}\mathrm{Pa}\), \({G}_{\text{LN}}=7.69231{10}^{10}\mathrm{Pa}\),
\({G}_{\text{TN}}=7.69231{10}^{10}\mathrm{Pa}\).
Density: \(\rho =7800\mathrm{kg}/{m}^{3}\).
1.3. Boundary conditions and loads#
Point \(A\): (\(u=v=w=0\), \({\theta }_{x}={\theta }_{y}={\theta }_{z}=0\))
Own weight along axis \(z\): \(\rho gz\)
Uniform tensile stress for the upper side:
\({\sigma }_{z}=\rho gL=+229554.\mathrm{Pa}\)