ElasticShell#
An ElasticShell section is meant to be used with Shells and represents a Gauss point with thickness and that is homogeneous with an Elastic Isotropic material.
- Model.section("ElasticShell", tag, E, nu, thickness)
- Parameters:
tag (integer) – integer tag identifying the section
E (float) – Young’s modulus, \(E\)
nu (float) – Poisson’s ratio, \(\nu\)
thickness (float) – section thickness, \(h\)
The constitutive relationship of a linear elastic isotropic shell is
\[\begin{split}\left(\begin{array}{c}
\boldsymbol{p} \\
\boldsymbol{m} \\
\boldsymbol{q}
\end{array}\right)
=\underbrace{\left[\begin{array}{ccc|ccc|cc}
M & \nu M & 0 & 0 & 0 & 0 & 0 & 0 \\
\nu M & M & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & G & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & -D & -\nu D & 0 & 0 & 0 \\
0 & 0 & 0 & -\nu D & -D & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & -\frac{1}{2}(1-\nu) D & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & k G & 0 \\
0 & 0 & 0 & 0 & 0 & 0 & 0 & k G
\end{array}\right]}_{\mathrm{D}}
\left(\begin{array}{c}
\overline{\boldsymbol{\epsilon}} \\
\boldsymbol{\kappa} \\
\boldsymbol{\gamma}
\end{array}\right)\end{split}\]
where \(M \triangleq \frac{E h}{1-\nu^2}\) is the membrane modulus, \(G \triangleq \frac{E h}{2(1+\nu)}\) is the shear modulus, \(D \triangleq \frac{E h^3}{12\left(1-\nu^2\right)}\) is the bending modulus and \(k \triangleq \frac{5}{6}\) the shear correction factor.