Composite Shell Structures#
Mathematical Model:
\[\begin{split}
\begin{align*}
&\text{Equilibrium:} \quad \nabla \cdot \boldsymbol{\sigma} + \mathbf{b} = \mathbf{0} \\
&\text{Constitutive Relation:} \quad \boldsymbol{\sigma} = \mathbf{D} : \boldsymbol{\varepsilon} \\
&\text{Kinematics:} \quad \boldsymbol{\varepsilon} = \frac{1}{2}\left(\nabla \mathbf{u} + (\nabla \mathbf{u})^T\right) \\
&\text{Compatibility:} \quad \nabla \times \nabla \times \mathbf{u} = \mathbf{0}
\end{align*}
\end{split}\]
Weak Formulation:
\[
\begin{align*}
&\int_{\Omega} \left(\boldsymbol{\sigma} : \boldsymbol{\varepsilon} + \mathbf{b} \cdot \mathbf{u}\right) \,d\Omega = 0
\end{align*}
\]