Linear buckling analysis

Linear buckling analysis is performed by solving the following eigenvalue problem:

\[ (K_L-\sigma K_{NL}(\mathbf{u}^L_h))\mathbf{v}_h = \lambda K_{NL}(\mathbf{u}_h) \mathbf{v}_h \]

Where \(K_L\) is the linear stiffness matrix, \(K_{NL}(\mathbf{u}_h)\) is the tangential stiffness matrix assembled around \(\mathbf{u}^L_h\). The solution \(\mathbf{u}^L_h\) is obtained by solving a linear problem \(K_L\mathbf{u}^L_h = \mathbf{P}\). Furthermore, \(\sigma\) is a shift and \((\lambda+\sigma\f)\mathbf{P}\) is the critical buckling load. The modeshape is represented by \(\phi\).

Examples with the use of this class are:

gsThinShell_Buckling.cpp

Linear modal analysis

Linear modal analysis is performed by solving the following eigenvalue problem:

\begin{align*} (K - \sigma M)\mathbf{v}_h = \lambda M\mathbf{v}_h \end{align*}

Where \(K\) is the linear stiffness matrix, \(M\) is the mass matrix. Furthermore, \(\sigma\) is a shift and \((\lambda+\sigma\f)\) is the eigenfrequency. The modeshape is represented by \(\phi\).

Examples with the use of this class are:

gsThinShell_Modal.cpp