Green functions

With the *GREEN keyword card Green functions $X_j$ can be calculated satisfying

$$[K-\omega_0^2 M] \cdot X_j = E_j,$$ (441)

where $K$ is the stiffness matrix of the structure, $M$ the mass matrix, $\omega_0$ a scalar frequency and $E_j$ a unit force at degree of freedom $j$. The degree of freedom $j$ corresponds to a specific coordinate direction in a specific node. For $\omega_0=0$ the Green function is the static answer of a system to a unit force at some location in one of the global coordinate directions. Usually, these Green functions are used in subsequent calculations. The Green function procedure is a linear perturbation procedure, i.e. nonlinear behavior from a previous *STATIC step can be taken into account (through the appropriately modified stiffness matrix) using the PERTURBATION parameter on the *STEP card in the Green step.

The degrees of freedom in which a unit force is to be applied can be defined by use of the *CLOAD card (the force value specified by the user is immaterial, a unit value is taken). $\omega_0$ is a parameter on the *CLOAD card.

If the input deck is stored in the file ``problem.inp'', where ``problem'' stands for any name, the Green functions, the stiffness matrix and the mass matrix are stored in binary form in a "problem.eig" file for further use (e.g. in a sensitivity step). Furthermore, the Green functions can be stored in the ``problem.frd'' file, using the standard *NODE FILE or *NODE OUTPUT card.

The sensitivity of the Green functions can be calculated in a subsequent *SENSITIVITY step in which the objective function is set to GREEN (cf. *OBJECTIVE).