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Green functions

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

$\displaystyle [K-\omega_0^2 M] \cdot X_j = E_j,$ (433)

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. Consequently, a Green function is the 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 linear, i.e. the material properties have to be linear (usually linear elastic properties and the density) and the parameter NLGEOM on the *STEP card is not taken into account.

The degrees of freedom in which a unit force is to applied can be defined by use of the *CLOAD card. $ \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).


next up previous contents
Next: Convergence criteria Up: Types of analysis Previous: Sensitivity   Contents
guido dhondt 2017-04-02