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*DYNAMIC

Keyword type: step

This procedure is used to calculate the response of a structure subject to dynamic loading using a direct integration procedure of the equations of motion. Geometrically nonlinear response is assumed. There are four optional parameters: DIRECT, ALPHA, EXPLICIT and SOLVER. The parameter DIRECT specifies that the user defined initial time increment should not be changed. In case of no convergence with this increment size, the calculation stops with an error message. If this parameter is not set, the program will adapt the increment size depending on the rate of convergence. The parameter ALPHA takes an argument between -1/3 and 0. It controls the dissipation of the high frequency responce: lower numbers lead to increased numerical damping ([19]). The default value is -0.05. The parameter EXPLICIT takes no argument and specifies that an explicit integration procedure should be activated. Default is implicit integration.

The last parameter SOLVER determines the package used to solve the ensuing system of equations. This only applies to implicit integration, since explicit integration does not require the solution of a system of equations. If selected in an explicit integration computation (triggered by the parameter EXPLICIT), the selection of a solver has no effect whatsoever. The default for SOLVER is SPOOLES, denoting the SPOOLES solver [2,3]. Alternatively, the iterative solver by Rank and Ruecker [20] can be chosen, which is based on the algorithms by Schwarz [21]. If SOLVER=ITERATIVE SCALING is selected, the preconditioning is limited to a scaling of the diagonal terms, SOLVER=ITERATIVE CHOLESKY triggers Incomplete Cholesky preconditioning. Cholesky preconditioning leads to a better convergence and maybe to shorter execution times, however, it requires additional storage roughly corresponding to the nonzeros in the matrix. If you are short of memory, diagonal scaling might be your last resort. The iterative methods perform well for truely three-dimensional structures. For instance, calculations for a hemisphere were about nine times faster with the ITERATIVE SCALING solver, and three times faster with the ITERATIVE CHOLESKY solver than with SPOOLES. For two-dimensional structures such as plates or shells, the performance might break down drastically and convergence often requires the use of Cholesky preconditioning. SPOOLES performs well in most situations with emphasis on slender structures but requires much more storage than the iterative solver.

First line:

- *DYNAMIC
- enter any parameters and their values, if needed.

Second line:

- Initial time increment. This value will be modfied due to automatic incrementation, unless the parameter DIRECT was specified.
- Time period of the step.
- Minimum time increment allowed. Only active if DIRECT is not specified. Default is the initial time increment or 1.e-5 times the time period of the step, whichever is smaller.
- Maximum time increment allowed. Only active if DIRECT is not specified. Default is 1.e+30.

    Examples:

    *DYNAMIC,DIRECT,EXPLICIT
    1.E-7,1.E-5

defines an explicit dynamic procedure with fixed time increment for a step of length .

    *DYNAMIC,ALPHA=-0.3,SOLVER=ITERATIVE CHOLESKY
    1.E-7,1.E-5,1.E-9,1.E-6

defines an implicit dynamic procedure with variable increment size. The numerical damping was increased ( instead of the default , and the iterative solver with Cholesky preconditioning was selected. The starting increment has a size , the subsequent increments should not have a size smaller than or bigger than . The step size is .

Example files: beamnldy, beamnldye, beamnldyp, beamnldype.

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