## Dynamic Linear Solver

The dynamic linear solver adopts for the implicit time integration the Newmark method with a fixed time step size. The solver is invoked by the MDL command analysis dynamic_linear; this command must be specified in the case block. The densities of the materials used must not be zero, otherwise the global mass matrix will evaluate to zero.

In general, the analysis duration is not 1 (second), and an analysis stage must be defined in the case definition, scaled by the duration. Refer to the example below for details.

## 1. MDL Commands

In addition to the MDL command analysis dynamic_linear, the following commands may be specified in the case block.

gradients istep

Controls the computation of the gradients (strains, stresses, heat transfer, etc.) for the current case. If istep is set to 0 (default) no gradients are computed and saved, i.e. only DOF solutions will be found on the database. If istep is set to -1, the gradients for the last converged step of at stage or the linear solution step are computed and saved. If istep is set to a positive value, the gradients will be computed at each istep step of at stage as well as for the last step of a stage.

rayleigh_alpha|rayleigh_beta v

Specifies the coefficients for Rayleigh damping (default is 0). If rayleigh_alpha and/or rayleigh_beta are set, Rayleigh damping will be performed where the global viscosity matrix C is a linear combination of the global mass and linear global stiffness matrices M and K:

C = α M + β K

step_size v

The step size for the stage. No default is given.