During nonlinear direct-integration time-history analysis, special consideration may be necessary for modeling the stiffness-proportional damping of stiff elements which experience inelastic softening. As explained in the CSI Analysis Reference Manual (Viscous Proportional Damping, page 79), the damping matrix for element j is computed as:
Here, c M and c K are the mass and stiffness-proportional damping coefficients, M j is the mass matrix, and K j is the initial stiffness matrix. Dynamic equilibrium is then computed as the sum of stiffness forces, damping forces, inertial forces, and applied loading.
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- In the time-history load case, leave the c M value, but change c K to zero.
- For all materials, set c K to the value originally used in the load case. This is done using interactive database editing under VisStiff > Material Properties 06 - Material Damping. Properties may also be managed through Define > Materials > Advanced Properties.
- Copy the material of softening objects, scale c K by a value between 10-2 and 10-3, then apply this material locally to the affected objects.
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If reduced damping creates convergence problems, users should apply Hilber-Hughes-Taylor (HHT) integration to the load case using a small negative HHT-alpha value. The prescriptive range is 0 to -1/3, while a value of -1/24 or -1/12 should improve the rate of convergence without significantly affecting the accuracy of results. Additional details and descriptions may be found in the CSI Analysis Reference Manual (Nonlinear Direct-Integration Time-History Analysis > Damping, page 415).
See Also
- Direct integration – Direct-integration time-history analysis