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During analysis, nonlinear elements may undergo significant softening due to yielding. This may generate significant damping forces in elements that are initially stiff if the softening results in significant deformation, and hence deformational velocity. These damping forces, while properly in equilibrium with other forces at a joint connected to the stiff element, may cause an unexpected a jump in stiffness forces between elements connected to Users may need to implement additional measures to capture the nonlinear response of stiff elements which soften under dynamic-inelastic behaviorthe softening element and connected elements. Such a condition may occur, for example, when adjacent columns are expected to demonstrate comparable dynamic performance, but experience significant axial-force discrepancy. When initially-stiff columns are in a concrete column modeled with multiple elements containing hinges. When the initially-stiff column is subjected to cyclic bending, cracking and the ratcheting of yielding tensile rebar will soften element response. Axial velocity and excessive c K K j damping contribution may then skew those results generated through default settingsgenerate large differences in the axial force between adjacent elements in the same column. While this jump is in axial force satisfies dynamic equilibrium, it may not be the desired behavior. Users may need to implement additional measures achieve the expected results.
Users may solve this problem by transferring stiffness from the load case, general to the entire structure, to the material of individual elements affected by softening. This may be done through the following process:
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Since material damping sums with that specified in load cases, this procedure reduces stiffness-proportional damping only in affected elements, without affecting the rest of the model. Nonlinear material behavior will then serve provide energy dissipation.
When If damping reduction disrupts creates convergence problems, users should apply Hilber-Hughes-Taylor integration to the load case using a small negative HHT-alpha value. The prescriptive range is 0 to -1/3. A value of -1/24 to -1/12 should improve the rate of convergence , cutting analysis duration by as much as a factor of threewithout significantly affecting the accuracy of the results.
Additional details and descriptions may be found in the CSI Analysis Reference Manual (Nonlinear Time-History Analysis > Nonlinear Direct-Integration Time-History Analysis > Damping).