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*Time-history analysis* provides for linear or [nonlinear|kb:Nonlinear] evaluation of dynamic structural response under loading which may vary with time. Dynamic equilibrium equations, given by K u(t) + C {^}d{^}/{~}dt{~}^d^/~dt~ u(t) + M d{^}2{^}/{~}dt{~}2^/~dt~ u(t) = r(t), are solved using either [modal|kb:Modal analysis] or direct-integration methods. LoadingA istime characterizedfunction bycharacterizes aloading, timeand function,is specified in a [load case|kb:Load case]. Initial conditions may be set by continuing the structural state from the end of a previous analysis. Time-step size, another input parameter, is sensitive to direct-integration methods, and should be decreased until results are not affected. A slightly negative [Hilber-Hughes-Taylor|kb:Time-history output-acceleration accuracy] alpha value is also advisable to [damp|kb:Damping] out higher frequency modes and encourage convergence of nonlinear direct-integration solution. [Material|kb:Material nonlinearity] and [geometric|kb:Geometric nonlinearity] nonlinearity, including P-delta and large-displacement effects, may be simulated during nonlinear direct-integration time-history analysis. [Link|kb:Link] objects capture nonlinear behavior during modal (FNA) applications. 

{list-of-resources2:label=time-history-analysis|drafts-root=Time history analysis drafts}


h1. See Also

* [Multi-support excitation|Manual multi-support excitation] article


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*Related Email:*
* [7/14/2010 email from bm: Impact of time-step size (relative to modal periods) on results|$3145753]

*Related Incident:*
* 26167: Explains reason for inconsistent results for acceleration time-history input and displacement time-history input
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