Chapter 5: Transient Dynamic Analysis
Transient dynamic analysis (sometimes called time-history analysis) is a technique used to determine
the dynamic response of a structure under the action of any general time-dependent loads. You can
use this type of analysis to determine the time-varying displacements, strains, stresses, and forces in a
structure as it responds to any combination of static, transient, and harmonic loads. The time scale of
the loading is such that the inertia or damping effects are considered to be important. If the inertia and
damping effects are not important, you might be able to use a static analysis instead (see Structural
Static Analysis (p. 9)).
The basic equation of motion solved by a transient dynamic analysis is
(M){ɺɺ} + (C){ɺ} + (K){u} = {F(t)}
where:
(M) = mass matrix
(C) = damping matrix
(K) = stiffness matrix
{ɺɺ} = nodal acceleration vector
{ɺ} = nodal velocity vector
{u} = nodal displacement vector
{F(t)} = load vectorAt any given time,t, these equations can be thought of as a set of "static" equilibrium equations that
also take into account inertia forces ((M){ɺɺ}) and damping forces ((C){ɺ}). The program uses the Newmark
time integration method or an improved method called HHT to solve these equations at discrete time
points. The time increment between successive time points is called the integration time step.
The following topics are available for transient dynamic analysis:
5.1. Preparing for a Transient Dynamic Analysis
5.2. Two Solution Methods
5.3. Performing a Full Transient Dynamic Analysis
5.4. Performing a Mode-Superposition Transient Dynamic Analysis
5.5. Performing a Prestressed Transient Dynamic Analysis
5.6. Transient Dynamic Analysis Options
5.7. Where to Find Other ExamplesFor more information, see Nonlinear Transient Analyses (p. 200).
5.1. Preparing for a Transient Dynamic Analysis
A transient dynamic analysis is more involved than a static analysis because it generally requires more
computer resources and more of your resources, in terms of the "engineering" time involved. You can
save a significant amount of these resources by doing some preliminary work to understand the physics
of the problem. For example, you can:
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