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).

The basic equation of motion solved by a transient dynamic analysis is:

where:

= mass matrix

= damping matrix

= stiffness matrix

= nodal acceleration vector

= nodal velocity vector

= nodal displacement vector

= load vector

At any given time, , these equations can be thought of as a set of "static" equilibrium equations that also take into account inertia forces () and damping forces (). 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.

For more information, see Nonlinear Transient Analyses.