Chapters about the theory behind particular analysis procedures in the software's documentation are usually useful in such cases. But if you want something more basic, many FEM textbooks cover structural dynamics as well. I can recommend, among others, books written by Bathe, Cook and Hutton.

FEA is based on solving differential equations, which, at some point, requires integration, hence, summations.

https://en.wikipedia.org/wiki/Finite_element_metho...

TTFN (ta ta for now)
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In the real world, physics is always transient so inertia and dissipation are always present. In the numerical world, we make useful approximations and one such approximation is running static analyses. If you understand how nonlinear static analyses are performed, then all you need to (additionally) think about is that time is real physical quantity so the loading rate, velocities, acceleration (i.e., force), etc. come in to play instead of a "pseudo time" (or "step time" in static analyses) which is just a scaling factor for the BC/load.

I do not know which specific commercial code you mean by ANSYS Structural Transient analysis but I assume it is an explicit code (e.g., explicit scheme in LS-DYNA). Explicit schemes are easy to understand - all you do is assume equilibrium with initial conditions and simply integrate the governing equations in time. There is no tangent stiffness matrix to compute and no convergence issues to deal with because you are not converging to anything. However, there is a time step size constraint which is why the time step sizes are extremely small in explicit analyses. This is why explicit analyses are typically used for short-time events such as explosions, car crashes, etc. [In right hands, even quasi-static analyses can be performed equally well.]

If the ANSYS Structural Transient analysis uses an implicit numerical time integrator, then all you are doing on top of a static nonlinear structural analysis is solving for the transient terms in the governing equations.

Lots of suggestions for background are available in this forum and elsewhere on the internet.

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