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# Transient structural analysis

Dynamics in the field of mechanics deals with the structural response to temporally changing loads. In contrast to statics, the dynamics also take into account the time-dependent terms of the general equation of motion. In addition to the displacement term, the inertial forces and the speed-dependent damping also contribute to the respective equilibrium of forces. The FE method refers to a transient or transient dynamic structural analysis.

If a simplified quasistatic view is no longer permissible, i.e. if the influence of the time-dependent terms is significant, a dynamic analysis must be carried out. The equation of motion is solved in the time domain. There are basically two different approaches to time integration, "Implicit" and "Explicit" with specific advantages and disadvantages and with predestined areas of application. Analogous to statics, non-linear as well as linear effects can be considered in the transient calculation.

Due to the additional complexity of the equation system, it becomes more difficult for the solver to find a stable solution in a transient simulation. For numerically complex problems or poorly conditioned simulation models it can sometimes be challenging to achieve convergence.

As an alternative to transient observation in the time domain, there are further FEM calculation methods to analyze the structural response in the frequency domain. However, all of these are purely linear considerations; non-linearities cannot be included.

## Computation time / model size

In principle, the transient FEM calculation is to be evaluated as time-consuming. The more high-frequent the load change takes place, the smaller the selected time step size must be and the total computing time becomes correspondingly longer. As a result, it may be necessary to reduce the model size or to change to a system view in the frequency domain.

A reduction of the model size usually requires a significantly higher effort in preprocessing. Increasing the element edge length is one way to reduce the model size. However, especially with complicated geometries, it leads to poorer element quality and inaccurate representation of the component contours. Sometimes the automated meshing algorithms fail and manual, time-consuming rework becomes necessary. In nonlinear analyses, inaccurate discrete FEM models are prone to instability. The use of substitute stiffnesses and masses also generates additional effort in modeling. The use of modal superposition offers a compromise between the effort involved in preprocessing, the stability of the solution and the depth and quality of the results.

## Relevance

Transient FEM structure analyses are less common in daily practice than static analyses. This is sometimes due to the fact that especially with larger models, highly dynamic processes can only be efficiently simulated with explicit solvers, despite the enormous progress in computing power. Because of the clear advantages with static or quasistatic problems, however, most current FEM programs, at least with the basic license, use an implicit solution algorithm.

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