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# How can I know my simulation is quasi-static or not?

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## What is quasi-static analysis?

In summary, in quasi-static analysis, the assumption is made that the problem can be treated as static at any specific moment in time. The key concept is that the applied loading changes very gradually, with a frequency significantly lower than that of the structure. As a result, the structure deforms as if it were under static conditions, and the influence of inertia is considered negligible. This assumption is effective when the effects of inertia are minimal, and it allows for the simplification of non-linear problems into linear systems.

In long term, Quasi-static analysis is a method used in engineering and physics to analyze the behavior of a system or structure under slowly varying loads or conditions. It is a simplified approach that assumes the system remains in equilibrium at each stage of the analysis, neglecting the dynamic effects and considering only the static forces.

In quasi-static analysis, the system is divided into a series of static equilibrium states, and the response of the system is determined at each step. The applied loads are assumed to change gradually or incrementally, allowing the system to adjust and reach a new equilibrium at each stage. This analysis technique is often used when the dynamic effects, such as inertia, vibration, and time-dependent behavior, can be considered negligible compared to the static forces and deformations.

Quasi-static analysis is commonly employed in various fields, including structural engineering, mechanical engineering, civil engineering, and materials science. It helps engineers and researchers understand how a structure or system will respond under various loads and allows for the calculation of stresses, strains, displacements, and other relevant parameters. By simplifying the analysis to static equilibrium states, it provides a practical and efficient approach for predicting the behavior of systems subject to slow or gradual changes.

## Difference between quasi-static analysis and dynamic analysis

The main difference between quasi-static and dynamic analyses lies in the consideration of time-dependent effects and the assumption of equilibrium.

Quasi-static analysis assumes that the system or structure remains in equilibrium at each stage of analysis and neglects the dynamic effects such as inertia, vibration, and time-dependent behavior. It is suitable for situations where the time scale of the loading or the response is much larger than the characteristic time scale of the dynamic effects. Quasi-static analysis is computationally simpler and often provides a reasonable approximation for slowly varying or static loads.

On the other hand, dynamic analysis explicitly accounts for the time-dependent behavior of a system or structure. It considers the effects of inertia, damping, and time-varying forces. Dynamic analysis is necessary when the time scale of the loading or the response is comparable to or larger than the characteristic time scale of the dynamic effects. It is used to study the behavior of structures subjected to rapid or impulsive loads, seismic events, vibrations, and other dynamic phenomena.

While quasi-static analysis is simpler and computationally less demanding, dynamic analysis provides a more accurate representation of the system’s behavior under time-varying conditions. However, there are cases where a combination of both approaches is needed.

In dynamic analysis, there are situations where quasi-static analysis is used as part of the overall analysis. This can occur when the dynamic response is dominated by certain frequencies or modes of vibration. In such cases, the dynamic analysis may be separated into two parts: a quasi-static analysis to determine the response at low frequencies or during initial stages, and a dynamic analysis to capture the higher-frequency or time-dependent behavior. For example, in seismic analysis of structures, a quasi-static analysis may be performed to evaluate the response under the predominant low-frequency ground motions, followed by a dynamic analysis considering the higher-frequency components and the interaction between the structure and the ground.

## Quasi-static analysis in Abaqus

As a rule of thumb, a simulation is static or quasi-static if the excitation frequency is less than 1/10 of the lowest natural frequency of the structure. This is mentioned in Abaqus Documentation:

It is usually desirable to increase the loading time to 10 times the period of the lowest mode to be certain that the solution is truly quasi-static.

In a static or quasi-static analysis, the lowest mode of the structure usually dominates the response. Therefore, knowing the frequency and, correspondingly, the period of the lowest mode, you can estimate the time required to obtain the proper static response. The natural frequencies can be calculated easily using the eigen frequency extraction procedure in Abaqus/Standard (Frequency analysis).

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