Question

In a structural FEA analysis, an analyst says that a dynamic problem must be handled differntly than a static problem. Explain.

Answer 1

Loading condition is constant in magnitude and direction then we do static analysis, and small variation wrt time is neglected to simplify the problem. For example : wooden block resting on a smooth surface

The structural analysis focuses on the changes occurring in the behavior of a physical structure under observation when provided with a force or in case of structures,load.Now if this load is quasi(very slow),the inertia forces from the basis of newton's first law of motion can be neglected and the analysis becomes static.The static loads are very slow on the time rate graph.Static structure analysis methods are:

• non-linear static analysis
• Linear static analysis

In dynamic analysis we take into account the variation of loading conditions wrt time.For example analysis of : gears ( in motion )

Static loading:

The distinction is made between the dynamic and the static analysis on the basis of whether the applied action has enough acceleration (X¨X¨) in comparison to the structure's natural frequency (√K/mK/m). The equation of equilibrium for a structure under static loading is: F=KX   

Where X is displacement.

Unlike static loading's which remain constant or act in such a manner so that there is no substantial variation in structural response with time, dynamic loading's vary substantially with time, thus the structural response needs to be calculated at every time instant. The equation of equilibrium for a structure under dynamic loading is:

mX¨(t)+cX˙(t)+kX(t)=F(t)

mX¨(t)+cX˙(t)+kX(t)=F(t)

where

X¨X¨ is the acceleration (the double derivative of the displacement) and

X˙X˙ is the velocity(the single derivative of the displacement).

if the force or load applied have a high rate of change of velocity during the process then it comes under DYNAMIC analysis,the cause and effect portion comes in to play here.The system under consideration is observed for the development occurring during a course of time and then analyzing the cause of those changes. A dynamic analysis is also related to the inertia forces developed by a structure when it is excited by means of dynamic loads applied suddenly (e.g., wind blasts, explosion, earthquake).

Now dynamic loads are always applied as a function of time or frequency and these time or frequency-varying load application induces time or frequency-varying response (displacements, velocities, accelerations, forces, and stresses). These time or frequency-varying characteristics make dynamic analysis more complicated and more realistic than static analysis.Dynamic structure analysis method are :

• Non-linear time history analysis
• Non-linear static analysis
• Linear elastic time history analysis
• Modal superposition
• Linear static analysis

All the loads are considered dynamic in nature as at some point of time they were absent and that includes the self weight of the structure also.

The applied action or force’s acceleration is compared with the structures natural frequency to find weather analysis is static or dynamic in nature.

This are the reason why In a structural FEA analysis,an analyst says that a dynamic problem must be handled differently than static problem.