I try to find a method to replace dynamic loading with equivalent static loading. As you know designing a structure with static loading is more easier than dynamic loading, especially when design is based on topology optimization process. Therefore, for dynamic events (for example impact loading), the problem must be replaced with equivalent static one. Complicated theoretical method can not be useful for industrial application. I need a simple method to be used for FEM analysis.
@Meysam Khodaei. I hope I understand your question correctly.
Suppose a machine of mass M is operated at a circular frequency of w.
It is intended to to replace the machine by an equivalent static system.
This can be achieved by using the static load
Mg + Mw2A
where A is the amplitude of the machine.
Of course if the machine is placed on soil it should be understood that the soil properties will be degraded as it undergoes cyclic loading.
What you are proposing is just not possible unless you know the full dynamic properties of the system under consideration. If the system is lightly damped (as most are), then the dynamic response around resonance could be quite high. This is known as dynamic amplification. A typical (measured) dynamic amplification factor could be as high as five (5). Are you willing to increase your loading by a factor of 5?
Dear Anyaegbunam,
Thank you for your answer. But you explained a special case. Could you please recommend a general method?
Dear Ancich, Thank you very much. If natural frequencies of the system are known, how to apply equivalent static load? What you recommend for non cyclic loadings like impact?
Knowing just the natural frequencies does not solve the problem. As I said earlier, if the system is lightly damped (as most are), then the dynamic response around resonance could be quite high. For impact loading, I would expect a DAF of 2 to be a reasonable approximation.
Please ESLM - Equivalent Static load Method
https://altairhyperworks.com/solution/Crash-Safety-Impact
Extracted are the Help Document from Altair HyperWorks
Equivalent Static Load Method (ESLM): A technique suitable for optimization of designs undergoing dynamic loads.
The equivalent static load method, originally published by Dr. Park, Hanyang University, is a technique suitable for optimization of designs undergoing dynamic loads. The method has been implemented for the optimization of the following solutions:
- Multi-body dynamics problems including flexible bodies
- Nonlinear responses from implicit static analysis, implicit dynamic analysis and explicit dynamic analysis
The equivalent static load method takes advantage of the well established static response optimization capabilities of OptiStruct.
- Equivalent Static Load
- ESLM for MBD The equivalent static load method has been implemented for the solution of multibody dynamics problems that include flexible bodies.
- ESLM for Nonlinear Response Optimization The equivalent static load method has been extended to support nonlinear response optimization.
The equivalent static load can be expressed as
Qeqs = Q(1 + N)
Based on a SDOF concept:
N = exp(-2πDwn/wd ) for a suddenly applied load
where D = damping ratio ; wn = natural frequency ; wd = damped natural frequency = wn* sqrt (1- D^2)
D = C/(2Mwn) ; C = coeff of viscous damping
N = 1/ sqr[ (1-r2)2 + 4(Dr)2 ] for a harmonic load
where r = frequency ratio = w/wn . w = operating machine frequency.
When there is zero damping then N = 1 and the static load needs to be doubled.
Dear Mey
Good Question, I think for reaserch work it is difficulte
Dear Meysam
Good Question, I think it is difficulte ( For reaserch work ) to make equivalent static load in state of dynamic load
Thaks
Dear all, Hello, conceptually I agree with Eric Ancich. However, it seems to me possible to define something like "design spectra" (well defined in earthquake engineering) in any area involved with dynamic behavior, that takes into account the dynamic properties including the damping natural frequencies and stiffness and linearity or nonlinearity, and result in the worst (critical) static loads to be put on the structural system instead of the dynamic load; see Fig. 2 in the 4th edition of the Iranian earthquake standard and the structural dynamics book of A.K. Chopra. In any way, surely the result would be an approximation, and it is more accurate to use a dynamic analysis method from which the most versatile is time history and time integration analysis. Have a nice day.
In my view, you are wasting your time with this approach as virtually every case will be different. The attached PowerPoint slide shown the resonant region where dynamic amplification is most prevalent.
I neglected to add the PowerPoint. If you are in the resonant region, what multiplier would you use for your static equivalent loading? Even a multiplier of 5 is probably an underestimate in the resonant region. My advice is to stop looking for shortcuts and undertake a proper dynamic study.
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