For Linear, Static stress analysis, we frequently say that the art of FEA is the art of the mesh. But when you do impact studies, then you must also take care about how you discretize Time, as well as Space. There is, of course, a Study Type that is available with a Simulation Professional license, called “Drop Test”, and this automates all the internal options for setting up the problem. But what if you also need to account for non-linear material? What if your load case is not a simple drop, but a specified impact time-curve? Then you will need to run this as a Non-Linear, Time-Dependent case. For this type of problem, you should NOT use the Auto Time-Stepper. In this tech tip, you’ll learn how to set the manual time step, and how long the analysis should run in ‘real’ time.
Determine Your Solution Time
Before running the non-linear, time-dependent study, you can run a simple, Linear case to help frame the problem. Set up a Modal Analysis. Use as many of the boundary conditions as you can from the final, non-linear impact study. What you are looking for is the lowest natural response frequency of the structure. Let’s say you discover the lowest mode for an assembly is 700Hz. The period of one vibration would be 1/700 or .0014 sec.
When you run your study, you want know if the propagation of the impact energy through the structure is going to interact with any of the structure’s natural modes, so you need to run your impact study for AT LEAST one period – and I often like to plot over two or three full waves. In my example, three periods of .0014 sec means the study should run for .0042 seconds.
Determine the Time-Step
In non-linear analysis, we compute the time-varying properties as a first-order explicit difference between time-steps, and we compute spatial gradients as a second-order implicit difference between adjacent mesh elements. The importance of this is that, at any given time, an element can only ‘see’ and react to, the conditions in the elements that are its immediate neighbors – it will NOT see what is coming at it from 2 or 3 elements away.
If you want a shock wave from an impact to propagate accurately, then your analysis time-step must not be too large. The wave will travel at the speed of sound through your material(s). Once you know the speed of a sound wave, you can divide that speed into your (smallest) mesh element size – this will give you the period (time required) for the wave to travel across one mesh element. Your Simulation time-step should be no bigger than that one-element-transit-time.
Time Step <= Mesh Size / C
What is the speed of sound through your solid materials? For long, slender structures, this is an easy function of the elastic spring stiffness, (that is E, the Young’s Modulus), and the material density, ?.
Speed of Sound = C = (E / ?)1/2
You have to compute this speed for each different material in your assembly, and then find the smallest mesh element size in that material, to determine that material’s time step. Usually you will find your minimum time-step required for the problem is driven by your stiffest material.
Let’s assume in my example that my assembly is mostly steel, with some other softer, (slower-speed) materials. The speed of sound through the Solidworks “Plain Carbon” steel is going to be, at the very least:
C = ( 2.1e11 N/m2 / 7800 kg/m3 ) 1/2 = 5188 m/s.
If your objects are not long and slender, then the speed of sound usually increases somewhat due to energy storage via poisson’s effect. The more-conservative way to compute the speed of sound will then be:
Speed of Sound = C = ( E(1-v) / (1+v)(1-2v) ? )1/2
Where ‘v’ is the Poisson’s Ratio. Again, using our Plain Carbon Steel, this would be:
C = ( 2.1e11 N/m2 (1-.28) / (1+.28) (1-.56) 7800 kg/m3 ) 1/2 = 5866 m/s.
If our example problem is assumed to have a smallest mesh size in the steel of 5.0mm, then the largest time-step we should contemplates would be:
Step = .005 m / 5866 m/s = 0.85 e-6 seconds
This is a very small time-step, but fortunately our example structure was rather stiff and have a lowest-natural-mode period of .0014 sec, so our drop-test will have to run for about 1650 iterations, for each full-wave response we wish to plot of the first natural mode. So, yes, drop-test and impact studies are time-consuming! And, they could eat a lot of space on your hard-drive. That is why it is also CRUCIAL in such cases that you do not take the default behavior under “Results Options”, to keep a copy of all post-processing results at each time-step.
That’s all there is to it!
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