A TWO-DIMENSIONAL VISCOUS-FLUID CONVECTION PROBLEM is a pdf translation of a Mathematica notebook that solves a two-dimensional (2D) viscous-fluid (heat-driven) convection problem.
The Mathematica notebook corresponding to the pdf file at the link above produces an animated visualization file, hydro_visc _liquid _T1.avi, renderable by Microsoft Media Manager, of the velocity and temperature fields. (This file is ~24 MB).
The files at the links above were last updated 6 August 2019/0950 US Central Time.
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Instrumented crash-test-dummy studies have provided valuable empirical insight into the dynamics of human bodies in passenger-vehicle crash regimes. Seat and shoulder belts have greatly decreased the severity of injuries in these regimes. The belts provide relatively little protection against neck whiplash, however. Air bags in conjunction with properly adjusted head supports can significantly mitigate the severity of the lash.
Although empirical experiments are essential to crash-test science, they are also expensive and time-consuming. Computer simulation of crashes can be used to augment crash-dummy studies to help cost-effectively characterize safety sensitivities that are beyond the reach of practical experimentation.
LS-DYNA ([1]) is a finite element simulator ([4]) for nonlinear dynamic analysis ([2]).
Here is a LS-DYNA-generated movie (in WMV format) of a simulation of the response of a human body to a head-on collision in a passenger vehicle. The body is restrained by a seat and seat and lap and shoulder belts, but not by a head-support or air bag. The initial velocity of the body is 14.8 m/s (about 30 mph) in the direction of vehicle travel. The entire event takes about 0.12 seconds in real-world time.
Note the severity of the whiplash, even in this relatively low-initial-velocity case. Also note that the torso response to the crash deceleration is left/right asymmetric, contributing a torsional (“twisting”) component to the lash.
The movie was produced from a setup file (mat_spring_belted-dummy.k ([3]), which I modified slightly) supplied with [1]. In the simulation, the dummy consists of 15 ellipsoidal rigid bodies connected through cylindrical joints, springs, and dampers (much in the spirit of [5]). The system contains simulations of approximately 140 materials and has approximately 2000 finite elements.
The simulated dynamics agree well with those of instrumented crash dummies. The entire simulation took approximately 20 seconds on a Dell Inspiron 545 with an Intel Core 2(TM) Quad CPU 8200 clocked at 2.33 GHz, and 8 GB memory.
References
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[1] Livermore Software Technology Corporation. (2018). LS-DYNA. Demo Version smp s R11.0, Rev 129956.
[2] Drazin PG. (1992). Nonlinear Systems. Cambridge.
[3] Livermore Software Technology Corporation. (1997). File mat_spring_belted-dummy.k. Bundled with [1].
[4] Thompson JF, Soni BK, and Weatherill NP. (1999). Handbook of Grid Generation. CRC Press.
[5] Borelli GA. (1685). De Motu Animalium. Lugduni in Batavis: apud Danielem à Gaesbeeck, Cornelium Boutesteyn, Iohannem de Vivie & Petrum vander Aa.
This page was last updated 20 October 2019/0707 US Central Time.