However, load balancing is not optimal as seen in Figure 6 since thetwo processors along the right boundary do not process any nodes. More sophisticated load balancingmethods will be considered as part of future development of EMU to improve efficiency in problemsinvolving large displacements.A graphics postprocessor was written to produce output that can be viewed or further processed intomany graphics formats, such as G or encapsulated postscript, using the RSCORS graphics system[Padilla and Thompson 1984]. Postprocessing software is also available to plot displacement historiesand fragmentation histories and distributions.5. Examples of large objects impacting concrete structuresWe consider two examples of aircraft impacts into reinforced concrete structures to illustrate the capabilityof EMU to model extreme impacts.In the first example, we simulated a test that was performed at Sandia National Laboratories [Suganoet al. 1993]. In the test, an F-4 Phantom aircraft impacted an massive, essentially rigid reinforced concretewall. The primary purpose of the test was to determine the impact force as a function of time for theimpact of an F-4 Phantom. Additional objectives of the test were to determine the crushing behavior ofthe aircraft, to determine if the engines broke away from the aircraft before their impact, and if so, tomeasure their impact velocity, and to record the dispersal of fuel after impact. Water was used insteadof jet fuel for this test. The target was a block of reinforced concrete 3.6576m thick in the direction ofimpact and 7.0104m square perpendicular to the impact direction. It was mounted on a platform. Theimpact was perpendicular to the target at a speed of 215m/s. The impacting mass of the aircraft and fuelsurrogate was slightly more that 18,000 kg. The length of the F-4 is about 1.7678m.Figure 7 shows a top and side view of materials in the EMU model at time zero and materials at 0.05 sand 0.09 s during the simulation of the experiment, and Figure 8 shows damage to the structure. Thedamage at a node is given by (15). It represents the fraction of bonds that are broken between this nodeand all nodes initially having bonds with it.In Figure 7, the concrete is yellow and the rebar is green, the fuel is gold and the remaining colorsare various parts of the aircraft. The simulation took about 36minutes using 8 processors, and the timesteps varied from 21µs to 36µs. The time simulated is about 0.09 s. The grid spacing is 0.229m, andthere are 36,244 nodes in the computational model.There is no perforation of the target because of the target’s strength. Only crush up of the aircraftoccurs during the simulation, as was observed during the experiment.Figure 8 shows side and front views of damage to the target impacted by the F-4. We did not showdamage to the aircraft in this figure. Only the concrete and its rebar reinforcement are shown in Figure8. This figure shows damage ranging from no damage (purple) to over 99% damage (orange). Althoughthe target was not perforated, there is considerable damage on the impacted surface that extends to theinterior. At 0.05 s, there is over 99% damage to a large part of the impacted surface, and by 0.09 s thisdamage leads to concrete falling away from the target.Figure 9 shows a penetrator impacting a target. This figure illustrates why peridynamics is usefulin penetration analysis. In this figure, a penetrator (red) impacts at target (blue), fracture occurs, andfragments are emitted from the nonimpacted side of the target. The ability to model fracture in perforation problems is important since fracture occurs before perfo-ration occurs, as shown in Figure 9, and a target starts to weaken long before a penetrator gets through.Furthermore, the fracture process determines fragment properties, and fragments leaving a target maydamage structures separated from the initial target.For another example of the capabilities of peridynamics, consider an aircraft impacting a cylindricalstructure made of reinforced concrete. The main part of the structure is a reinforced concrete cylinderwith an inside radius 19.812m, height 27.432m, and wall thickness 0.9144m. Rebar is placed in hoopscoaxial with the cylinder axis and vertically parallel to the cylinder axis. The rebar is embedded in theconcrete inside its inner and outer surfaces. The rebar is #18 rebar with 0.3048m spacing. Rebar wasomitted in the roof of the structure for simplicity since the roof concrete is in compression. The roofis 0.9144m thick. The structure includes a 9.525mm steel liner that is the color yellow in Figure 10and coaxial with the concrete cylinder. 极限荷载近场动力学建模英文文献和中文翻译(5):http://www.youerw.com/fanyi/lunwen_34840.html