| Author | Message | |||
     gqzhang (zgqfem) Member Username: zgqfem Post Number: 7 Registered: 07-2003 |
I want to know how to apply concentration load, for example in heat diffusion problem. The following is one example, and I want to apply Q at the point (0,0). The alternative is to the natual(p)=Q/A along the small circle around the point(0,0). This may cause trouble, because if there are many points at which Qs are different, and the small circles will make meshing impossible. The same question will happen in the problems of mechanics, for example there is a rectangle whose left side is fixed, i.e. value(u)=value(v)=0, and at the right upper point there is a concentration force. HOw can I solve this type of problem? is the direct treatment beyond flexpde? thanks so much. the heat diffusion example: TITLE 'TRANSIENT PRESSURE' SELECT errlim=1e-3 nodelimit=900 ngrid=7 VARIABLES pressure(RANGE=10000) DEFINITIONS mu=1e-9 kper=0.3e-15 comp=1.7e-3 fai= 0.15 Q=1e-5 Pai= 3.1415926 R1=0.1143/2 R2=R1*50 k=kper rcp=fai*comp pressurei=0 fluxd_x=-k/mu*dx(pressure) fluxd_y=-k/mu*dy(pressure) fluxd=vector( fluxd_x, fluxd_y) fluxdm=magnitude( fluxd) q0=Q/(2*Pai*R1) {to treat the concentration Q to be the second b.c.} INITIAL VALUES pressure=pressurei EQUATIONS div(fluxd)+rcp*dt( pressure)=0 {this region is one-fourth of solid circle} { BOUNDARIES region 'domain' START (0,0) NATURAL(PRESSURE)=0 LINE TO (R2,0) VALUE(PRESSURE)=0 ARC (RADIUS=R2) TO (0,R2) NATURAL(PRESSURE)=0 LINE TO (0,0) {a point Q is needed at the point (0,0)} } {this region is one-fourth of hollow circle} BOUNDARIES region 'domain' START (R1,0) NATURAL(PRESSURE)=0 LINE TO (R2,0) VALUE(PRESSURE)=0 ARC (RADIUS=R2) TO (0,R2) NATURAL(PRESSURE)=0 LINE TO (0,R1) natural(PRESSURE)=q0 ARC (CENTER=0,0) TO (R1,0) TIME from 0 to 800 PLOTS for t=0.3,5,15,30,50,70,90,120,130,500,800 contour( pressure) end | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 27 Registered: 06-2003 |
You can use the statement "POINT LOAD(u)=load" to apply a load of value "load" to the equation defining "u". The load is applied at the point immediately preceding the "Point Load" statement. You can use "Fixed Point(x,y)" to generate unconnected individual nodes in space. In 3D, the "Fixed point" command generates a line throughout z. See the Help Index under "Point Load" and Fixed Point". Be aware, however, that a point load is a mathematical abstraction that has no analog in the real world. But I point out that small circles do not make meshing impossible. See "Samples | Steady_State | Groundwater | water.pde". Small squares can also be used, and they cause less mesh density near the load. | |||
| gqzhang (zgqfem) Member Username: zgqfem Post Number: 8 Registered: 07-2003 |
Thank you for your reply. Now I knew how to apply point loads in thermal problems. As for the small circles you mensioned at the end, what I mean is that what will happen if there are many circles not only several circles? thank you again! | |||
| Manoranjan Acharya (bubuisonline) Member Username: bubuisonline Post Number: 4 Registered: 05-2007 |
Hello Sir, I have a similar problem.I wanted my heat source Q to be given on a certain point lets say at 0,0,0 but not sure how to do that.Please let me know.
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 867 Registered: 06-2003 |
There is no mechanism for placing point loads in 3D. "POINT LOAD()" is a 2D construct that has no ability to specify a Z coordinate. As I said in an earlier posting, point loads are a mathematical fiction. A point load either has zero energy or infinite density. Computers do not deal well with infinities. You are better off specifying something physically realizable. One way to do this is with a small circle or square with a volume source. In 3D this requires a localizing layer. Or, you can use a Gaussian source shape in 3D surrounding the putative point. In this case, you should put a FIXED POINT in the 2D base mesh and run an extrusion surface through the Z coordinate. If you do not do these things to identify the source position, it may be totally overlooked. (FlexPDE does not scan the volume at infinite precision looking for tiny sources.) | |||
| Manoranjan Acharya (bubuisonline) Member Username: bubuisonline Post Number: 5 Registered: 05-2007 |
Hello, Thanks for your help.But in my problem if I want my source Q to be from the top surface at the point x=0,y=0 with a circular area what change I have to make.Will you please let me know I am little new to FLEXPDE so struggling. Thanks | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 871 Registered: 06-2003 |
In that case, you want to specify a boundary flux, not a volume source. Build a circular patch around (0,0), roughly as follows: LIMITED REGION "Patch" SURFACE "Top" NATURAL(variable)=Flux START(Rpatch,0) ARC(CENTER=0,0) ANGLE=360 Here "Top" is the name you gave to your top surface, "Variable" is the name of your concentration variable, "Flux" is the flux you want to impose. The "LIMITED" qualifier says to put this region only in the explicitly mentioned layers or surfaces, in this case "Top". The "NATURAL" BC is qualified by following the SURFACE declarator, so it is applied only on the "Top" surface. | |||
| Manoranjan Acharya (bubuisonline) Member Username: bubuisonline Post Number: 6 Registered: 05-2007 |
Thanks again for your help.I ran as you suggested but it is showing some error regarding the grid size.I really need my heat source area to be small.I am not wrong in following your last mail I took variable as Tp in my case and flux as Q. I am attaching the file I will be really great full if you have a look. thanks
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| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 875 Registered: 06-2003 |
I assume you are using a student version of FlexPDE, or you would not have got a grid size diagnostic. The free student version of FlexPDE puts a limit on the size of the computation mesh. Computing a tiny source spot in 3D requires a large mesh to resolve the sharply peaked shape of the solution. This is incompatible with the student version mesh-size limit. There are a lot of other things wrong with this script, but it is pointless to detail them if the student version won't do it anyway. Why don't you recast this problem in 2D cylindrical geometry. There don't seem to be any asymmetries that would requre 3D. Simply put a POINT LOAD on the top axis corner of a cylinder. The mesh size is still limited, so you will not be able to see details of the early solution shape. But it will probably be better than trying to do it in 3D. |
