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Re: need your help

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  Re: need your help Arezoo Sadrinezhad <as144@zips.uakron.edu> - 2011-04-24 12:25 +0000

#1867 — Re: need your help

Hello Mathematica Friends,

I am stuck with this problem, where I use NDSolve[] to solve a partial
differential equation.

The error is: NDSolve::ndnum: Encountered non-numerical value for a
derivative at t==0!

The sample code is below.

Please suggest me ways to solve this problem. Thank
you.


 --
 Best regards,

 Arezoo Sadrinezhad
 Ph.D. Student
 Department of Civil Engineering
 University of Akron
 Akron, Ohio 44325-3905
 Email: as144@zips.uakron.edu <mailto:as144@zips.uakron.edu>

This is my code:

AC11=10;

AC22=5;

DC1111=25;

DC2222=6.25;

LB=-0.06;

RB=0.1;



StressIC[s11_,s22_]:=Limit[(1/((2Pi)*c*c))*Exp[-(1/2)*(((s11-0)/c)^2+((s22-0)/c)^2)],c->0.001];

Plot3D[StressIC[s11,s22],{s11,-0.1,0.1},{s22,-0.1,0.1},AxesLabel->{"sigma11","sigma22","P[s11,s22,0]"}]



YieldStressDistribution=NormalDistribution[0.05,0.5*0.05];

CDF[YieldStressDistribution,h]

Plot[CDF[YieldStressDistribution,h],{h,-0.2,0.2}]

YF[s11_,s22_]=Abs[s11-s22];

cumuldist[s11_,s22_]=0.5*(1+Erf[28.2843*(-0.05+YF[s11,s22])])

Plot3D[cumuldist[s11,s22],{s11,-0.4,0.4},{s22,-0.25,0.25},PlotRange->All]



AC11p[s11_,s22_]=AC11*(1-cumuldist[s11,s22])

AC22p[s11_,s22_]=AC22*(1-cumuldist[s11,s22])

DC1111p[s11_,s22_]=DC1111*(1-cumuldist[s11,s22])

DC2222p[s11_,s22_]=DC2222*(1-cumuldist[s11,s22])



ElasticPlasticEq={D[AC11p[s11,s22]*P[s11,s22,t],s11]+2*D[AC22p[s11,s22]*P[s11,s22,t],s22]+D[P[s11,s22,t],t]-D[DC1111p[s11,s22]*P[s11,s22,t]*t,{s11,2}]-2*D[DC2222p[s11,s22]*P[s11,s22,t]*t,{s22,2}]==0,P[s11,s22,0]==StressIC[s11,s22],

AC11p[LB,s22]*P[LB,s22,t]-(D[DC1111p[s11,s22]*P[s11,s22,t]*t,s11]/.
s11->LB)==0,

AC11p[RB,s22]*P[RB,s22,t]-(D[DC1111p[s11,s22]*P[s11,s22,t]*t,s11]/.
s11->RB)==0,

2*AC22p[s11,LB]*P[s11,LB,t]-2*(D[DC2222p[s11,s22]*P[s11,s22,t]*t,s22]/.
s22->LB)==0,

2*AC22p[s11,RB]*P[s11,RB,t]-2*(D[DC2222p[s11,s22]*P[s11,s22,t]*t,s22]/.
s22->RB)==0}

Off[General::stop];



t=.;

ElasticPlasticSol=NDSolve[ElasticPlasticEq,P[s11,s22,t],{s11,LB,RB},{s22,LB,RB},{t,0,0.03},
StepMonitor:>Print[t],SolveDelayed->True]



I would be really grateful if you could help me! I really get stuck.

>
> On 04/23/11 18:01, Arezoo Sadrinezhad wrote:
>
>>  Hello Mathematica Friends,
>>
>>  I am stuck with this problem, where I use NDSolve[] to solve a partial
>> differential equation.
>>
>>  The error is: NDSolve::ndnum: Encountered non-numerical value for a
>> derivative at t==0!
>>
>>  The sample code is attached to this email.
>>
>>  Please suggest me ways to solve this problem. Thank
>>  you.
>>
>>
>> --
>> Best regards,
>>
>> Arezoo Sadrinezhad
>> Ph.D. Student
>> Department of Civil Engineering
>> University of Akron
>> Akron, Ohio 44325-3905
>> Email: as144@zips.uakron.edu <mailto:as144@zips.uakron.edu>
>>
>


-- 
Best regards,

Arezoo Sadrinezhad
Ph.D. Student
Department of Civil Engineering
University of Akron
Akron, Ohio 44325-3905
Email: as144@zips.uakron.edu

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