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system of simple PDE

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127988] system of simple PDE
  • From: Nguyen Thanh Tam <hacaoideas at gmail.com>
  • Date: Fri, 7 Sep 2012 04:57:50 -0400 (EDT)
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  • Delivered-to: l-mathgroup@wolfram.com
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Dear all,

I'm a newbie and I'm running into this problem as I cannot solve this very simple system of PDE using Mathematica. It keeps giving me error that "Supplied equations are not differential equations of the given
functions."


Balance of a tiny cube 

The balance equation for 2 dimensional case

In[12]:= Eq=Hold[{D[Subscript[\[Sigma], X][x,y],x]+D[Subscript[\[Tau], XY][x,y],y]+Subscript[f, BX][x,y]==0, D[Subscript[\[Sigma], Y][x,y],y]+ D[Subscript[\[Tau], XY][x,y],x]+Subscript[f, BY][x,y]==0}];

For the beam with constant loading along x axis

In[28]:= para={Subscript[\[Sigma], X][x,y]-> (1/2*q*x^2)/J*y, Subscript[f, BX][x,y]->0, Subscript[f, BY][x,y]-> 0 };

In[35]:= Eq1=Release[Eq/.para]

Out[35]= {(q x y)/J+(Subscript[\[Tau], XY]^(0,1))[x,y]==0,(Subscript[\[Sigma], Y]^(0,1))[x,y]+(Subscript[\[Tau], XY]^(1,0))[x,y]==0}

The solution

In[30]:= DSolve[{Eq1, Subscript[\[Tau], Y][x,c]==0, Subscript[\[Tau], Y][x,-c]==0, Subscript[\[Sigma], Y][x,c]==-q/b},{Subscript[\[Sigma], Y][x,y]},{x,y}]

During evaluation of In[30]:= DSolve::deqx: Supplied equations are not differential equations of the given functions. >>

Out[30]= DSolve[{{(q x y)/J+(Subscript[\[Tau], XY]^(0,1))[x,y]==0,(Subscript[\[Sigma], Y]^(0,1))[x,y]+(Subscript[\[Tau], XY]^(1,0))[x,y]==0},Subscript[\[Tau], Y][x,c]==0,Subscript[\[Tau], Y][x,-c]==0,Subscript[\[Sigma], Y][x,c]==-(q/b)},{Subscript[\[Sigma], Y][x,y]},{x,y}]

Please tell me why the error prompted. Thank you



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