Thermoelasticity - Free FEM

General Discussion
1

Hi,
How can I write the code of the following equation??

11111111

epsilon is strain, and T hat is weight function.

2

A small exemple of Thermo elasticity with

  • alpha * T*([ 1, 1, 0. ]’* AA*epsilon(uu,vv)) = \alpha T\ tr( AA *\varepsilon(uu,uu))

This is not exactly the same but it is simple modif.

// file lame.edp
mesh Th=square(10,10,[20*x,2*y-1]);
fespace Vh(Th,P2);
Vh u,v,uu,vv,T,TT;

macro epsilon(u1,u2)  [dx(u1),dy(u2),(dy(u1)+dx(u2))*0.5]// EOM
macro  AA  [ 
 [ l2mu, lambda, 0. ],
 [ lambda, l2mu, 0. ],
 [ 0.,     0.,   mu2 ] ] //
macro Grad(u) [dx(u),dy(u)] //



real E = 21e5, nu = 0.28, mu= E/(2*(1+nu)); 
real lambda = E*nu/((1+nu)*(1-2*nu)), f = 0; //  
real l2mu = lambda + 2*mu;
real mu2 = mu*2;
real K=1;
real ft=1;
real alpha =1e-2;

solve lame([u,v,T],[uu,vv,TT])
  = int2d(Th)(  
               epsilon(u,v)'*AA*epsilon(uu,vv) 
            - alpha * T*([  1, 1, 0. ]'* AA*epsilon(uu,vv))
            +  K*(Grad(T)'*Grad(TT))
             )
        - int2d(Th)(f*vv+ ft*TT) 
        + on(4,u=0,v=0,T=0);
real coef=100;
plot([u,v],T,wait=1,ps="lamevect.eps",coef=coef);
plot(T,wait=1,fill=1);

mesh th1 = movemesh(Th, [x+u*coef, y+v*coef]);
 plot(th1,wait=1,ps="lamedeform.eps");
real dxmin  = u[].min; 
real dymin  = v[].min; 

cout << " - dep.  max   x = "<< dxmin<< " y=" << dymin << endl; 
cout << "   dep.  (20,0)  = " << u(20,0) << " " << v(20,0) << endl;
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