Elasticity_2D.pro

Group {
  DefineGroup[Domain_Disp, Domain_Force, Domain_Force_Sur, Domain_Force_Lin] ;
  DomainTot = Region[ {Domain_Disp, Domain_Force} ];
}

Group {
  DefineGroup[ DomainInf ] ;
  DefineVariable[ Val_Rint, Val_Rext ] ;
}

Jacobian {
  { Name Vol ;
    Case {
      { Region DomainInf ; Jacobian VolSphShell {Val_Rint, Val_Rext} ; }
      { Region All ; Jacobian Vol ; }
    }
  }
  { Name Sur ;
    Case { { Region All ; Jacobian Sur ; }
    }
  }
  { Name Lin ;
    Case { { Region All ; Jacobian Lin ; }
    }
  }
  { Name SurLinVol ;
    Case {
      { Region Domain_Force_Sur ; Jacobian Sur ; }
      { Region Domain_Force_Lin ; Jacobian Lin ; }
      { Region All ; Jacobian Vol ; }
    }
  }
}

Integration {
  { Name GradGrad ;
    Case { 
      { Type Gauss ;
        Case { 
          { GeoElement Point       ; NumberOfPoints  1 ; }
          { GeoElement Line        ; NumberOfPoints  2 ; } 
          { GeoElement Triangle    ; NumberOfPoints  4 ; } 
          { GeoElement Quadrangle  ; NumberOfPoints  4 ; }
        }
      }
    }
  }
}

/* --------------------------------------------------------------------------*/

/* Mechanics - Displacement ux, uy formulations */

FunctionSpace {
  { Name H_u_Mec2D ; Type Vector ;
    BasisFunction {
      { Name sxn ; NameOfCoef uxn ; Function BF_NodeX ;
        dFunction {BF_NodeX_D12, BF_Zero} ;
        Support DomainTot ; Entity NodesOf[ All ] ; }
      { Name syn ; NameOfCoef uyn ; Function BF_NodeY ;
        dFunction {BF_NodeY_D12, BF_Zero} ;
        Support DomainTot ; Entity NodesOf[ All ] ; }
    }
    Constraint {
      { NameOfCoef uxn ;
        EntityType NodesOf ; NameOfConstraint DeplacementX ; }
      { NameOfCoef uyn ;
        EntityType NodesOf ; NameOfConstraint DeplacementY ; }
    }
  }
}

/*------------------------------------------------------------------------*/

Formulation {
  { Name Mec2D_u ; Type FemEquation ;
    Quantity {
      { Name u ; Type Local ; NameOfSpace H_u_Mec2D ; }
    }
    Equation {
      Galerkin { [ C_m[] * Dof{D1 u}, {D1 u} ] ;
                 In Domain_Disp ; Jacobian Vol ; Integration GradGrad ; } 
      Galerkin { [ -F[] , {u} ] ;     
                 In Domain_Force; Jacobian SurLinVol; Integration GradGrad; }  
    }
  }
}

/*------------------------------------------------------------------------*/

Resolution {
  { Name Mec2D_u ;
    System {
      { Name Sys_Mec ; NameOfFormulation Mec2D_u ; }
    }
    Operation { Generate Sys_Mec ; Solve Sys_Mec ; SaveSolution Sys_Mec ; }
  }
}

/*------------------------------------------------------------------------*/

PostProcessing {
  { Name Mec2D_u ; NameOfFormulation Mec2D_u ;  
    PostQuantity {
        { Name u ; Value { Term { [ {u} ]   ; In Domain_Disp ; } } }
        { Name um ; Value { Term { [Norm[{u}]] ; In Domain_Disp ; } } }
        { Name F ; Value { Term { [F[]]   ; In Domain_Force ; } } }
        { Name Vm ; Value { Term {      
           [Sqrt[ CompX[C_m[]*{D1 u}]#1^2 + CompY[C_m[]*{D1 u}]#2^2 - #1*#2 
                +  3*(CompZ[C_m[]*{D1 u}])^2   ] ] ; In Domain_Disp ; } } } 
    } 
  }
}

test.pro

Group {
  Slab = Region[1001]; 

  Bottom = Region[111] ; 
  Top = Region[113] ;  
  Left = Region[114];
  Right = Region[112];

  PointForce1 = Region[101] ;
  PointForce2 = Region[102] ;
  PointForce3 = Region[103] ;
  PointForce4 = Region[104] ;
 
  Domain_Force_Sur = Region[ { Top } ];
  Domain_Force = Region[ {Domain_Force_Sur} ];
  //Domain_Force = Region[ {} ];
  Domain_Disp = Region[ Slab ] ;
}

Function {
  c11 = 162.0e9; c12 = 77.5e9;  c22 = 166.0e9; c33 = 42.9e9;

  C_m[ Slab ] = TensorSym[ c11, c12, 0, c22, 0, c33 ];

  F[Top] = Vector[0, -1e12, 0 ];
}

Constraint {
  { Name DeplacementX ; Type Assign ;
    Case {
      //{ Region PointForce3; Value -1 ; }
      { Region Bottom; Value 0.0 ; }
    }
  }
  { Name DeplacementY ; Type Assign ;
    Case {
      //{ Region PointForce3; Value -1 ; }
      { Region Bottom; Value 0.0 ; }
    }
  }
}

Include "Elasticity_2D.pro"

PostOperation Map_u UsingPost Mec2D_u { 
  Print [ u,  OnElementsOf Domain_Disp, File "u.pos"] ;
  Print [ um, OnElementsOf Domain_Disp,  File "um.pos"] ;
  Print [ F,  OnElementsOf Domain_Force,  File "F.pos"] ;
  Print [ Vm , OnElementsOf Domain_Disp, File "Vm.pos"] ;
}

test.geo

p = 0.1;
a = 1;
s=1.0;

Point(1) = { 0 , 0 , 0 , p/10};
Point(2) = { a , 0 , 0 , p/10};
Point(3) = { a , a , 0 , p};
Point(4) = { 0 , a , 0 , p};

Line(1) = {1,2};
Line(2) = {2,3};
Line(3) = {3,4};
Line(4) = {4,1};

Line Loop(5) = {2,3,4,1};
Plane Surface(6) = {5};

Physical Surface(1001) =  { 6 }; // Slab

Physical Point(101) = {1};  // PointForce1
Physical Point(102) = {2};  // PointForce2
Physical Point(103) = {3};  // PointForce3
Physical Point(104) = {4};  // PointForce4

Physical Line(111) = {1};  // Bottom
Physical Line(113) = {3};  // Top
Physical Line(114) = {4};  // Left
Physical Line(112) = {2};  // Right