iso_axi.c

C 开发的有限元软件

   for (i = 1 ; i <= ninteg ; i++) {
      sg  = VectorData (xpoints) [i];
      rr=(minx+maxx)/2+sg*(maxx-minx)/2;

      ZeroMatrix(NN);
      for (j = 1 ; j <= numnodes ; j++) {
        MatrixData (NN) [1][2*j - 1] = MatrixData (N) [j][i] ;
        MatrixData (NN) [1][2*j]     = 0.0;
        MatrixData (NN) [2][2*j - 1] = 0.0;
        MatrixData (NN) [2][2*j]     = MatrixData (N) [j][i] ;
      }

      MatrixRows (Nt) = MatrixRows (temp) = MatrixCols (NN);
      TransposeMatrix (Nt, NN);

      MultiplyMatrices (tempM, Nt, NN);

      ScaleMatrix (tempM, tempM, VectorData (weights) [i]*VectorData (jac) [i], 0.0);
      ScaleMatrix (tempM, tempM, rr*4*acos(0), 0.0);
      AddMatrices (element -> M, element -> M, tempM);

   }
   ScaleMatrix (element -> M, element -> M, element -> material -> rho, 0.0);

}



 
Matrix IsoAQuadLocalB (element, numnodes, N, dNdx, dNdy, point,xpoints)
   Element	element;
   unsigned	numnodes;
   Matrix	dNdx, dNdy, N;
   unsigned	point;
   Vector xpoints;
{
   unsigned		i;
   double xc1,xc3,maxx,minx,rr;
   double sg;
   static Matrix	B = NullMatrix;

   if (B == NullMatrix) 
      B = CreateMatrix (4,8);
    
      xc1 = element -> node[1] -> x;
      xc3 = element -> node[3] -> x;
	  maxx=xc3;
	  minx=xc1; 
      sg  = VectorData (xpoints) [point];
      rr=(minx+maxx)/2+sg*(maxx-minx)/2; 


   for (i = 1 ; i <= numnodes ; i++) {

      MatrixData (B) [1][2*i - 1] = MatrixData (dNdx) [i][point];
      MatrixData (B) [1][2*i]     = 0.0;
      MatrixData (B) [2][2*i - 1] = MatrixData (N) [i][point] / rr;
      MatrixData (B) [2][2*i]     = 0.0;
      MatrixData (B) [3][2*i - 1] = 0.0;
      MatrixData (B) [3][2*i]     = MatrixData (dNdy) [i][point];
      MatrixData (B) [4][2*i - 1] = MatrixData (dNdy) [i][point];
      MatrixData (B) [4][2*i]     = MatrixData (dNdx) [i][point];
   }

   MatrixCols (B) = numnodes*2;

   return B;
}
    
Vector GlobalAQuadShapeFunctions (element, dNdxi, dNde, dNdx, dNdy, 
                                 ninteg,nodes)
   Element	element;
   int		ninteg;
   Matrix	dNdxi, dNde,
		dNdx, dNdy;
   unsigned	nodes;
{
   unsigned		i,j;
   static Vector	jac,
			dxdxi, dxde,
			dydxi, dyde = NullMatrix;

   if (dyde == NullMatrix) {

      dxdxi = CreateVector (4);
      dxde  = CreateVector (4);
      dydxi = CreateVector (4);
      dyde  = CreateVector (4);
      jac = CreateVector (4);
   }
 
   for (i = 1 ; i <= 4 ; i++) {
      VectorData (dxdxi) [i] = 0.0; 
      VectorData (dxde) [i] = 0.0; 
      VectorData (dydxi) [i] = 0.0; 
      VectorData (dyde) [i] = 0.0; 
      VectorData (jac) [i] = 0.0;
   }

   for (i = 1 ; i <= ninteg ; i++) {
      for (j = 1 ; j <= nodes ; j++) {

         VectorData (dxdxi) [i] += MatrixData (dNdxi) [j][i]*
                                   (element -> node[j] -> x);

         VectorData (dxde) [i] += MatrixData (dNde) [j][i]*
                                   (element -> node[j] -> x);

         VectorData (dydxi) [i] += MatrixData (dNdxi) [j][i]*
                                   (element -> node[j] -> y);
     
         VectorData (dyde) [i] += MatrixData (dNde) [j][i]*
                                   (element -> node[j] -> y);
      }

      VectorData (jac) [i] = VectorData (dxdxi)[i] * VectorData (dyde)[i] -
                         VectorData (dxde)[i] * VectorData (dydxi)[i];

      for (j = 1 ; j <= nodes ; j++) {
         MatrixData (dNdx)[j][i] = (MatrixData (dNdxi) [j][i]*VectorData (dyde)[i] -
                               MatrixData (dNde)[j][i]*VectorData (dydxi)[i])/
                               VectorData (jac)[i];

         MatrixData (dNdy)[j][i] = -(MatrixData (dNdxi)[j][i]*VectorData (dxde)[i] -
                                MatrixData (dNde)[j][i]*VectorData (dxdxi)[i])/
                                VectorData (jac)[i]; 
      }
   }

   return jac;
}

/*****************************************************************************
*
* Function:	LocalQuadShapeFunctions
*
* Description:  calculates the shape functions and the derivatives (w/ respect
*		to xi, eta coordinates) of the shape function for a four to 
*		nine node axisymmetrix element	
*
* Note:		The approach looks rather brutish, but it seems much clearer
*		to me this way and we have to do each individual computation 
*		anyways, whether we put ourselves in a loop and use index
*		notation or not ...
*
******************************************************************************/

unsigned LocalAQuadShapeFunctions (element, ninteg, N, 
                                  dNdx, dNde, weights, xpoints, force_init)
   Element	element;
   unsigned	ninteg;
   Matrix	N,
		dNdx,
		dNde;
   unsigned	force_init;
   Vector	weights,xpoints;
{
   unsigned		i,j,k;
   double		eta,xi;
   double		Nt[5];
   double		de[5],dx[5];
   double		*gauss_points;
   double		*gauss_wts;
   unsigned		numnodes;
   static unsigned	prev_nodes = 0;
   

   if (element -> node[3] -> number == element -> node[4] -> number) 
      numnodes = 3;
   else   
      numnodes = 4;   

   if (numnodes == prev_nodes && !force_init)
      return numnodes;

   ninteg /= 2;	/* how many in each dimension? */

   GaussPoints (ninteg, &gauss_points, &gauss_wts);
   
   for (i = 0 ; i < ninteg ; i++) {
      xi  = gauss_points [i];
      for (j = 0 ; j < ninteg ; j++) {

         eta = gauss_points [j];

         Nt [1] = 0.25*(1 - eta)*(1 - xi);
         dx [1] = 0.25*(-1 + eta);
         de [1] = 0.25*(-1 + xi);
         Nt [2] = 0.25*(1 - eta)*(1 + xi);
         dx [2] = 0.25*(1 - eta);
         de [2] = 0.25*(-1 - xi);
         Nt [3] = 0.25*(1 + eta)*(1 + xi);
         dx [3] = 0.25*(1 + eta);
         de [3] = 0.25*(1 + xi);
         Nt [4] = 0.25*(1 + eta)*(1 - xi);
         dx [4] = 0.25*(-1 - eta);
         de [4] = 0.25*(1 - xi);

         if (numnodes == 3) {
             Nt [3] += Nt [4];
             dx [3] += dx [4];
             de [3] += de [4];
         }

         for (k = 1 ; k <= 4 ; k++) {
            MatrixData (N) [k][i*ninteg + j+1] = Nt [k];
            MatrixData (dNdx) [k][i*ninteg + j+1] = dx [k];
            MatrixData (dNde) [k][i*ninteg + j+1] = de [k];
         }

         VectorData (weights) [i*ninteg + j+1] = gauss_wts [j];
         VectorData (xpoints)  [i*ninteg + j+1] = xi;
         VectorData (xpoints)  [4+i*ninteg + j+1] = eta; 
      }
   }

   prev_nodes = numnodes;
   return numnodes;
}

Vector IsoAQuadEquivNodalForces (element, err_count)
   Element	element;
   int		*err_count;
{
   double		L;
   double		wa,wb;
   double		force1,
			force2;
   int			count;
   double		xc1,xc2,
			yc1,yc2;
   double		thick;
   unsigned		node_a,
			node_b;
   unsigned		i;
   static Vector 	equiv = NullMatrix;
 
   if (equiv == NullMatrix) 
      equiv = CreateVector (8);

   count = 0;
 
   if (element -> numdistributed > 2) {
      error ("quad element %d can have at most two distributed loads",
              element -> number);
      count++;
   }

   thick = element -> material -> t;

   for (i = 1 ; i <= 8 ; i++)
      VectorData (equiv) [i] = 0.0;

   for (i = 1 ; i <= element -> numdistributed ; i++) {

      if (element -> distributed[i] -> nvalues != 2) {
         error ("load %s does not have 2 nodal values (element %d)",
                 element -> distributed[i] -> name,element -> number);
         count++;
      }

      if (element -> distributed[i] -> direction != GlobalX &&
         element -> distributed[i] -> direction != GlobalY) {
          error ("invalid direction specified for load %s (element %d)",
                 element -> distributed[i] -> name,element -> number);
          count++;
      }

      node_a = element -> distributed[i] -> value[1].node;
      node_b = element -> distributed[i] -> value[2].node;

      if (node_a < 1 || node_a > 4 || node_b < 1 || node_b > 4) {
         error ("incorrect node numbering for load %s (element %d)", 
                element -> distributed[i] -> name,element -> number);
         count++;
      }

      if (node_a == node_b) {
         error ("incorrect node numbering for load %s (element %d)", 
                element -> distributed[i] -> name,element -> number);
         count++;
      }

      xc1 = element -> node[node_a] -> x;
      xc2 = element -> node[node_b] -> x;
      yc1 = element -> node[node_a] -> y;
      yc2 = element -> node[node_b] -> y;

      L = sqrt ((xc1 - xc2)*(xc1 - xc2) + (yc1 - yc2)*(yc1 - yc2));

      if (L <= TINY) {
         error ("length of side of element %d is zero to machine precision",
                 element -> number);
         count ++;
      } 

	/* 
	 * Thats all the error checking, bail out if we've had any
	 */

      if (count) {
         *err_count = count;
         return NullMatrix;
      }

      wa = element -> distributed[i] -> value[1].magnitude;
      wb = element -> distributed[i] -> value[2].magnitude;

      if (wa == wb) 		          /* uniform distributed load */
         force1 = force2 = wa*L*thick/2.0;
      else if (fabs(wa) > fabs(wb)) {     /* load sloping node1 to node2 */
         force2 = wb*L*thick/2.0 + (wa - wb)*L*thick/6.0;
         force1 = wb*L*thick/2.0 + (wa - wb)*L*thick/3.0; 
      }
      else if (fabs(wa) < fabs(wb)) {     /* load sloping node2 to node1 */
         force2 = wa*L*thick/2.0 + (wb - wa)*L*thick/6.0;
         force1 = wa*L*thick/2.0 + (wb - wa)*L*thick/3.0; 
      } 

      if (element -> distributed[i] -> direction == GlobalX) {
         VectorData (equiv) [2*node_a - 1] += force1;
         VectorData (equiv) [2*node_b - 1] += force2;
      }
      else {
         VectorData (equiv) [2*node_a] += force1;
         VectorData (equiv) [2*node_b] += force2;
      } 
   }

	/*
	 * Now that we know all is okay, allocate some memory if we
	 * haven't already done so for some other element
	 */

   SetEquivalentForceMemory (element);

   *err_count = 0;
   return equiv; 
}

*********************************************************
procedure in misc.c
*********************************************************

 
/*****************************************************************************
 *
 * Function:	AxisymD
 *
 *****************************************************************************/

Matrix AxisymD (element)
   Element	element;
{
   static Matrix	D = NullMatrix;
   static double	prev_nu = -99;
   static double	prev_E = -99;
   double 		poisson,
			factor,c11,c33,c12,c13,c44,c23,c22;

   if (D == NullMatrix) 
      D = CreateMatrix (4,4);

   if (element -> material -> nu != prev_nu || 
       element -> material -> E != prev_E) {
      ZeroMatrix (D);}

      poisson = element -> material -> nu;
	  if (element -> material -> nu == 1 &&
		  element -> material -> E  == 1)  {
		  /* PZT5A */

		  c11=12.1e10;
		  c33=11.1e10;
		  c12=7.54e10;
		  c13=7.52e10;
		  c44=2.11e10;
		  c22=c11;
		  c23=c13;

      MatrixData (D) [1][1] = c11;
      MatrixData (D) [1][2] = c12; 
      MatrixData (D) [1][3] = c13;
      MatrixData (D) [1][4] = 0.0;
      MatrixData (D) [2][1] = c12;
      MatrixData (D) [2][2] = c22; 
      MatrixData (D) [2][3] = c23;
      MatrixData (D) [2][4] = 0.0;
      MatrixData (D) [3][1] = c13;
      MatrixData (D) [3][2] = c23; 
      MatrixData (D) [3][3] = c33;
      MatrixData (D) [3][4] = 0.0;
      MatrixData (D) [4][1] = 0.0;
      MatrixData (D) [4][2] = 0.0; 
      MatrixData (D) [4][3] = 0.0;
      MatrixData (D) [4][4] = c44;

      prev_E = element -> material -> E;
      prev_nu = element -> material -> nu;
   }

   return D;
}