2.5 Restrictions on support displacements

Restrictions on the support displacements (see Fig. 1.10) of the system (2.1) are given in excerpt 2.7 from the computing diary and are described in global coordinates.

Computing diary excerpt 2.7 ( spESTframe93LaheWFI.m )  

========================================================
 Restrictions on support displacements (on - 1, off - 0) 
   No    Node No   u  w  fi
--------------------------------------------------------
   1         1     1  1  0 
   2         3     1  1  1 
   3         5     1  1  0 
--------------------------------------------------------

The global displacements of the structure at a support node are obtained by transforming the element displacements to the global coordinate system.

The program selects the row index and finds column and element indexes (see excerpts 2.7 and 2.8). Restrictions on the support displacements are inserted into Eq. (2.1).

Computing diary excerpt 2.8 ( spESTframe93LaheWFI.m )  

======================================================
 Support |  Restrictions    | Element | Displacements 
  node   |(on - 1, off - 0) |   No    | u_   w_   fi_ 
    No   |  u_   w_   fi_   |         |   indexes 
------------------------------------------------------
    1       1    1    0         1        7    8    9
    3       1    1    1         3       31   32   33
    5       1    1    0         5       49   50   51
------------------------------------------------------

The program inserts the displacement component of an element at a support into Eq. (2.1) with the command cmd = spA=spInsertBtoA(spA,61,7,SpTMUv); (see excerpt 2.9), SpTUv=SpToeSiirdeUvektor(NSARV,NEARV,VarrasS,krdn,selem) , SpTWv=SpToeSiirdeWvektor(NSARV,NEARV,VarrasS,krdn,selem) , SpTFiV=SpToeSiirdeFiVektor(1).

The support shift is inserted with the command cmd = B(61,1)=tSiire(1,1,1). The program multiplies the support shifts by the basic stiffness ^2.7, $i_{0}= EI_{basic}/l_{basic}$.

Computing diary excerpt 2.9 ( spESTframe93LaheWFI.m )  

#====================================================================  

-----Side conditions are inserted into spA  ----  
  
side_condition_rows =  2
non_zero_elements_in_side_condition =  2


#==================================================================== 
 Restrictions on support displacements 
Restrictions on support displacements begin from row: 61
#====================================================================  

cmd = spA=spInsertBtoA(spA,61,7,SpTUv);
Support shift  tSiire(1,1,1) = 0  in x direction at node 1
cmd = B(61,1)=tSiire(1,1,1);
  
cmd = spA=spInsertBtoA(spA,62,7,SpTWv);
Support shift  tSiire(2,1,1) = 0  in z direction at node 1
cmd = B(62,1)=tSiire(2,1,1);
  
cmd = spA=spInsertBtoA(spA,63,31,SpTUv);
Support shift  tSiire(1,1,3) = 0  in x direction at node 3
cmd = B(63,1)=tSiire(1,1,3);
  
cmd = spA=spInsertBtoA(spA,64,31,SpTWv);
Support shift  tSiire(2,1,3) = 0  in z direction at node 3
cmd = B(64,1)=tSiire(2,1,3);
  
cmd = spA=spInsertBtoA(spA,65,31,SpTFiV);
Support shift  tSiire(3,1,3) = 0  in y direction at node 3
cmd = B(65,1)=tSiire(3,1,3);
  
cmd = spA=spInsertBtoA(spA,66,49,SpTUv);
Support shift  tSiire(1,1,5) = 0  in x direction at node 5
cmd = B(66,1)=tSiire(1,1,5);
  
cmd = spA=spInsertBtoA(spA,67,49,SpTWv);
Support shift  tSiire(2,1,5) = 0  in z direction at node 5
cmd = B(67,1)=tSiire(2,1,5); \Eq.~
----- 
 
spA_rows =  67
spA_cols =  67
spA_nnz = non_zero_elements_in_spA: 181
  
-----Restrictions equations on displacements are inserted into spA   
  
restrictions_equations_rows =  7
non_zero_elements_in_restrictions_equations =  7
  
#==================================================================== 
spA_rank =  67
spA =

Compressed Column Sparse (rows = 67, cols = 67, nnz = 181 [4%])

#====================================================================