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Highlights from
Space Truss Systems as Linear Static Analysis

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from Space Truss Systems as Linear Static Analysis by Ali OZGUL
Space truss

Spacetruss

Contents

%_______________________________________________________________
%2Node-6DOF SPACE TRUSS SYSTEM  FEM          [A.Ö]      (C)(R)  |
%#############################                                  |
%              Shape function : Lineer (Axial normal)           |
%              Stifness       : Topology +Accumulate method     |
%              Solve Equation : Cholesky-[L][D][u]              |
%_______________________________________________________________|
% Maxima 5.9.0.9beta2 http://maxima.sourceforge.net             |
% Using Lisp Kyoto Common Lisp GCL 2.6.3 (aka GCL)              |
% Distributed under the GNU Public License. See the file COPYING|
% Dedicated to the memory of William Schelter.                  |
% This is a development version of Maxima. The function bug_rep |
% provides bug reporting information.                           |
%_______________________________________________________________|




clc
clear
%## INPUT DATA ##

## MATERIAL PROPERTIES ##

%Materials matrix
   %  Cross-sectional areas(m**2)   Elasticity (KN/m**2)

%_______________________________________Example (1)
%Properties=[0.050  2E7   %1 Element No
%            0.050  2E7   %2
%            0.050  2E7   %3
%            0.050  2E7 ];%4
%___________________________|

%_______________________________________Example (2)
%Properties=[0.020  2E7   %1 Element No
%            0.020  2E7   %2
%            0.020  2E7   %3
%            0.020  2E7   %4
%            0.020  2E7 ];%5
%___________________________|


%_______________________________________Example (3)
%Properties=[0.060  2E7   %1 Element No
%            0.060  2E7   %2
%            0.060  2E7   %3
%            0.060  2E7   %4
%            0.060  2E7   %5
%            0.060  2E7   %6
%            0.060  2E7   %7
%            0.060  2E7 ];%8
%___________________________|


%_______________________________________Example (4)
%Properties=[0.050  2E7   %1 Element No
%            0.050  2E7   %2
%            0.050  2E7   %3
%            0.050  2E7   %4
%            0.050  2E7 ] %5
%___________________________|

%_______________________________________Example (5)
Properties=[0.050  2E7   %1 Element No
            0.050  2E7   %2
            0.050  2E7   %3
            0.050  2E7   %4
            0.050  2E7   %5
            0.050  2E7   %6
            0.050  2E7  ]%7

%for i=1:7
%    Properties(i,:)=[0.050 2E7];
%end
%___________________________|
No=size(Properties,1); %Elements Number


%All element's Areas A(i) and Elasticity E(i)
for i=1:No
    A(i,:)=Properties(i,1);
    E(i,:)=Properties(i,2);
end

Properties =

  1.0e+007 *

    0.0000    2.0000
    0.0000    2.0000
    0.0000    2.0000
    0.0000    2.0000
    0.0000    2.0000
    0.0000    2.0000
    0.0000    2.0000

## GLOBAL NODE COORDINATES ##

%_______________________________________Example (1)
% Cor=[   X      Y      Z ]
% Cor=[ 0.00   3.00   4.00
%       0.00   3.00  -4.00
%       0.00   6.00   0.00
%       0.00   0.00   0.00
%       4.00   3.00   0.00 ];
%_______________________________|

%_______________________________________Example (2)
%Cor=[   X      Y      Z ]
% Cor=[ 0.00   4.00   4.00
%       8.00   4.00   0.00
%       4.00   4.00  -4.00
%       4.00   0.00   4.00 ];
%_______________________________|

%_______________________________________Example (3)
% Cor=[   X      Y      Z ]
% Cor=[ 0.00  12.00   0.00
%       3.00   3.00   0.00
%       6.00  12.00   0.00
%       3.00   0.00   4.00
%       3.00   0.00  -4.00  ];
%_______________________________|

%_______________________________________Example (4)
% Cor=[   X      Y      Z ]
%  Cor=[ 0.00   6.00   4.00
%       16.00   6.00   4.00
%       16.00   6.00   0.00
%        0.00   6.00   0.00
%        8.00   3.00   0.00
%        8.00   0.00   4.00 ];
%_______________________________|

%_______________________________________Example (5)
% Cor=[   X      Y      Z ]
  Cor=[ 3.00    0.00   4.00
        5.00    0.00   4.00
        4.00    0.00  -4.00
        0.00    4.00   0.00
        4.00    8.00   0.00
        8.00    4.00   0.00 ];
%_______________________________|
Node=size(Cor,1);

## ELEMENT POSITION MATRIX ##

%_______________________________________Example (1)
%Pos=[3 5
%     2 5
%     1 5
%     4 5];
%________________________________|

%_______________________________________Example (2)
%Pos=[1 3
%     1 2
%     4 3
%     3 2
%     4 2];
%________________________________|

%_______________________________________Example (3)
%Pos=[4 1
%     1 5
%     4 2
%     2 3
%     4 3
%     5 2
%     5 3
%     2 1];
%________________________________|

%_______________________________________Example (4)
%Pos=[4 5
%     1 6
%     5 3
%     6 2
%     6 5];
%________________________________|

%_______________________________________Example (5)
Pos=[4 5
     1 4
     1 5
     6 5
     2 5
     2 6
     3 5];
%________________________________|

%Element`s Node Topology
for i=1:Node;
    Re(i,:)=[1 1 1];
end

## SYSTEM SUPPORTS ##

%Re(Node number,:)=[ux vy wz](0=Connected,1=free)
%_______________________________________Example (1)
%      Re(1,:)= [0 0 0];
%      Re(2,:)= [0 0 0];
%      Re(3,:)= [0 0 0];
%      Re(4,:)= [0 0 0];
%_______________________|

%_______________________________________Example (2)
%      Re(1,:)= [0 0 0];
%      Re(2,:)= [0 0 1];
%      Re(4,:)= [0 0 0];
%_______________________|

%_______________________________________Example (3)
%      Re(1,:)= [1 0 0];
%      Re(3,:)= [1 0 0];
%      Re(4,:)= [0 0 0];
%      Re(5,:)= [0 0 0];
%_______________________|

%_______________________________________Example (4)
%      Re(1,:)= [0 0 0];
%      Re(2,:)= [0 0 0];
%      Re(3,:)= [0 0 0];
%      Re(4,:)= [0 0 0];
%      Re(6,:)= [1 0 0];
%_______________________|

%_______________________________________Example (5)
       Re(1,:)= [0 0 0];
       Re(2,:)= [0 0 0];
       Re(3,:)= [0 0 0];
       Re(4,:)= [1 0 0];
       Re(6,:)= [1 0 0];
%_______________________|
Topology=Re;
Nom=size(Re,2); % Element node d.o.f Number

%Topology---->Accumulate
sayman=0;
for i=1:Node;
    for j=1:Nom;
        if Re(i,j)==1 ;
        sayman = sayman +1;
            Re(i,j) = sayman;
        end
    end
end
Item=sayman;     %System total displacement value


for i=1:No
    R(i,:)=[Re(Pos(i,1),:) Re(Pos(i,2),:)];
end


P(Item)=0;

## SYSTEM GLOBAL LOAD ##

%P(Re(Node number, freedom number))=LOAD
%_______________________________________Example (1)
%P(Re(5,1))= 10.00;
%P(Re(5,2))= -8.00;
%__________________________|

%_______________________________________Example (2)
%P(Re(3,2))= -10.00;
%__________________________|

%_______________________________________Example (3)
%P(Re(1,1))= -10.00;
%P(Re(2,2))= -30.00;
%P(Re(3,1))=  10.00;
%__________________________|

%_______________________________________Example (4)
% P(Re(5,1))=  10.00;
% P(Re(5,2))= -10.00;
% P(Re(6,1))= -10.00;
%__________________________|

%_______________________________________Example (5)
P(Re(4,1))= 10.00 ;
P(Re(5,2))=-30.00 ;
P(Re(6,1))=-10.00 ;
%__________________________|
% ###########

%SYSTEM_ANALYSIS
%

Global system node is moving per element nodes

for s=1:No;
    px1(s,:)=Cor(Pos(s,1),1);
    px2(s,:)=Cor(Pos(s,2),1);

    py1(s,:)=Cor(Pos(s,1),2);
    py2(s,:)=Cor(Pos(s,2),2);

    pz1(s,:)=Cor(Pos(s,1),3);
    pz2(s,:)=Cor(Pos(s,2),3);
end

Element Stiffness Applications

for s=1:No

%Element length
Ln = sqrt( (px2(s)-px1(s))^2+(py2(s)-py1(s))^2+(pz2(s)-pz1(s))^2 );

%Element direction cosinesses of global coordinat system
Dcos= [ (px2(s)-px1(s))      %ly
        (py2(s)-py1(s))      %my
        (pz2(s)-pz1(s))]/Ln; %ny


Dataport(s,:)=[Ln Dcos(1) Dcos(2)  Dcos(3)];

%Analytical tranformation matrix
%[T]= [  ly(i)   my(i)   ny(i)     0       0     0
%       -my(i)   ly(i)     0       0       0     0
%       -ny(i)    0      ly(i)     0       0     0
%          0      0        0     ly(i)   my(i)  ny(i)
%          0      0        0    -my(i)   ly(i)   0
%          0      0        0     ny(i)     0    ly(i) ]


%Global-->Local axis transformation matrix
T(:,:,s)= [  Dcos(1)  Dcos(2)  Dcos(3)      0        0        0
            -Dcos(2)  Dcos(1)     0         0        0        0
            -Dcos(3)     0     Dcos(1)      0        0        0
                0        0        0      Dcos(1)  Dcos(2)   Dcos(3)
                0        0        0     -Dcos(2)  Dcos(1)     0
                0        0        0     -Dcos(3)     0      Dcos(1)];

%Per element local axis stiffness matrix
K(:,:,s)=[  A(s)*E(s)/Ln     0.00      0.00     -A(s)*E(s)/Ln  0.00   0.00
                  0.00       0.00      0.00         0.00       0.00   0.00
                  0.00       0.00      0.00         0.00       0.00   0.00
           -A(s)*E(s)/Ln     0.00      0.00      A(s)*E(s)/Ln  0.00   0.00
                  0.00       0.00      0.00         0.00       0.00   0.00
                  0.00       0.00      0.00         0.00       0.00   0.00 ];

%Element global axis stiffness matrix
%[K]global=[C].[K]local.[C]' or
%[K]global=[T]'[K]local.[T]
Kg(:,:,s)=T(:,:,s)'*K(:,:,s)*T(:,:,s);

end

System Stiffness Matrix (Superposition)

%Element stiffness matrix superposition of system global axis
Ksis(Item,Item)=0;
    for n=1:No;
        for sat=1:6;
            for sut=1:6;
               if (R(n,sat)~=0)
                  if (R(n,sut)~=0);
                    Ksis(R(n,sut),R(n,sat))=Ksis(R(n,sut),R(n,sat)) + Kg(sat,sut,n);
                  end
               end
            end
        end
    end

System global stiffness matrix singularity check

equation=size(Ksis);
if equation(1)~=rank(Ksis)
    display('This system stiffness matrix is badly scaled')
    R
    error('Control system support boundary conditions')
else
    Ku = inv(Ksis);
    D = Ku *P';
end
clear equation

%Element per unit node topology matrix
    for  v = 1 : No;
        for m = 1 :2*Nom;%6 degree of freedom
             u = R(v, m);
             if u ~=0
                 Hu(v, m,:) = D(u) ;
             else
                 Hu(v,m)=0;
             end
        end
    end

Element global and local node's reactions

 for s=1 :No;
%Element global node reactions
     Pg(:,s) = Kg(:,:,s)*Hu(s,:)';
%Element local node reactions
     Pl(:,s) = T(:,:,s)*Pg(:,s);
 end

Pf(3*Node)=0;
Af(3*Node)=0;

 for s=1:No;     %Total element number
     for Nm=1:2; %One node d.o.f
Poss=Pos(s,Nm);
        Pf((Poss-1)*3+1:Poss*3)=Pg((Nm-1)*3+1:Nm*3,s);
        Af((Poss-1)*3+1:Poss*3)=Af((Poss-1)*3+1:Poss*3)+Pf((Poss-1)*3+1:Poss*3);
     end
 end
clear Nm
% for j=1:size(Re,1)
%     if Topology(j,:)~=[1 1 1]
%         Af(3*(j-1)+1:3*(j-i)+3)'
%     end
% end

Analysis Results

%_______________________________SYSTEM DESCRIPTION
display ('====SYSTEM ANALYSIS PROPERTIES');
fprintf(' \n');
fprintf(' System total degree of freedom=    [%.f] \n',Item);
fprintf(' System total element value    =    [%.f] \n',No);
fprintf(' One node degree of freedom    =    [%.f] \n',Nom);
%whos
fprintf('\n \n ');



 %_______________________________PROPERTIES
display ('====PER ELEMENTS PROPERTIES');
fprintf(' \n');
fprintf('       Area(m**2) E. Module (KN/m**2) \n');
for s=1:size(Properties,1);
fprintf('  (%.f)  [% .4f]  [% .f] \n',s,Properties(s,:));
end

fprintf('\n \n ');

%_______________________________COORDINATES
display ('====ALL NODE GLOBAL CARTESIAN COORDINATE (metre)');
fprintf(' \n');
fprintf('        Xglobal       Yglobal        Zglobal \n');
for s=1:size(Cor,1);
fprintf('  (%.f)  [% .4f]     [% .4f]      [% .4f] \n',s,Cor(s,:));
end

fprintf('\n \n ');


%_______________________________ELEMENT Length and Direction Coninesses
display ('====ELEMENT SPACE POSITON (metre)');
fprintf(' \n');
fprintf('        Length(m.)  ly       my       ny   (Direction Cosinesses) \n');
for s=1:size(Dataport,1);
fprintf('  (%.f)   [% .2f] [% .4f] [% .4f] [% .4f] \n',s,Dataport(s,:));
end

fprintf('\n \n ');


%_______________________________POSITION MATRIX
display ('====ALL ELEMENT (i) and (j) NODE POSITION ');
fprintf(' \n');
fprintf('        Pos(i)      Pos(j) \n');
for s=1:size(Pos,1);
fprintf('  (%.f)   (% .f)o--->---o(% .f) \n',s,Pos(s,:));
end

fprintf('\n \n ');


%_______________________________TOPOLOGY
display ('====SYSTEM ALL NODE TOPOLOGY MATRIX ');
fprintf(' \n');
fprintf('        u(x)  v(y)  w(z)    (Connected=0   Free=1) \n');
for s=1:size(Topology,1);
fprintf('  (%.f)   [% .f]  [% .f]  [% .f] \n',s,Topology(s,:));
end

fprintf('\n \n ');


%_______________________________REOLOGY
display ('====SYSTEM ALL NODE REOLOGY MATRIX ');
fprintf(' \n');
fprintf('        u(x)  v(y)  w(z)    (Connected=0  else Free) \n');
for s=1:size(Re,1);
fprintf('  (%.f)   [% .f]  [% .f]  [% .f] \n',s,Re(s,:));
end

fprintf('\n \n ');


%_______________________________LOCAL [K]local
display ('====PER ELEMENT LOCAL STIFFNESS MATRIX ');
fprintf(' \n');
K
fprintf('\n \n ');

%_______________________________TRANSFORM [T]
display ('====PER ELEMENT GLOBAL to LOCAL TRANSFORM MATRIX ');
fprintf(' \n');
T
fprintf('\n \n ');

%_______________________________GLOBAL [K]global
display ('====PER ELEMENT GLOBAL STIFFNESS MATRIX ');
fprintf(' \n');
Kg
fprintf('\n \n ');

%_______________________________SYSTEM STIFFNESS  [K]system
display ('====SYSTEM STIFFNESS MATRIX ');
fprintf(' \n');
Ksis
fprintf('\n \n ');

%_______________________________SYSTEM FORCES  [P]
display ('====SYSTEM STIFFNESS MATRIX ');
fprintf(' \n');
Ksis
fprintf('\n \n ');


%_______________________________GLOBAL NODE DISPLACEMENT
display ('====PER ELEMENTS NODE GLOBAL DISPLACEMENT===[Du Dv Dw]global (metre)');
fprintf('\n');
fprintf('            u(i)         v(i)          w(i)          u(j)          v(j)         w(j) \n');
for s=1:size(Hu,1);
fprintf('  (%.f)  [% .7f]  [% .7f]  [% .7f]  [% .7f]  [% .7f] [% .7f] \n',s,Hu(s,:));
%fprintf('         [% .7f]%.f    [% .7f]%.f   [% .7f]%.f   [% .7f]%.f  \n',Pg(s,1),R(1,s)',Pg(s,2),R(2,s)',Pg(s,3),R(3,s)',Pg(s,4),R(4,s)');
%if mod(s,3)==0; fprintf(' \n');end;
end

fprintf('\n \n ');



%_______________________________GLOBAL NODE DISPLACEMENT
display ('====PER ELEMENTS NODE GLOBAL DISPLACEMENT===[Du Dv Dw]global (metre)');
fprintf('\n');
fprintf('            u(i)         v(i)          w(i)          u(j)          v(j)         w(j) \n');
for s=1:size(Hu,1);
fprintf('  (%.f)  [% .7f]  [% .7f]  [% .7f]  [% .7f]  [% .7f] [% .7f] \n',s,Hu(s,:));
%fprintf('         [% .7f]%.f    [% .7f]%.f   [% .7f]%.f   [% .7f]%.f  \n',Pg(s,1),R(1,s)',Pg(s,2),R(2,s)',Pg(s,3),R(3,s)',Pg(s,4),R(4,s)');
%if mod(s,3)==0; fprintf(' \n');end;
end

fprintf('\n \n ');



%_______________________________GLOBAL NODE REACTIONS
display ('====PER ELEMENTS GLOBAL NODE REACTION===[Fx Fy Fz]global (KN)');
fprintf('\n');
fprintf('            [fx(i)     fy(i)      fz(i)]o-------o[fx(j)     fy(j)     fz(j)] \n');
for s=1:size(Pg,2);
fprintf('  (%.f)  [% .5f]  [% .5f]  [% .5f]       [% .5f]  [% .5f] [% .5f] \n',s,Pg(:,s)');
end

fprintf('\n \n ');


%_______________________________LOCAL NODE REACTIONS
display ('====PER ELEMENTS LOCAL NODE REACTION===[Fx Fy Fz]global (KN)');
fprintf('\n');
fprintf('  [ fnormal(i) ]o--->----o[ fnormal(j) ] \n');
for s=1:size(Pl,2);

if Pl(1,s) <= 0
fprintf('  (%.f)  [% .5f]        [% .5f]    (Tansion  effect) stretch motion \n',s,Pl(1,s)',Pl(4,s)');
else
fprintf('  (%.f)  [% .5f]        [% .5f]    (Pressure effect) buckling motion\n',s,Pl(1,s)',Pl(4,s)');
end
end

fprintf('\n \n ');


%_______________________________NODE and SUPPORT REACTIONS (superposition)

display ('====SYSTEM ALL NODE and SUPPORT REACTIONS===[Fx Fy Fz]global (KN)');
fprintf('\n');
fprintf('      fx(g)     fy(g)      fz(g) \n');
for s=1:size(Af)';
fprintf('  [% .5f]  [% .5f]  [% .5f]       \n',Af');
end

fprintf('\n \n ');

====SYSTEM ANALYSIS PROPERTIES
 
 System total degree of freedom=    [5] 
 System total element value    =    [7] 
 One node degree of freedom    =    [3] 

 
 ====PER ELEMENTS PROPERTIES
 
       Area(m**2) E. Module (KN/m**2) 
  (1)  [ 0.0500]  [ 20000000] 
  (2)  [ 0.0500]  [ 20000000] 
  (3)  [ 0.0500]  [ 20000000] 
  (4)  [ 0.0500]  [ 20000000] 
  (5)  [ 0.0500]  [ 20000000] 
  (6)  [ 0.0500]  [ 20000000] 
  (7)  [ 0.0500]  [ 20000000] 

 
 ====ALL NODE GLOBAL CARTESIAN COORDINATE (metre)
 
        Xglobal       Yglobal        Zglobal 
  (1)  [ 3.0000]     [ 0.0000]      [ 4.0000] 
  (2)  [ 5.0000]     [ 0.0000]      [ 4.0000] 
  (3)  [ 4.0000]     [ 0.0000]      [-4.0000] 
  (4)  [ 0.0000]     [ 4.0000]      [ 0.0000] 
  (5)  [ 4.0000]     [ 8.0000]      [ 0.0000] 
  (6)  [ 8.0000]     [ 4.0000]      [ 0.0000] 

 
 ====ELEMENT SPACE POSITON (metre)
 
        Length(m.)  ly       my       ny   (Direction Cosinesses) 
  (1)   [ 5.66] [ 0.7071] [ 0.7071] [ 0.0000] 
  (2)   [ 6.40] [-0.4685] [ 0.6247] [-0.6247] 
  (3)   [ 9.00] [ 0.1111] [ 0.8889] [-0.4444] 
  (4)   [ 5.66] [-0.7071] [ 0.7071] [ 0.0000] 
  (5)   [ 9.00] [-0.1111] [ 0.8889] [-0.4444] 
  (6)   [ 6.40] [ 0.4685] [ 0.6247] [-0.6247] 
  (7)   [ 8.94] [ 0.0000] [ 0.8944] [ 0.4472] 

 
 ====ALL ELEMENT (i) and (j) NODE POSITION 
 
        Pos(i)      Pos(j) 
  (1)   ( 4)o--->---o( 5) 
  (2)   ( 1)o--->---o( 4) 
  (3)   ( 1)o--->---o( 5) 
  (4)   ( 6)o--->---o( 5) 
  (5)   ( 2)o--->---o( 5) 
  (6)   ( 2)o--->---o( 6) 
  (7)   ( 3)o--->---o( 5) 

 
 ====SYSTEM ALL NODE TOPOLOGY MATRIX 
 
        u(x)  v(y)  w(z)    (Connected=0   Free=1) 
  (1)   [ 0]  [ 0]  [ 0] 
  (2)   [ 0]  [ 0]  [ 0] 
  (3)   [ 0]  [ 0]  [ 0] 
  (4)   [ 1]  [ 0]  [ 0] 
  (5)   [ 1]  [ 1]  [ 1] 
  (6)   [ 1]  [ 0]  [ 0] 

 
 ====SYSTEM ALL NODE REOLOGY MATRIX 
 
        u(x)  v(y)  w(z)    (Connected=0  else Free) 
  (1)   [ 0]  [ 0]  [ 0] 
  (2)   [ 0]  [ 0]  [ 0] 
  (3)   [ 0]  [ 0]  [ 0] 
  (4)   [ 1]  [ 0]  [ 0] 
  (5)   [ 2]  [ 3]  [ 4] 
  (6)   [ 5]  [ 0]  [ 0] 

 
 ====PER ELEMENT LOCAL STIFFNESS MATRIX 
 

K(:,:,1) =

  1.0e+005 *

    1.7678         0         0   -1.7678         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
   -1.7678         0         0    1.7678         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0


K(:,:,2) =

  1.0e+005 *

    1.5617         0         0   -1.5617         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
   -1.5617         0         0    1.5617         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0


K(:,:,3) =

  1.0e+005 *

    1.1111         0         0   -1.1111         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
   -1.1111         0         0    1.1111         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0


K(:,:,4) =

  1.0e+005 *

    1.7678         0         0   -1.7678         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
   -1.7678         0         0    1.7678         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0


K(:,:,5) =

  1.0e+005 *

    1.1111         0         0   -1.1111         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
   -1.1111         0         0    1.1111         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0


K(:,:,6) =

  1.0e+005 *

    1.5617         0         0   -1.5617         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
   -1.5617         0         0    1.5617         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0


K(:,:,7) =

  1.0e+005 *

    1.1180         0         0   -1.1180         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0
   -1.1180         0         0    1.1180         0         0
         0         0         0         0         0         0
         0         0         0         0         0         0


 
 ====PER ELEMENT GLOBAL to LOCAL TRANSFORM MATRIX 
 

T(:,:,1) =

    0.7071    0.7071         0         0         0         0
   -0.7071    0.7071         0         0         0         0
         0         0    0.7071         0         0         0
         0         0         0    0.7071    0.7071         0
         0         0         0   -0.7071    0.7071         0
         0         0         0         0         0    0.7071


T(:,:,2) =

   -0.4685    0.6247   -0.6247         0         0         0
   -0.6247   -0.4685         0         0         0         0
    0.6247         0   -0.4685         0         0         0
         0         0         0   -0.4685    0.6247   -0.6247
         0         0         0   -0.6247   -0.4685         0
         0         0         0    0.6247         0   -0.4685


T(:,:,3) =

    0.1111    0.8889   -0.4444         0         0         0
   -0.8889    0.1111         0         0         0         0
    0.4444         0    0.1111         0         0         0
         0         0         0    0.1111    0.8889   -0.4444
         0         0         0   -0.8889    0.1111         0
         0         0         0    0.4444         0    0.1111


T(:,:,4) =

   -0.7071    0.7071         0         0         0         0
   -0.7071   -0.7071         0         0         0         0
         0         0   -0.7071         0         0         0
         0         0         0   -0.7071    0.7071         0
         0         0         0   -0.7071   -0.7071         0
         0         0         0         0         0   -0.7071


T(:,:,5) =

   -0.1111    0.8889   -0.4444         0         0         0
   -0.8889   -0.1111         0         0         0         0
    0.4444         0   -0.1111         0         0         0
         0         0         0   -0.1111    0.8889   -0.4444
         0         0         0   -0.8889   -0.1111         0
         0         0         0    0.4444         0   -0.1111


T(:,:,6) =

    0.4685    0.6247   -0.6247         0         0         0
   -0.6247    0.4685         0         0         0         0
    0.6247         0    0.4685         0         0         0
         0         0         0    0.4685    0.6247   -0.6247
         0         0         0   -0.6247    0.4685         0
         0         0         0    0.6247         0    0.4685


T(:,:,7) =

         0    0.8944    0.4472         0         0         0
   -0.8944         0         0         0         0         0
   -0.4472         0         0         0         0         0
         0         0         0         0    0.8944    0.4472
         0         0         0   -0.8944         0         0
         0         0         0   -0.4472         0         0


 
 ====PER ELEMENT GLOBAL STIFFNESS MATRIX 
 

Kg(:,:,1) =

  1.0e+004 *

    8.8388    8.8388         0   -8.8388   -8.8388         0
    8.8388    8.8388         0   -8.8388   -8.8388         0
         0         0         0         0         0         0
   -8.8388   -8.8388         0    8.8388    8.8388         0
   -8.8388   -8.8388         0    8.8388    8.8388         0
         0         0         0         0         0         0


Kg(:,:,2) =

  1.0e+004 *

    3.4282   -4.5709    4.5709   -3.4282    4.5709   -4.5709
   -4.5709    6.0946   -6.0946    4.5709   -6.0946    6.0946
    4.5709   -6.0946    6.0946   -4.5709    6.0946   -6.0946
   -3.4282    4.5709   -4.5709    3.4282   -4.5709    4.5709
    4.5709   -6.0946    6.0946   -4.5709    6.0946   -6.0946
   -4.5709    6.0946   -6.0946    4.5709   -6.0946    6.0946


Kg(:,:,3) =

  1.0e+004 *

    0.1372    1.0974   -0.5487   -0.1372   -1.0974    0.5487
    1.0974    8.7791   -4.3896   -1.0974   -8.7791    4.3896
   -0.5487   -4.3896    2.1948    0.5487    4.3896   -2.1948
   -0.1372   -1.0974    0.5487    0.1372    1.0974   -0.5487
   -1.0974   -8.7791    4.3896    1.0974    8.7791   -4.3896
    0.5487    4.3896   -2.1948   -0.5487   -4.3896    2.1948


Kg(:,:,4) =

  1.0e+004 *

    8.8388   -8.8388         0   -8.8388    8.8388         0
   -8.8388    8.8388         0    8.8388   -8.8388         0
         0         0         0         0         0         0
   -8.8388    8.8388         0    8.8388   -8.8388         0
    8.8388   -8.8388         0   -8.8388    8.8388         0
         0         0         0         0         0         0


Kg(:,:,5) =

  1.0e+004 *

    0.1372   -1.0974    0.5487   -0.1372    1.0974   -0.5487
   -1.0974    8.7791   -4.3896    1.0974   -8.7791    4.3896
    0.5487   -4.3896    2.1948   -0.5487    4.3896   -2.1948
   -0.1372    1.0974   -0.5487    0.1372   -1.0974    0.5487
    1.0974   -8.7791    4.3896   -1.0974    8.7791   -4.3896
   -0.5487    4.3896   -2.1948    0.5487   -4.3896    2.1948


Kg(:,:,6) =

  1.0e+004 *

    3.4282    4.5709   -4.5709   -3.4282   -4.5709    4.5709
    4.5709    6.0946   -6.0946   -4.5709   -6.0946    6.0946
   -4.5709   -6.0946    6.0946    4.5709    6.0946   -6.0946
   -3.4282   -4.5709    4.5709    3.4282    4.5709   -4.5709
   -4.5709   -6.0946    6.0946    4.5709    6.0946   -6.0946
    4.5709    6.0946   -6.0946   -4.5709   -6.0946    6.0946


Kg(:,:,7) =

  1.0e+004 *

         0         0         0         0         0         0
         0    8.9443    4.4721         0   -8.9443   -4.4721
         0    4.4721    2.2361         0   -4.4721   -2.2361
         0         0         0         0         0         0
         0   -8.9443   -4.4721         0    8.9443    4.4721
         0   -4.4721   -2.2361         0    4.4721    2.2361


 
 ====SYSTEM STIFFNESS MATRIX 
 

Ksis =

  1.0e+005 *

    1.2267   -0.8839   -0.8839         0         0
   -0.8839    1.7952   -0.0000         0   -0.8839
   -0.8839   -0.0000    4.4180   -0.4307    0.8839
         0         0   -0.4307    0.6626         0
         0   -0.8839    0.8839         0    1.2267


 
 ====SYSTEM STIFFNESS MATRIX 
 

Ksis =

  1.0e+005 *

    1.2267   -0.8839   -0.8839         0         0
   -0.8839    1.7952   -0.0000         0   -0.8839
   -0.8839   -0.0000    4.4180   -0.4307    0.8839
         0         0   -0.4307    0.6626         0
         0   -0.8839    0.8839         0    1.2267


 
 ====PER ELEMENTS NODE GLOBAL DISPLACEMENT===[Du Dv Dw]global (metre)

            u(i)         v(i)          w(i)          u(j)          v(j)         w(j) 
  (1)  [ 0.0000423]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (2)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000423]  [ 0.0000000] [ 0.0000000] 
  (3)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (4)  [-0.0000423]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (5)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (6)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000423]  [ 0.0000000] [ 0.0000000] 
  (7)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 

 
 ====PER ELEMENTS NODE GLOBAL DISPLACEMENT===[Du Dv Dw]global (metre)

            u(i)         v(i)          w(i)          u(j)          v(j)         w(j) 
  (1)  [ 0.0000423]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (2)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000423]  [ 0.0000000] [ 0.0000000] 
  (3)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (4)  [-0.0000423]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (5)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 
  (6)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000423]  [ 0.0000000] [ 0.0000000] 
  (7)  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [ 0.0000000]  [-0.0000544] [-0.0000354] 

 
 ====PER ELEMENTS GLOBAL NODE REACTION===[Fx Fy Fz]global (KN)

            [fx(i)     fy(i)      fz(i)]o-------o[fx(j)     fy(j)     fz(j)] 
  (1)  [ 8.54975]  [ 8.54975]  [ 0.00000]       [-8.54975]  [-8.54975] [ 0.00000] 
  (2)  [-1.45025]  [ 1.93366]  [-1.93366]       [ 1.45025]  [-1.93366] [ 1.93366] 
  (3)  [ 0.40314]  [ 3.22512]  [-1.61256]       [-0.40314]  [-3.22512] [ 1.61256] 
  (4)  [-8.54975]  [ 8.54975]  [ 0.00000]       [ 8.54975]  [-8.54975] [ 0.00000] 
  (5)  [-0.40314]  [ 3.22512]  [-1.61256]       [ 0.40314]  [-3.22512] [ 1.61256] 
  (6)  [ 1.45025]  [ 1.93366]  [-1.93366]       [-1.45025]  [-1.93366] [ 1.93366] 
  (7)  [ 0.00000]  [ 6.45025]  [ 3.22512]       [ 0.00000]  [-6.45025] [-3.22512] 

 
 ====PER ELEMENTS LOCAL NODE REACTION===[Fx Fy Fz]global (KN)

  [ fnormal(i) ]o--->----o[ fnormal(j) ] 
  (1)  [ 12.09118]        [-12.09118]    (Pressure effect) buckling motion
  (2)  [ 3.09537]        [-3.09537]    (Pressure effect) buckling motion
  (3)  [ 3.62826]        [-3.62826]    (Pressure effect) buckling motion
  (4)  [ 12.09118]        [-12.09118]    (Pressure effect) buckling motion
  (5)  [ 3.62826]        [-3.62826]    (Pressure effect) buckling motion
  (6)  [ 3.09537]        [-3.09537]    (Pressure effect) buckling motion
  (7)  [ 7.21159]        [-7.21159]    (Pressure effect) buckling motion

 
 ====SYSTEM ALL NODE and SUPPORT REACTIONS===[Fx Fy Fz]global (KN)

      fx(g)     fy(g)      fz(g) 
  [-1.04711]  [ 5.15878]  [-3.54622]       
  [ 1.04711]  [ 5.15878]  [-3.54622]       
  [ 0.00000]  [ 6.45025]  [ 3.22512]       
  [ 10.00000]  [ 6.61609]  [ 1.93366]       
  [ 0.00000]  [-30.00000]  [ 0.00000]       
  [-10.00000]  [ 6.61609]  [ 1.93366]


Published with MATLAB® 7.1

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