FEM-Course-Matlab/10.四节点八节点四边形单元悬臂梁的Matlab有限元编程/4_nodes/main_node4.m

clear all;clc;close all;
%<EFBFBD><EFBFBD>׼<EFBFBD><EFBFBD><EFBFBD>ʵ<EFBFBD>λ<EFBFBD><EFBFBD>
Length=2;%2m
min_H=0.2;max_H=0.6;%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>߶<EFBFBD>
Width=1;%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
E=3e10;%Pa 3e4MPa
u=0.2;%  <EFBFBD><EFBFBD><EFBFBD>ɱ<EFBFBD>
q0=1000;%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>1kN/m
F_jizhong=2e3;%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>2/kN

%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD><EFBFBD>͵<EFBFBD>Ԫ
Ne_x=16;%<EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>4 
Ne_y=8;%<EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>2
D=[E/(1-u^2),u*E/(1-u^2),0;
       u*E/(1-u^2),E/(1-u^2),0;
       0,0,E/(2*(1+u))];
       

Ne=Ne_x*Ne_y;          % <EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
Nnod=(Ne_x+1)*(Ne_y+1);;    % <EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
%<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
x=linspace(-1,1,Ne_x+1); %<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ҵĺ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
rt=[repmat(Ne_y+1,1,Ne_x+1)]; % ÿ<EFBFBD>нڵ<EFBFBD><EFBFBD><EFBFBD> 5 3 5 3 5 3  <EFBFBD><EFBFBD><EFBFBD><EFBFBD>
x=repelem(x,rt);       % x<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>չΪ<EFBFBD><EFBFBD><EFBFBD>нڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
y=[];
dy=(max_H-min_H)/Ne_x/4;
for i=1:Ne_x
    y=[y,linspace(-max_H/2+(i-1)*2*dy,max_H/2-(i-1)*2*dy,Ne_y+1)];
end
y=[y,linspace(-min_H/2,min_H/2,Ne_y+1)];
Nodes=[x;y]';

% <EFBFBD><EFBFBD>Ԫ<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
num=0;
for i=1:Ne_x
    for j=1:Ne_y
        num=num+1;
        Elements(num,:)=[(i-1)*(Ne_y+1)+j,(i-1)*(Ne_y+1)+j+1,i*(Ne_y+1)+j+1,i*(Ne_y+1)+j];
    end
end
%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֲ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
E_ID_p1 = Ne_y:Ne_y:Ne_x*Ne_y;      % <EFBFBD>ֲ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>õ<EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>

N_ID_p1 = zeros(size(E_ID_p1,2),size(Elements,2));%<EFBFBD>ֲ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD>Ԫ<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
j = 1; 
for i_q = E_ID_p1
 N_ID_p1(j,:) = Elements(i_q,:);              %<EFBFBD>ֲ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD>Ԫ<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
 j = j+1;
end

%ʩ<EFBFBD>Ӽ<EFBFBD><EFBFBD>к<EFBFBD><EFBFBD>صĽڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
E_ID_p2 = max(Ne_y:Ne_y:Ne);            % <EFBFBD><EFBFBD><EFBFBD>к<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>õ<EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>***
Nod_1=Elements(E_ID_p2,4);                % <EFBFBD><EFBFBD><EFBFBD>к<EFBFBD><EFBFBD>ؽڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>***

%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>нڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Elt_p3=max(Ne_y:Ne_y:Ne/2);            % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>е<EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Nod_mid=Elements(Elt_p3,3) ;               % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>нڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>

%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>˽ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Elt_p4=Ne_y           ;              % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>˵<EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Nod_left=Elements(Elt_p4,2)    ;            % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>˽ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>

%<EFBFBD>߽<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>type = 1 -- fixed disp [ 1--<EFBFBD>ڵ<EFBFBD><EFBFBD>̶<EFBFBD>; 0--<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> ]; 
%          type = 2 -- point load 
% node, x, y, z, rx, ry, rz, type 

Boundary =  [1 1.0 1.0 0.0 0.0 0.0 0.0 1; 
Nod_left 1.0 1.0 0.0 0.0 0.0 0.0 1; 
Nod_1 0.0 F_jizhong 0.0 0.0 0.0 0.0 2 ];

% <EFBFBD><EFBFBD>ʼ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>洢<EFBFBD>ռ<EFBFBD>
K = zeros( 2 * Nnod , 2 * Nnod );
F = zeros( 2 * Nnod , 1 );

for i=1:Ne
    ke=ele_stiff_matrix(i,Nodes,Elements,E,u,Width);
    ENodes( : , 1 ) = Elements( i , : ); 
    %<EFBFBD><EFBFBD>װΪ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ն<EFBFBD><EFBFBD><EFBFBD>
    iEnum = size( ENodes , 1 );      % <EFBFBD><EFBFBD>Ԫ<EFBFBD>Ľ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
    iDOFnum = 2 * iEnum;              % <EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɶ<EFBFBD><EFBFBD><EFBFBD> 
    iDof = zeros( 2 * iEnum , 1 );   % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɶȱ<EFBFBD><EFBFBD><EFBFBD> 

    for il=1:iEnum 
      inod = ENodes( il ); 
      iDof( 2 * il-1 : 2 * il) = 2 * inod-1 : 2 * inod; 
    end
    % ƴװ<EFBFBD><EFBFBD>irΪ<EFBFBD>оֲ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, irgΪ<EFBFBD><EFBFBD>Ӧ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
    for ir = 1 : iDOFnum 
      irg = iDof( ir ); 
      % icΪ<EFBFBD>оֲ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, icgΪ<EFBFBD><EFBFBD>Ӧ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
      for ic = 1 : iDOFnum 
        icg = iDof( ic ); 
        K( irg , icg ) = K( irg , icg ) + ke( ir , ic ); 
      end 
    end
end
%ʩ<EFBFBD>Ӻ<EFBFBD><EFBFBD>ر߽<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
iLenElt = size(N_ID_p1,1);          %<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
for ie = 1:iLenElt
  for ind = 1:2                   % ind<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɶȱ<EFBFBD><EFBFBD><EFBFBD>
    iNode = N_ID_p1(ie,:);           %<EFBFBD><EFBFBD>ȡ<EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
    irow = (iNode-1)*2+ind;
    Pe = UniLoad(ie,N_ID_p1,q0,Nodes,Elements,Width);    % 3<EFBFBD><EFBFBD><EFBFBD>ӳ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>EquivalentLoad(ie)
    F(irow) = F(irow)+Pe(ind:2:end,:);
  end
end

% <EFBFBD><EFBFBD><EFBFBD>к<EFBFBD><EFBFBD><EFBFBD>
iBct = size( Boundary , 1 ); 
for ib = 1 : iBct 
  iNode = Boundary( ib , 1 ); 
  iType = Boundary( ib , 8 ); 
  if iType == 2                       % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ر߽<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
    for ind = 1 : 2                   
      irow = ( iNode-1 ) * 2 + ind; 
      F( irow ) = F( irow ) + Boundary( ib , ind + 1 ); 
    end 
  end 
end 
%ʩ<EFBFBD><EFBFBD>֧<EFBFBD><EFBFBD><EFBFBD>߽<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
for ib = 1 : iBct
    iNode = Boundary( ib , 1 );       % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
    iType = Boundary( ib , 8 );
    if iType == 1             % <EFBFBD>̶<EFBFBD><EFBFBD><EFBFBD><EFBFBD>߽<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
        for ind = 1 : 2
            irow = ( iNode-1 ) * 2 + ind;
            if ( Boundary( ib , ind + 1 ) == 1 )
                K( irow , : ) = 0.0;
                K( : , irow ) = 0.0;
                K( irow , irow ) = 1.0;       % <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><EFBFBD>
                F(irow)=0.0;
                %         gKA( irow , irow ) = 1.0e+20;  % <EFBFBD>˴<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
            end
        end
    end
end
Disp = K \ F;
% <EFBFBD>洢<EFBFBD><EFBFBD><EFBFBD><EFBFBD>λ<EFBFBD><EFBFBD>
gNTu = zeros( Nnod , 2 );
for id = 1 : Nnod
    gNTu( id , 1 : 2 ) = Disp( 2 * id - 1 : 2 * id );
end
% <EFBFBD><EFBFBD><EFBFBD>Ʊ<EFBFBD><EFBFBD><EFBFBD>ͼ
SF=1000;
PlotResults2(Nodes,Elements,gNTu,SF);
fprintf('<EFBFBD><EFBFBD><EFBFBD>ɶ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӷ<EFBFBD>%fmm\n',max(abs(gNTu(Nnod,2)))*1000);
ElementNodeCount=4;
[NodeStrain,NodeStress]=CalculateStrainAndStress2(Disp,D,Nodes,Elements);
 PlotContour(Nodes,Elements,Disp,NodeStress(1,:))