134 lines
3.6 KiB
Matlab
134 lines
3.6 KiB
Matlab
clear;clc;;close all
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tic
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format short
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E=210e9;%弹性模量，单位Pa
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u=0.4;%泊松比，无量纲
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q=100;%外载荷（面力），单位N/㎡
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t=0.1;%厚度，单位m
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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))];%应力应变矩阵
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bt=(3+0.5407762)*10^51;%乘大数法的大数
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DOF=2;%每个节点自由度
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%定义每个单元的节点号
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fname='M1.mphtxt';
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[node, element] = Readmesh( fname );
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%定义每个单元的节点号
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for i=1:length(element(:,1))
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x1=node(element(i,1),1);
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x2=node(element(i,2),1);
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x3=node(element(i,3),1);
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y1=node(element(i,1),2);
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y2=node(element(i,2),2);
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y3=node(element(i,3),2);
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A(i)=(x1*y2+x2*y3+x3*y1-x1*y3-x2*y1-x3*y2);%单元面积S=(x1y2-x1y3+x2y3-x2y1+x3y1-x2y2)
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end
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ele_num=length(element(:,1));%单元数
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node_num=length(node(:,1));%节点数
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%每个单元自由度在整体矩阵中的索引位置
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ele_DOF=zeros(ele_num,DOF*3);
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for i=1:ele_num
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for j=1:length(element(i,:))%三角形三个节点循环
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ele_DOF(i,1+2*(j-1):2+2*(j-1))=2*(element(i,j)-1)+1:2*(element(i,j)-1)+2;
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end
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end
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KZ=zeros(node_num*2,node_num*2);
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for i=1:ele_num
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ke=ele_stiff_matrix(element,node,i,A,D,t);%单元刚度矩阵
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KZ(ele_DOF(i,:),ele_DOF(i,:)) = KZ(ele_DOF(i,:),ele_DOF(i,:))+ke;
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end
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%find constrained side and force side
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num=0;
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num2=0;
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num3=0;
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for i=1:node_num
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min_x=min(node(:,1));
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max_x=max(node(:,1));
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min_y=min(node(:,2));
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if node(i,1)==min_x
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num=num+1;
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const_side_y(num)=i;%左边界
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elseif node(i,1)==max_x
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num2=num2+1;
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force_side(num2)=i;%右边界
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elseif node(i,2)==min_y
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num3=num3+1;
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const_side_x(num3)=i;%下边界
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end
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end
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P=zeros(1,node_num*2);
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for i=1:length(force_side)
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P(force_side(i)*2-1)=q;%5/10是每个单元的长度
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end
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PZ=P';%总结点载荷列阵
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%乘大数法施加约束条件，最左侧节点全部固定
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for i=1:length(const_side_y)
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cons_DOF_y(i)=[const_side_y(i)*2-1];%左边界对称边界条件
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end
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for i=1:length(const_side_x)
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cons_DOF_x(i)=[const_side_x(i)*2];%下边界对称边界条件
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end
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cons_DOF=[cons_DOF_y,cons_DOF_x];
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Disp=zeros(length(cons_DOF),1);%位移为0
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for i=1:length(cons_DOF)
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KZ(cons_DOF(i),cons_DOF(i))=bt*KZ(cons_DOF(i),cons_DOF(i));
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PZ(cons_DOF(i))=Disp(i)*KZ(cons_DOF(i),cons_DOF(i));
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end
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KZ_xishu=sparse(KZ);%为了加快计算速度，采用稀疏矩阵进行计算
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% a=KZ_xishu\PZ;%结点位移列阵
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a=KZ\PZ;%结点位移列阵
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for i=1:ele_num%80个单元
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sgm(:,i)=stress_calculate(element,node,i,A,D,t,a);%单元应力
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end
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%重新排列位移矩阵
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SF=1/5*1/max(abs(a));%位移放大系数
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new_node=node+SF*reshape(a,2,length(a)/2)';%计算变形后的坐标
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figure
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patch('Faces',element,'Vertices',node,'FaceColor','none','EdgeColor','r')
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hold on;
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patch('Faces',element,'Vertices',new_node,'FaceColor','none')
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xlabel('x-coordinate')
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ylabel('y-coordinate')
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title('deformation')
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axis equal
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%应力
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figure
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patch('Faces',element,'Vertices',node,'FaceVertexCData',sgm(1,:)','FaceColor','flat','EdgeColor','none')
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axis equal
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xlabel('x-coordinate')
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ylabel('\sigma (Pa)')
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title('\sigma_{11}')
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colorbar
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colormap(jet)
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%验证圆孔出1：3的mises应力比
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node_ID1=10818; %(0.1,0)
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node_ID2=12373;%(0,0.1)
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ele1=find(element(:,2)==node_ID1);
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ele2=find(element(:,2)==node_ID2);
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mises1=sqrt((sgm(1,ele1)+sgm(2,ele1))^2-3*(sgm(1,ele1)*sgm(2,ele1)-sgm(3,ele1)^2));
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mises2=sqrt((sgm(1,ele2)+sgm(2,ele2))^2-3*(sgm(1,ele2)*sgm(2,ele2)-sgm(3,ele2)^2));
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ratio=mises2/mises1
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toc
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% figure
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% patch('Faces',element,'Vertices',node,'FaceVertexCData',sgm(2,:)','FaceColor','flat')
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% axis equal
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% colorbar
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% colormap(jet)
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% title('sigma22')
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% figure
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% patch('Faces',element,'Vertices',node,'FaceVertexCData',sgm(3,:)','FaceColor','flat')
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% xlabel('x-coordinate')
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% ylabel('\sigma (Pa)')
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% axis equal
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% colorbar
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% colormap(jet)
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% title('sigma12') |