113 lines
3.0 KiB
Matlab
113 lines
3.0 KiB
Matlab
clear;clc;;close all
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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)*10^11;%乘大数法的大数
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long=5;%长5m
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height=1;%高1m
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ele_size=[0.2,0.2];%单元的两个直角边尺寸；5m长，十个单元,1m高，4个单元
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ele_H=long/ele_size(1);%水平单元数
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ele_V=height/ele_size(2);%竖向单元数
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ele_num=ele_H*ele_V*2;%单元数
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node_num=(ele_H+1)*(ele_V+1);%节点数
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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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num=0;
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for i=1:ele_H
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for j=1:ele_V
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num=num+1;
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element(num,1)=1+(j-1)+(i-1)*(ele_V+1);
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element(num,2)=1+(j-1)+i*(ele_V+1);
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element(num,3)=2+(j-1)+(i-1)*(ele_V+1);
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num=num+1;
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element(num,1)=1+j+(i-1)*(ele_V+1);
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element(num,2)=1+(j-1)+i*(ele_V+1);
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element(num,3)=2+(j-1)+i*(ele_V+1);;
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end
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end
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%定义节点坐标
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num=0;
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for i=1:ele_H+1
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for j=1:ele_V+1
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num=num+1;
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node(num,1)=(i-1)*ele_size(1);%x
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node(num,2)=(j-1)*ele_size(2);%y
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end
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end
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A=1/2*ele_size(1)*ele_size(2);%单元面积5/10*1/4矩形
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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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P=[]; P(2*(ele_V+1))=-1/2*q*t*long/ele_H;
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for i=1:ele_H
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P(10+2*(ele_V+1)*(i-1))=-q*t*long/ele_H;%5/10是每个单元的长度
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end
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P(node_num*2)=-1/2*q*t*5/10;
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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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cons_DOF=[1:(ele_V+1)*2];%约束自由度编号
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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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a=inv(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')
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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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% 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') |