72 lines
2.7 KiB
Matlab
72 lines
2.7 KiB
Matlab
%**************************************************************************
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function [U, Strain, Stress, AxialForce]=PlaneTrussFEA(x,y,ele,Load,Constr,Scale)
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Dofs=2*size(x,2); %总自由度数
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EleCount=size(ele,1); %单元总数
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K=zeros(Dofs,Dofs); %总体刚度矩阵
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F=zeros(Dofs,1); %总体载荷列阵
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U=zeros(Dofs,1); %总体位移列阵
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BarLength=BarsLength(x,y,ele);
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figure('Name','Undeformed Truss')
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RenderTruss(ele,Load,Constr,x,y,U,1,'-k',1) %绘制桁架
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figure('Name','Deformed Truss')
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RenderTruss(ele,Load,Constr,x,y,U,0.5,'-k',1) %绘制变形后桁架
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hold on
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%遍历所有单元，将各单元刚度阵分块组装到总体刚度阵
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for iEle =1:EleCount
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%该单元的两个节点的编号
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n1=ele(iEle,2);n2=ele(iEle,3);
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%计算坐标变换矩阵
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R=CoordTransform([x(n1) x(n2)],[y(n1) y(n2)],BarLength(iEle));
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%计算单元刚度矩阵 Ke=R'*ke*R;局部坐标系下的单元刚度阵转换为全局坐标下的单元刚度阵
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ke= BarElementKe(ele(iEle,4),ele(iEle,5),R,BarLength(iEle));
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%将各单元刚度分块组装到总刚相应位置
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K(2*n1-1:2*n1,2*n1-1:2*n1)=K(2*n1-1:2*n1,2*n1-1:2*n1)+ke(1:2,1:2);
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K(2*n1-1:2*n1,2*n2-1:2*n2)=K(2*n1-1:2*n1,2*n2-1:2*n2)+ke(1:2,3:4);
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K(2*n2-1:2*n2,2*n1-1:2*n1)=K(2*n2-1:2*n2,2*n1-1:2*n1)+ke(3:4,1:2);
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K(2*n2-1:2*n2,2*n2-1:2*n2)=K(2*n2-1:2*n2,2*n2-1:2*n2)+ke(3:4,3:4);
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end
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%形成载荷列阵--1、2、3、4自由度赋载荷值
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for LoadNum=1:size(Load,1)
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for i=2:3
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F(2*Load(LoadNum)+i-3,1)=Load(LoadNum,i);
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end
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end
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%施加约束--乘大数法
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for iConstr=1:size(Constr,1)
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for j=2:3
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if ~isnan(Constr(iConstr,j))
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K(2*Constr(iConstr,1 )+j-3,2*Constr(iConstr,1 )+j-3)=...
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1e12*K(2*Constr(iConstr,1 )+j-3,2*Constr(iConstr,1 )+j-3);
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F(2*Constr(iConstr,1)+j-3)=1e12*Constr(iConstr,j)*...
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K(2*Constr(iConstr,1 )+j-3,2*Constr(iConstr,1)+j-3);
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end
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end
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end
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U=K\F; %全局坐标系下位移,此处原来为逆但是矩阵奇异，故改成伪逆
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for iEle =1:EleCount
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%计算杆局部坐标下的位移
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n1=ele(iEle,2);n2=ele(iEle,3);
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R=CoordTransform([x(n1) x(n2)],[y(n1) y(n2)],BarLength(iEle));
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localU = R*[U(2*n1-1:2*n1,1);U(2*n2-1:2*n2,1)];
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Strain(1, iEle)=[-1/BarLength(iEle) 1/BarLength(iEle)]*localU; %应变
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Stress(1, iEle)=ele(iEle,5)* Strain(1, iEle); %应力
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AxialForce(1, iEle)=ele(iEle,4)* Stress(1, iEle); %轴力
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end
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%保存位移，应力与轴力到文本文件
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fp=fopen('Result.txt','a');
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str = [char(13,10)','U',' ',num2str(U'),char(13,10)','Stress',' ',...
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num2str(Stress),char(13,10)','AxialForce',' ',num2str(AxialForce)];
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fprintf(fp,str);
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fclose(fp);
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RenderTruss(ele,Load,Constr,x,y,U,1,'-.b',Scale) %绘制变形后桁架
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figure
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AxisForcePlot(ele,Load,Constr,x,y,U,3,'-b',Scale,AxialForce)%绘制轴力图
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end %主程序结束
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