148 lines
4.3 KiB
Matlab
148 lines
4.3 KiB
Matlab
clc,clear,close all
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global m b D
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height=20;%桩总高
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deep=9;%挖土深度
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width=2;%桩间距
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D=0.8;%直径
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E1=3e10;%桩弹性模量
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E2=3e10;%连梁弹性模量
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b=0.8;%连梁高
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h=0.6;%连梁宽
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m=4e6;%弹簧反力系数
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%%%%%%%%计算q1 q2%%%%%%%%%%%%
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phi=25;%内摩擦角
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q=10;%q为超载
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y=19.2;%土重度
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c=12;%土体粘聚力
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ka=tand(45-phi/2)^2;
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sigma_a=(q+y*deep)*ka-2*c*sqrt(ka);
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L0=deep*tand(45-phi/2);
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beta=2*width/L0-(width/L0)^2;
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Pa1=beta*sigma_a;%KPa
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Pa2=(1-beta)*sigma_a;%KPa
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p1=-Pa1*1e3;%Pa
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p2=-Pa2*1e3;%Pa
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%define nodes
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for i=1:height+1
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nodeCoord(i,:)=[0,i-1];%1m一个单元
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end
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nodeCoord(height+2,:)=[width,height];
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for i=1:height
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nodeCoord(height+2+i,:)=[width,height-i];%1m一个单元
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end
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node_num=length(nodeCoord(:,1));
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x=nodeCoord(:,1)'; % 节点x轴方向坐标
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y=nodeCoord(:,2)'; % 节点y轴方向坐标
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A(1:height)=pi*D^2/4;
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A(height+1)=b*h;
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A(height+2:2*height+1)=pi*D^2/4;
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I(1:height)=pi*D^4/36;
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I(height+1)=b*h^3/12;
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I(height+2:2*height+1)=pi*D^4/36;
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E(1:height)=E1;
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E(height+1)=E2;
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E(height+2:2*height+1)=E1;
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%单元信息：编号，节点1编号，节点2编号，截面面积，弹性模量
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%define ele
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for i=1:node_num-1
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ele(i,:)=[i,i,i+1,A(i),E(i),I(i)];
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end
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q1=D*p1;%桩1的线荷载
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q2=D*p2;%桩2的线荷载
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%载荷信息：节点编号，x方向力，y方向力，z方向力
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for i=1:node_num
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if y(i)<=deep && x(i)==min(x)
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Load(i,:)=[i q1 0 0];
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elseif y(i)>deep && x(i)==min(x)
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Load(i,:)=[i q1/(height-deep)*(height-y(i)) 0 0];
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elseif y(i)<=deep && x(i)==max(x)
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Load(i,:)=[i q2 0 0];
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elseif y(i)>deep && x(i)==max(x)
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Load(i,:)=[i q2/(height-deep)*(height-y(i)) 0 0];
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end
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end
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%约束：节点编号，x方向约束，y方向约束，z方向约束
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Constr=[1 NaN 0 NaN;node_num NaN 0 NaN];
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Dofs=3*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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RenderFrame(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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RenderFrame(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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if y(n1)<=deep
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ke= FrameElementKe2(ele(iEle,4),ele(iEle,5),ele(iEle,6),R,BarLength(iEle));
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else
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ke= FrameElementKe1(ele(iEle,4),ele(iEle,5),ele(iEle,6),R,BarLength(iEle));
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end
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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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eleDof=[n1*3-2:n1*3,n2*3-2:n2*3];
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K(eleDof,eleDof)=K(eleDof,eleDof)+ke;
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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=1:3
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F(3*Load(LoadNum)+i-3,1)=Load(LoadNum,i+1);
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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=2:4
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if ~isnan(Constr(iConstr,j))
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K(3*Constr(iConstr,1 )+j-4,3*Constr(iConstr,1 )+j-4)=...
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1e12*K(3*Constr(iConstr,1 )+j-4,3*Constr(iConstr,1 )+j-4);
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F(3*Constr(iConstr,1)+j-4)=1e12*Constr(iConstr,j)*...
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K(3*Constr(iConstr,1 )+j-4,3*Constr(iConstr,1)+j-4);
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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(3*n1-2:3*n1,1);U(3*n2-2:3*n2,1)];
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if y(n1)<=deep
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[Ke_local] = FrameElementKeLocal1(ele(iEle,4),ele(iEle,5),ele(iEle,6),R,BarLength(iEle));
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else
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[Ke_local] = FrameElementKeLocal2(ele(iEle,4),ele(iEle,5),ele(iEle,6),R,BarLength(iEle));
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end
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EleForce(:, iEle)=Ke_local*localU; %轴力
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end
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MomentForce=EleForce([3,6],:);
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figure
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MomentForcePlot1=[-MomentForce(1,1:20)];
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plot(MomentForcePlot1,[-19:0])
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hold on;
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MomentForcePlot2=[MomentForce(2,22:41)];
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plot(-MomentForcePlot2,[0:-1:-19])
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legend('前','后')
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title('Moment');
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figure
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for i=1:node_num
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Ux(i)=U((i-1)*3+1);
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end
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plot(Ux(1:21),[-20:0])
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hold on;
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plot(Ux(22:42),[0:-1:-20])
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title('Displacement');
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legend('前','后')
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figure
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MomentForce(1,:)=-MomentForce(1,:);
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ForcePlot(ele,Load,Constr,x,y,U,3,'-b',MomentForce)%绘制轴力图
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title('弯矩图'); |