137 lines
3.8 KiB
Matlab
137 lines
3.8 KiB
Matlab
clc,clear,close all
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tic
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nodeCoord=[0 0;0 3;0 6 ;0 9; 5 0;5 3;5 6;5 9];
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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=0.08;E=3e10;I=0.0128/12; % 定义截面面积和弹性模量
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rho=3000;
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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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ele=[1 1 2 A E I;2 2 3 A E I; 3 3 4 A E I;4 5 6 A E I; 5 6 7 A E I;6 7 8 A E I;7 2 6 A E I;8 3 7 A E I;9 4 8 A E I];;
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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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Load=[4 2e5 0 0];
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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 0 0 0;5 0 0 0];
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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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M=zeros(Dofs,Dofs); %总体质量矩阵
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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) %绘制框架
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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= FrameElementKe(ele(iEle,4),ele(iEle,5),ele(iEle,6),R,BarLength(iEle));
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me= FrameElementMe(A,rho,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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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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M(eleDof,eleDof)=M(eleDof,eleDof)+me;
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end
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for i=1:length(Constr(:,1))
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restrainedDof(1+(i-1)*3:3+(i-1)*3)=(Constr(i,1)-1)*3+[1:3];
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end
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activeDof=setdiff([1:Dofs]',restrainedDof);
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if det(M(activeDof,activeDof))>0
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A=M(activeDof,activeDof)\K(activeDof,activeDof);
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[Vo,Do]=eig(A);
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fo=diag(sqrt(Do)/(2*pi));
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Vf=sortrows([Vo',fo],size(Vo,1)+1);
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V=Vf(:,1:size(Vo,1))';%sort eignvectgors
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elseif det(K(activeDof,activeDof))>0
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A=K(activeDof,activeDof)\M(activeDof,activeDof);
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[Vo,Do]=eig(A);
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fo=power(diag(sqrt(Do)),-1)/(2*pi);
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Vf=sortrows([Vo',fo],size(Vo,1)+1);
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V=Vf(:,1:size(Vo,1))';%sort eignvectgors
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end
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f=sort(fo);%自振频率
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figure
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for i=1:5
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subplot(1,5,i)
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ModeNum=i;%第五阶模态
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U=zeros(Dofs,1);
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U(activeDof)=V(:,ModeNum)';
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RenderFrame(ele,Load,Constr,x,y,U,1,'-.b',200) %绘制模态振型
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axis off
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end
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%自振角频率
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w1=2*pi*f(1);
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w2=2*pi*f(2);
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w3=2*pi*f(3);
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w4=2*pi*f(4);
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w5=2*pi*f(5);
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epsilon=0.05;%阻尼比
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a00=(2*epsilon*w1*w3)/(w1+w3);%假定控制频率为w1 w3
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a11=(2*epsilon)/(w1+w3);
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C=a00*M+a11*K; %形成阻尼矩阵
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%读取加速度时程
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[t,acc_x]=textread('x_acceleration.txt','%f,%f,');
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dt=t(2)-t(1);
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n=length(t);
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vel_x = zeros(length(t),1);
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dis_x = zeros(length(t),1);
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for i = 2:length(t)
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vel_x(i) = trapz(acc_x(1:i),t(1:i));
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end
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for i = 2:length(t)
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dis_x(i) = trapz(vel_x(1:i),t(1:i));
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end
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figure
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subplot(3,1,1)
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plot(t,acc_x)
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subplot(3,1,2)
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plot(t,vel_x)
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subplot(3,1,3)
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plot(t,dis_x)
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title('地震波')
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mm=M(activeDof,activeDof);
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kk=K(activeDof,activeDof);
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cc=C(activeDof,activeDof);
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% plot(tt,vw);
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% %%%%%%%%%%%%%%%%
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beta=0.25;
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gamma=0.5;
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%注意newmark-beta法代入的三大类矩阵，可以是划行划列后的，也可以是结构整体矩阵，但后者需要在NewmarkBeta1中施加约束
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[uu,vv,aa,ttt]=NewmarkBeta1(t,dt,gamma,beta,mm,cc,kk,acc_x,Constr);%相对位移速度加速度
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uuu=zeros(size(M,1),length(t));%位移
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vvv=zeros(size(M,1),length(t));%位移
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aaa=zeros(size(M,1),length(t));%位移
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uuu(activeDof,:)=uu;
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vvv(activeDof,:)=vv;
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aaa(activeDof,:)=aa;
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for i=1:size(uuu,1)
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base_disp(i,:)=dis_x;
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end
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% uuu_t=uuu+base_disp;
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figure%绘制顶部节点的位移速度和加速度
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toc %disp(['运行时间: ',num2str(toc)])
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subplot(3,1,1);
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plot(ttt,uu(end-2,:));
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subplot(3,1,2);
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plot(ttt,vv(end-2,:));
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subplot(3,1,3);
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plot(ttt,aa(end-2,:));
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figure%绘制最后时刻框架变形
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RenderFrame(ele,Load,Constr,x,y,uuu(:,end),1,'-.b',200) %
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speed=1;%动画播放速度的
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delaytime=0;
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RenderFrameMotion(ele,Load,Constr,x,y,uuu,1,'-.b',delaytime,speed) %
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