78 lines
1.8 KiB
Matlab
78 lines
1.8 KiB
Matlab
clear all;close all;clc;
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%SI:m,kN,kPa
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h=0.007;b=0.3;
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E=3e7;A=b*h;I=b*h^3/12;v=0.2;
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G=E*0.5/(1+v);
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EI=E*I;
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GA=G*A;
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L=5;%杆件长度
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Ele_L=0.01;%单元尺寸
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ele_num=L/Ele_L;%单元个数
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q=1;%1kN/m
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W=q*L^4/(8*EI)%材料力学挠度计算公式
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linetype={'-','--','-.'}
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figure;
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hold on;
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for way=1:3
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for i=1:ele_num
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if way==1
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ke(:,:,i)=BeamElementStiffness(EI,Ele_L);%欧拉梁单元
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elseif way==2
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ke(:,:,i)=TimoshenkoStiffness(EI,GA,Ele_L);%完全积分铁木辛柯梁单元（剪切自锁现象）
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elseif way==3
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ke(:,:,i)=TimoshenkoReduceStiffness(EI,GA,Ele_L);%减缩积分铁木辛柯梁单元
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end
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end
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K=zeros((ele_num+1)*2);
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for i=1:ele_num
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K=BeamAssemble(K,ke(:,:,i),i,i+1); %全局刚度矩阵
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end
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k=[K(3:(ele_num+1)*2,3:(ele_num+1)*2)]; %***去除约束对应的刚度矩阵
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f=zeros(2*(ele_num),1); %节点力f
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for i=1:ele_num
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f(2*(i-1)+1)=q*Ele_L;%****分布力大小为1*单元长度就是每个单元节点上的节点力，均布荷载转节点力
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end
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u=k\f;
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U=zeros((ele_num+1)*2,1);%节点位移
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U(3:(ele_num+1)*2)=u;%
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for i=1:ele_num
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Fe(i,:)=ke(:,:,i)*U((i-1)*2+1:(i-1)*2+4); %单元力=单元刚度矩阵*节点位移
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end
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% F=K*U; %全局刚度矩阵*节点位移=节点力
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x = [0 : Ele_L:L]';
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% figure;
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% M=Fe(:,2);
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% M(ele_num+1)=-Fe(end,4);
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% hold on;
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% title('Bending Moment Diagram');
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% plot(x,M);
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% y1 = zeros(1,ele_num+1);
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% plot(x,y1,'k')
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% xlabel('length')
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% ylabel('Moment')
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% title('moment diagram with constant thickness');
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title('Displacment Diagram');
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for i=1:length(x)
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disp_plot_constant(i)=U(2*(i-1)+1);
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end
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aa=plot(x,disp_plot_constant,linetype{way},'linewidth',2);
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aa.Color(4)=0.5
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% figure;
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% hold on;
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% title('Rotation Diagram');
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% for i=1:length(x)
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% rot_plot_constant(i)=U(2*(i));
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% end
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% plot(x,rot_plot_constant);
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% save data disp_plot_constant
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end
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legend('欧拉梁','铁木辛柯梁-完全积分','铁木辛柯梁-减缩积分'); |