78 lines
1.8 KiB
Mathematica
78 lines
1.8 KiB
Mathematica
|
clear all;close all;clc;
|
|||
|
|
%SI:m,kN,kPa
|
|||
|
|
h=0.007;b=0.3;
|
|||
|
|
E=3e7;A=b*h;I=b*h^3/12;v=0.2;
|
|||
|
|
G=E*0.5/(1+v);
|
|||
|
|
EI=E*I;
|
|||
|
|
GA=G*A;
|
|||
|
|
L=5;%<EFBFBD>˼<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
|||
|
|
Ele_L=0.01;%<EFBFBD><EFBFBD>Ԫ<EFBFBD>ߴ<EFBFBD>
|
|||
|
|
ele_num=L/Ele_L;%<EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
|||
|
|
q=1;%1kN/m
|
|||
|
|
W=q*L^4/(8*EI)%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ѧ<EFBFBD>Ӷȼ<EFBFBD><EFBFBD>㹫ʽ
|
|||
|
|
linetype={'-','--','-.'}
|
|||
|
|
figure;
|
|||
|
|
hold on;
|
|||
|
|
for way=1:3
|
|||
|
|
for i=1:ele_num
|
|||
|
|
if way==1
|
|||
|
|
ke(:,:,i)=BeamElementStiffness(EI,Ele_L);%ŷ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ
|
|||
|
|
elseif way==2
|
|||
|
|
ke(:,:,i)=TimoshenkoStiffness(EI,GA,Ele_L);%<EFBFBD><EFBFBD>ȫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ľ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
|
|||
|
|
elseif way==3
|
|||
|
|
ke(:,:,i)=TimoshenkoReduceStiffness(EI,GA,Ele_L);%<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ľ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ
|
|||
|
|
|
|||
|
|
end
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
K=zeros((ele_num+1)*2);
|
|||
|
|
for i=1:ele_num
|
|||
|
|
K=BeamAssemble(K,ke(:,:,i),i,i+1); %ȫ<EFBFBD>ָնȾ<EFBFBD><EFBFBD><EFBFBD>
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
k=[K(3:(ele_num+1)*2,3:(ele_num+1)*2)]; %***ȥ<EFBFBD><EFBFBD>Լ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ӧ<EFBFBD>ĸնȾ<EFBFBD><EFBFBD><EFBFBD>
|
|||
|
|
|
|||
|
|
f=zeros(2*(ele_num),1); %<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD>f
|
|||
|
|
|
|||
|
|
for i=1:ele_num
|
|||
|
|
f(2*(i-1)+1)=q*Ele_L;%****<EFBFBD>ֲ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>СΪ1*<EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD><EFBFBD>Ⱦ<EFBFBD><EFBFBD><EFBFBD>ÿ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ԫ<EFBFBD>ڵ<EFBFBD><EFBFBD>ϵĽڵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ת<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD>
|
|||
|
|
end
|
|||
|
|
|
|||
|
|
|
|||
|
|
u=k\f;
|
|||
|
|
U=zeros((ele_num+1)*2,1);%<EFBFBD>ڵ<EFBFBD>λ<EFBFBD><EFBFBD>
|
|||
|
|
U(3:(ele_num+1)*2)=u;%
|
|||
|
|
for i=1:ele_num
|
|||
|
|
Fe(i,:)=ke(:,:,i)*U((i-1)*2+1:(i-1)*2+4); %<EFBFBD><EFBFBD>Ԫ<EFBFBD><EFBFBD>=<EFBFBD><EFBFBD>Ԫ<EFBFBD>նȾ<EFBFBD><EFBFBD><EFBFBD>*<EFBFBD>ڵ<EFBFBD>λ<EFBFBD><EFBFBD>
|
|||
|
|
end
|
|||
|
|
% F=K*U; %ȫ<EFBFBD>ָնȾ<EFBFBD><EFBFBD><EFBFBD>*<EFBFBD>ڵ<EFBFBD>λ<EFBFBD><EFBFBD>=<EFBFBD>ڵ<EFBFBD><EFBFBD><EFBFBD>
|
|||
|
|
x = [0 : Ele_L:L]';
|
|||
|
|
% figure;
|
|||
|
|
|
|||
|
|
% M=Fe(:,2);
|
|||
|
|
% M(ele_num+1)=-Fe(end,4);
|
|||
|
|
% hold on;
|
|||
|
|
% title('Bending Moment Diagram');
|
|||
|
|
% plot(x,M);
|
|||
|
|
% y1 = zeros(1,ele_num+1);
|
|||
|
|
% plot(x,y1,'k')
|
|||
|
|
% xlabel('length')
|
|||
|
|
% ylabel('Moment')
|
|||
|
|
% title('moment diagram with constant thickness');
|
|||
|
|
|
|||
|
|
title('Displacment Diagram');
|
|||
|
|
for i=1:length(x)
|
|||
|
|
disp_plot_constant(i)=U(2*(i-1)+1);
|
|||
|
|
end
|
|||
|
|
aa=plot(x,disp_plot_constant,linetype{way},'linewidth',2);
|
|||
|
|
aa.Color(4)=0.5
|
|||
|
|
% figure;
|
|||
|
|
% hold on;
|
|||
|
|
% title('Rotation Diagram');
|
|||
|
|
% for i=1:length(x)
|
|||
|
|
% rot_plot_constant(i)=U(2*(i));
|
|||
|
|
% end
|
|||
|
|
% plot(x,rot_plot_constant);
|
|||
|
|
% save data disp_plot_constant
|
|||
|
|
end
|
|||
|
|
legend('ŷ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>','<EFBFBD><EFBFBD>ľ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>-<EFBFBD><EFBFBD>ȫ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>','<EFBFBD><EFBFBD>ľ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>-<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>');
|