test.m

薄壁结构有限元计算

% 输入转动惯量（x向、y向、二向混合、翘曲、x向翘曲、y向翘曲）
Ix=input('Please input the x-direction of inertia-moment of the section: ');
Iy=input('Please input the y-direction of inertia-moment of the section: ');
Ixy=input('Please input the xy-direction of inertia-moment of the section: ');
If=input('Please input the warp of inertia-moment of the section: ');
Ixf=input('Please input the x-direction warp of inertia-moment of the section: ');
Iyf=input('Please input the y-direction warp of inertia-moment of the section: ');

% 输入面积（截面、x向剪切、y向剪切、混合剪切、x向翘曲剪切、y向翘曲剪切、翘曲剪切）
A=input('Please input the area of the section: ');
Ax=input('Please input the x-direction of shear-area of the section: ');
Ay=input('Please input the y-direction of shear-area of the section: ');
Axy=input('Please input the mixed shear-area of the section: ');
Axr=input('Please input the x-direction warp of shear-moment of the section: ');
Ayr=input('Please input the y-direction warp of shear-moment of the section: ');
Ar=input('Please input the warp of shear-moment of the section: ');

% 输入x向静矩、y向静矩、弹性模量、剪切模量、扭转常数、密度、固有频率
Sx=input('Please input the x-direction of shear-moment of the section: ');
Sy=input('Please input the y-direction of shear-moment of the section: ');
E=input('Please input the elastic modulus of the material: ');
G=input('Please input the shear modulus of the material: ');
J=input('Please input the torsion-constant of the section: ');
rho=input('Please input the density of the material: ');
omega=input('Please input the inherence frequency of the construction: ');

% 计算各参数与AA矩阵
b2=rho*omega*omega*A;
b3=rho*omega*omega*Sy;
b4=rho*omega*omega*Sx;
b5=G*Ax;
b6=G*Axy;
b7=G*Axr;
b8=-G*Ax+rho*omega*omega*Iy;
b9=G*Axy-rho*omega*omega*Ixy;
b10=G*Axr-rho*omega*omega*Iyf;
b11=G*Ay;
b12=G*Ayr;
b13=-G*Ay+rho*omega*omega*Ixy;
b14=-G*Ayr+rho*omega*omega*Ixf;
b15=rho*omega*omega*If;
b16=G*Ar;
b17=-G*Ar+rho*omega*omega*If;
AA=[0 1 0 0 0 0 0 0 0 0 0 0 0 0;
   b2/E/A 0 0 0 -b3/E/A 0 0 0 b4/E/A 0 0 0 0 0;
   0 0 0 1 0 0 0 0 0 0 0 0 0 0;
   0 0 b2/G/Ax 0 0 -b5/G/Ax 0 0 0 b6/G/Ax -b4/G/Ax 0 0 b7/G/Ax;
   0 0 0 0 0 1 0 0 0 0 0 0 0 0;
   -b3/E/Iy 0 0 b5/E/Iy b8/E/Iy 0 0 b6/E/Iy b9/E/Iy 0 0 b7/E/Iy b10/E/Iy 0;
   0 0 0 0 0 0 0 1 0 0 0 0 0 0;
   0 0 0 0 0 -b6/G/Ay b2/G/Ay 0 0 b11/G/Ay b3/G/Ay 0 0 b12/G/Ay;
   0 0 0 0 0 0 0 0 0 1 0 0 0 0;
   b4/E/Ix 0 0 -b6/E/Ix b9/E/Ix 0 0 -b11/E/Ix b13/E/Ix 0 0 -b12/E/Ix b14/E/Ix 0;
   0 0 0 0 0 0 0 0 0 0 0 1 0 0;
   0 0 -b4/G/(J+Ar) 0 0 -b7/G/(J+Ar) b3/G/(J+Ar) 0 0 b12/G/(J+Ar) b15/G/(J+Ar) 0 0 b16/G/(J+Ar);
   0 0 0 0 0 0 0 0 0 0 0 0 0 1;
   0 0 0 -b7/E/If b10/E/If 0 0 -b12/E/If b14/E/If 0 0 -b16/E/If b17/E/If 0];

% 计算各参数与BB矩阵
k2=-E*A;
k3=E*Sy;
k4=-E*Sx;
k5=-G*Ax;
k6=-G*Axy;
k7=-G*Axr;
k8=-E*Iy;
k9=E*Ixy;
k10=E*Iyf;
k11=-G*Ay;
k12=-G*Ayr;
k13=-E*Ix;
k14=-E*Ixf;
k15=-G*J-G*Ar;
k16=-E*If;
BB=[1 0 0 0 0 0 0 0 0 0 0 0 0 0;
   0 k2/E/A 0 0 0 k3/E/A 0 0 0 k4/E/A 0 0 0 0;
   0 0 1 0 0 0 0 0 0 0 0 0 0 0;
   0 0 0 k5/G/Ax 0 0 0 k6/G/Ax 0 0 0 k7/G/Ax 0 0;
   0 0 0 0 1 0 0 0 0 0 0 0 0 0;
   0 k3/E/Iy 0 0 0 k8/E/Iy 0 0 0 k9/E/Iy 0 0 0 k10/E/Iy;
   0 0 0 0 0 0 1 0 0 0 0 0 0 0;
   0 0 0 k6/G/Ay 0 0 0 k11/G/Ay 0 0 0 k12/G/Ay 0 0;
   0 0 0 0 0 0 0 0 1 0 0 0 0 0;
   0 k4/E/Ix 0 0 0 k9/E/Ix 0 0 0 k13/E/Ix 0 0 0 k14/E/Ix;
   0 0 0 0 0 0 0 0 0 0 1 0 0 0;
   0 0 0 k7/G/(J+Ar) 0 0 0 k12/G/(J+Ar) 0 0 0 k15/G/(J+Ar) 0 0;
   0 0 0 0 0 0 0 0 0 0 0 0 1 0;
   0 0 0 0 0 k10/E/If 0 0 0 k14/E/If 0 0 0 k16/E/If];

% 计算特征值与特征向量
[Z,lambda]=eig(AA,BB,'qz');