求整体刚度矩阵matlab程序.docx

姓名：吴佳侣
班级：机自11-13
学号：03111323

例：如图所示有限元模型，弹性模量为，厚度为，为简化计算取，求整体刚度矩阵。

部分分析思路：
各单元信息
单元编号①②③④整体编码1,2,32,4,55,3,23,5,6局部编码
以整编码体表示的单元刚度矩阵
整体刚度矩阵

程序：
%%%%%%%%%%%%%%%求整体刚度矩阵
clc
clearall
symsEuta%%定义变量
%%%%%%%%%%%%%%%%%%%%%%%%写出单元刚度矩阵,单元面积为a^2/2
%%%%%%%%%%%%单元1
bi=0;ci=a;
bj=-a;cj=-a;
bm=a;cm=0;
mianji=a^2/2;
B1=1/2/mianji*[bi0bj0bm0
0ci0cj0cm
cibicjbjcmbm];
u=0;E=1;t=1;
D=E/(1-u^2)*[1u0
u10
00(1-u)/2];%%%弹性矩阵D
k1=transpose(B1)*D*B1*t*mianji;
%%%%%%%%%%%%单元2
bi=0;ci=a;
bj=-a;cj=a;
bm=a;cm=0;
mianji=a^2/2;
B2=1/2/mianji*[bi0bj0bm0
0ci0cj0cm
cibicjbjcmbm];
u=0;E=1;t=1;
D=E/(1-u^2)*[1u0
u10
00(1-u)/2];%%%弹性矩阵D
K3=transpose(B2)*D*B2*t*mianji;
%%%%%%%%%%%%单元3
bi=0;ci=-a;
bj=a;cj=-a;
bm=-a;cm=0;
mianji=a^2/2;
B3=1/2/mianji*[bi0bj0bm0
0ci0cj0cm
cibicjbjcmbm];
u=0;E=1;t=1;
D=E/(1-u^2)*[1u0
u10
00(1-u)/2];%%%弹性矩阵D
k2=transpose(B3)*D*B3*t*mianji;
%%%%%%%%%%%%单元4
bi=0;ci=a;
bj=-a;cj=-a;
bm=a;cm=0;
mianji=a^2/2;
B4=1/2/mianji*[bi0bj0bm0
0ci0cj0cm
cibicjbjcmbm];
u=0;E=1;t=1;
D=E/(1-u^2)*[1u0
u10
00(1-u)/2];%%%弹性矩阵D
K4=transpose(B4)*D*B4*t*mianji;
%%%%%%%%%%%%%%%%%%%%%%%%%单元刚度矩阵再分解
k1_11=k1(1:2,1:2);
k1_12=k1(1:2,3:4);
k1_13=k1(1:2,5:6);
k1_21=k1(3:4,1:2);
k1_22=k1(3:4,3:4);
k1_23=k1(3:4,5:6);
k1_31=k1(5:6,1:2);
k1_32=k1(5:6,3:4);
k1_33=k1(5:6,5:6);
%%%%%%%%%%%%%
k2_22=k2(1:2,1:2);
k2_24=k2(1:2,3:4);
k2_25=k2(1:2,5:6);
k2_42=k2(3:4,1:2);
k2_44=k2(3:4,3:4);
k2_45=k2(3:4,5:6);
k2_52=k2(5:6,1:2);
k2_54=k2(5:6,3:4);
k2_55=k2(5:6,5:6);
%%%%%%%%%%%%%
k3_55=k2(1:2,1:2);
k3_53=k2(1:2,3:4);
k3_52=k2(1:2,5:6);
k3_35=k2(3:4,1:2);
k3_33=k2(3:4,3:4);
k3_32=k2(3:4,5:6);
k3_25=k2(5:6,1:2);
k3_23=k2(5:6,3:4);
k3_22=k2(5:6,5:6);
%%%%%%%%%%%%%
k4_33=k2(1:2,1:2);
k4_35=k2(1:2,3:4);
k4_36=k2(1:2,5:6);
k4_53=k2(3:4,1:2);
k4_55=k2(3:4,3:4);
k4_56=k2(3:4,5:6);
k4_63=k2(5:6,1:2);
k4_65=k2(5:6,3:4);
k4_66=k2(5:6,5:6);
%%%%%%%%%%%%%%%%%%%%%%%%%单元刚度矩阵组装，形成整体刚度矩阵%%%%%%%
k_11=k1_11;k_12=k1_12;k_13=k1_13;k_14=zeros(2,2);
k_15=zeros(2,2);k_16=zeros(2,2);k_21=k1_21;k_22=k1_22+k2_22+k3_22;
k_23=k1_23+k3_23