求整体刚度矩阵matlab程序.doc
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求整体刚度矩阵matlab程序.doc
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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
①
②
③
④
整体编码
1,2,3
2,4,5
5,3,2
3,5,6
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;
k_24=k2_24;k_25=k2_25+k3_25;k_26=zeros(2,2);k_31=k1_31;
k_32=k1_32+k3_32;k_33=k1_33+k3_33+k4_33;k_34=zeros(2,2);
k_35=k3_35+k4_35;
k_36=k4_36;k_41=zeros(2,2);k_42=k2_42;k_43=zeros(2,2);k_44=k2_44;
k_45=k2_45;k_46=zeros(2,2);k_51=zeros(2,2);k_52=k2_52+k3_52;
k_53=k3_53+k4_53;k_54=k2_54;k_55=k2_55+k3_55+k4_55;k_56=k4_56;
k_61=zeros(2,2);k_62=zeros(2,2);k_63=k4_63;k_64=zeros(2,2);
k_65=k4_65;
k_66=k4_66;
%%%%
k=[k_11k_12k_13k_14k_15k_16;
k_21k_22k_23k_24k_25k_26;
k_31k_32k_33k_34k_35k_36;
k_41k_42k_43k_44k_45k_46;
k_51k_52k_53k_54k_55k_56;
k_61k_62k_63k_64k_65k_66];
运行结果截图:
运行过程:
各单元刚度矩阵计算:
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- 关 键 词:
- 整体 刚度 矩阵 matlab 程序