有限元课程设计

有限元分析课程设计

题目：

如图所示简支梁，高3米，长15米，承受图示载荷P=2000KN,Q=600KN,E=83Gpa,μ=0.167,厚度t=1米，ρ=1567kg/m3，按平面应力问题分析。用有限元方法计算该梁的变形及应力分布情况。要求用矩形单元。

二、分析过程

一 划分单元

划分单元，标出单元号，和节点号选取坐标，见图。

二 输入参数 1. 基本参数

(1) 单元数 NE=45; (2) 节点数 NJ=64; (3) 支承数 NZ=3；

(4) 节点载荷数 NPJ=4； (5) 半带宽 DD=12；

(6) 节点位移数 NJ2=128； 2. 其他参数

(1) 问题类型码LXM，平面应力问题LXM=0；

(2) 弹性常数E，μ，弹性模量E=83GP 泊松比μ=0.167； (3) 容重ρ，LOU=1567； (4) 板厚t，TE=1m； (5) 节点坐标组AJZ

（1）节点坐标数组：AJZ

AJZ[NJ+1][3]={{0,0,0},{0,0,0},{0,0,1},{0,0,2},{0,0,3},

{0,1,0},{0,1,1},{0,1,2},{0,1,3}, {0,2,0},{0,2,1},{0,2,2},{0,2,3}, {0,3,0},{0,3,1},{0,3,2},{0,3,3}, {0,4,0},{0,4,1},{0,4,2},{0,4,3},

{0,5,0},{0,5,1},{0,5,2},{0,5,3}, {0,6,0},{0,6,1},{0,6,2},{0,6,3}, {0,7,0},{0,7,1},{0,7,2},{0,7,3}, {0,8,0},{0,8,1},{0,8,2},{0,8,3}, {0,9,0},{0,9,1},{0,9,2},{0,9,3}, {0,10,0},{0,10,1},{0,10,2},{0,10,3}, {0,11,0},{0,11,1},{0,11,2},{0,11,3}, {0,12,0},{0,12,1},{0,12,2},{0,12,3}, {0,13,0},{0,13,1},{0,13,2},{0,13,3}, {0,14,0},{0,14,1},{0,14,2},{0,14,3}, {0,15,0},{0,15,1},{0,15,2},{0,15,3}};（2）节点码数组：JM

JM[NE+1][5]={{0,0,0,0,0},{0,1,5,6,2},{0,5,9,10,6},{0,9,13,14,10},{0,13,17,18,14},{0,17,21,22,18}, {0,21,25,26,22},{0,25,29,30,26},{0,29,33,34,30},{0,33,37,38,34},{0,37,41,42,38},

{0,41,45,46,42},{0,45,49,50,46},{0,49,53,54,50},{0,53,57,58,54},{0,57,61,62,58},

{0,2,6,7,3},{0,6,10,11,7},{0,10,14,15,11},{0,14,18,19,15},{0,18,22,23,19},

{0,22,26,27,23},{0,26,30,31,27},{0,30,34,35,31},{0,34,38,39,35},{0,38,42,43,39},

{0,42,46,47,43},{0,46,50,51,47},{0,50,54,55,51},{0,54,58,59,55},{0,58,62,63,59},

{0,3,7,8,4},{0,7,11,12,8},{0,11,15,16,12},{0,15,19,20,16},{0,19,23,24,20},

{0,23,27,28,24},{0,27,31,32,28},{0,31,35,36,32},{0,35,39,40,36},{0,39,43,44,40},

{0,43,47,48,44},{0,47,51,52,48},{0,51,55,56,52},{0,55,59,60,56},{0,59,63,64,60}}; 支撑数组：NZC

NZC[NZ+1]={0,1,2,122}

节点载荷数组PJ

(6) PJ[NPJ+1][2+1]={{0,0,0},{0,-600000,32},{0,-100000,64},{0,-100000,72},{0,-600000,104}}; 等效载荷图：

由上图可知：受外载荷力的节点有16、32、36、52号节点所受力的大小分别为-600000N，-100000N，-100000N和-6000N.,由节点号可知位移数依次为，16,32,36,52可得：

(7) PJ[NPJ+1][2+1]={{0,0,0},{0,-600000,32},{0,-100000,64},{0,-100000,72},{0,-600000,104}};

PJ(NPJ,2)中的元素列排列原则为：一个节点载荷存一行，同一行中第一列世界点

在和值，第二列是载荷对应的位移。 程序框图及程序

三、程序设计

#include #include

#define NE 45 #define NJ 64 #define NZ 3 #define NPJ 4 #define NJ2 128 #define DD 12

int LXM=0; double E0=[1**********]; double MU=0.167; double LOU=1567; double TE=1;

double AJZ[NJ+1][3]={{0,0,0},{0,0,0},{0,0,1},{0,0,2},{0,0,3},

{0,1,0},{0,1,1},{0,1,2},{0,1,3}, {0,2,0},{0,2,1},{0,2,2},{0,2,3}, {0,3,0},{0,3,1},{0,3,2},{0,3,3}, {0,4,0},{0,4,1},{0,4,2},{0,4,3}, {0,5,0},{0,5,1},{0,5,2},{0,5,3}, {0,6,0},{0,6,1},{0,6,2},{0,6,3}, {0,7,0},{0,7,1},{0,7,2},{0,7,3},

{0,8,0},{0,8,1},{0,8,2},{0,8,3}, {0,9,0},{0,9,1},{0,9,2},{0,9,3}, {0,10,0},{0,10,1},{0,10,2},{0,10,3}, {0,11,0},{0,11,1},{0,11,2},{0,11,3}, {0,12,0},{0,12,1},{0,12,2},{0,12,3}, {0,13,0},{0,13,1},{0,13,2},{0,13,3}, {0,14,0},{0,14,1},{0,14,2},{0,14,3}, {0,15,0},{0,15,1},{0,15,2},{0,15,3}}; int

JM[NE+1][5]={{0,0,0,0,0},{0,1,5,6,2},{0,5,9,10,6},{0,9,13,14,10},{0,13,17,18,14},{0,17,21,22,18},

{0,21,25,26,22},{0,25,29,30,26},{0,29,33,34,30},{0,33,37,38,34},{0,37,41,42,38},

{0,41,45,46,42},{0,45,49,50,46},{0,49,53,54,50},{0,53,57,58,54},{0,57,61,62,58},

{0,2,6,7,3},{0,6,10,11,7},{0,10,14,15,11},{0,14,18,19,15},{0,18,22,23,19},

{0,22,26,27,23},{0,26,30,31,27},{0,30,34,35,31},{0,34,38,39,35},{0,38,42,43,39},

{0,42,46,47,43},{0,46,50,51,47},{0,50,54,55,51},{0,54,58,59,55},{0,58,62,63,59},

{0,3,7,8,4},{0,7,11,12,8},{0,11,15,16,12},{0,15,19,20,16},{0,19,23,24,20},

{0,23,27,28,24},{0,27,31,32,28},{0,31,35,36,32},{0,35,39,40,36},{0,39,43,44,40},

{0,43,47,48,44},{0,47,51,52,48},{0,51,55,56,52},{0,55,59,60,56},{0,59,63,64,60}}; int NZC[NZ+1]={0,1,2,122}; double

PJ[NPJ+1][2+1]={{0,0,0},{0,-600000,32},{0,-100000,64},{0,-100000,72},{0,-600000,104}};

double

AE,KZ[NJ2+1][DD+1],P[NJ2+1],S[3+1][8+1],KE[8+1][8+1],SA[7+1][3+1][8+1],a=0.5,b=0.25,jhyl[NJ][3+1]; int v=4;

double xrr[4+1]={0,-1,1,1,-1},yrr[4+1]={0,-1,-1,1,1};

void DUGD(int,int);

void main() {

int NJ1,k,IN,IM,jn,m,n,i,j,z,J0,ii,jj,h,dh,E,l,zl,dl;

double WY[6+1],YL[3+1]; if(LXM!=0) { E0=E0/(1.0-MU*MU); MU=MU/(1.0-MU); }

for(i=0;i

for(E=1;E0) { KZ[dh][dl]=KZ[dh][dl]+KE[h][l]; } } } } } }

//**********************生成p*************************** for(i=1;i0) {

{ j=(int)PJ[i][2]; P[j]=PJ[i][1]; } }

if(LOU>0) { for(E=1;E

//**********************边界条件*************************** for(i=1;iDD) J0=DD; else J0=z; for(j=2;j

//************************高斯消元******************************* NJ1=NJ2-1; for(k=1;kk+DD-1)

IM=k+DD-1; else IM=NJ2; IN=k+1; for(i=IN;i

}

//*************************带回矩********************************** P[NJ2]=P[NJ2]/KZ[NJ2][1]; for(i=NJ1;i>=1;i--) { if(DD>NJ2-i+1) J0=NJ2-i+1; else J0=DD; for(j=2;j

printf("\n");

printf("JD U V\n"); for(i=1;i

// printf("%d\n",n); for(E=1;E

阵

应力

{ DUGD(E,2); for(i=1;i

for(n=1;n

for(n=1;n

ls=(AJZ[JM[E][1]][1]+AJZ[JM[E][2]][1]+AJZ[JM[E][3]][1]+AJZ[JM[E][4]][1])/4+xrr[n]*a;

lss=(AJZ[JM[E][1]][2]+AJZ[JM[E][2]][2]+AJZ[JM[E][3]][2]+AJZ[JM[E][4]][2])/4+yrr[n]*b; for(i=1;i

jhyl[i][3]=jhyl[i][3]+SIG[E][3][n]; } } } }

for(i=1;i

void DUGD(int E,int ASK) {

double B[3+1][8+1],D[3+1][3+1],AEC; int i,j,k,m,p,q;

double xr[5]={0,-1,1,1,-1},yr[5]={0,-1,-1,1,1};

AE=4*a*b;

if(ASK>1) { for (m=1;m

sy=%-9.6f s2=%-9.6f

{ p=i/2+1; B[1][i]=b*xr[p]*(1+yr[p]*yrr[m])/AE; }

for(i=2;i

B[3][1]=B[2][2]; B[3][2]=B[1][1]; B[3][3]=B[2][4]; B[3][4]=B[1][3]; B[3][5]=B[2][6]; B[3][6]=B[1][5]; B[3][7]=B[2][8]; B[3][8]=B[1][7];

D[1][1]=E0/(1-MU*MU);

D[1][2]=E0*MU/(1-MU*MU); D[1][3]=0;

D[2][1]=D[1][2]; D[2][2]=D[1][1]; D[2][3]=0; D[3][1]=0; D[3][2]=0;

D[3][3]=E0/(2*(1+MU));

for(i=1;i

if(ASK>2) { for(i=1;i

for(j=1;j

KE[i][j]=(b*b*xr[p]*xr[q]*(1.0+(yr[p]*yr[q])/3)+((1-MU)/2)*a*a*yr[p]*yr[q]*(1+(xr[p]*xr[q])/3))*AEC; } } for(i=1;i

KE[i][j]=a*b*(MU*xr[p]*yr[q]+(1-MU)/2*yr[p]*xr[q])*AEC; } } for(i=2;i

KE[i][j]=a*b*(MU*yr[p]*xr[q]+(1-MU)/2*xr[p]*yr[q])*AEC; } } for(i=2;i

KE[i][j]=(a*a*yr[p]*yr[q]*(1+(xr[p]*xr[q])/3)+(1-MU)/2*b*b*xr[p]*xr[q]*(1+(y

r[p]*yr[q])/3))*AEC; } } } } }

四、程序结果：

JD U V 1 0.000000 0.000000 2 0.000119 -0.000028 3 0.000215 -0.000039 4 0.000312 -0.000041 5 0.000010 -0.000141 6 0.000119 -0.000140 7 0.000214 -0.000141 8 0.000311 -0.000142 9 0.000026 -0.000245 10 0.000120 -0.000247 11 0.000209 -0.000247 12 0.000302 -0.000244 13 0.000045 -0.000337 14 0.000126 -0.000340 15 0.000203 -0.000341 16 0.000284 -0.000346 17 0.000069 -0.000413 18 0.000134 -0.000416 19 0.000197 -0.000417 20 0.000260 -0.000413 21 0.000095 -0.000471 22 0.000142 -0.000474 23 0.000188 -0.000473 24 0.000235 -0.000471 25 0.000122 -0.000510 26 0.000151 -0.000513 27 0.000179 -0.000513 28 0.000208 -0.000510 29 0.000151 -0.000530 30 0.000160 -0.000533

31 0.000170 -0.000534 32 0.000180 -0.000532 33 0.000179 -0.000530 34 0.000170 -0.000533 35 0.000160 -0.000534 36 0.000150 -0.000532 37 0.000208 -0.000510 38 0.000179 -0.000513 39 0.000151 -0.000513 40 0.000122 -0.000510 41 0.000235 -0.000471 42 0.000188 -0.000474 43 0.000142 -0.000473 44 0.000095 -0.000471 45 0.000261 -0.000413 46 0.000196 -0.000416 47 0.000133 -0.000417 48 0.000070 -0.000413 49 0.000285 -0.000337 50 0.000204 -0.000340 51 0.000127 -0.000341 52 0.000046 -0.000346 53 0.000304 -0.000245 54 0.000210 -0.000247 55 0.000121 -0.000247 56 0.000028 -0.000244 57 0.000320 -0.000141 58 0.000211 -0.000140 59 0.000116 -0.000141 60 0.000019 -0.000142 61 0.000330 0.000000 62 0.000211 -0.000028 63 0.000115 -0.000039 64 0.000018 -0.000041 NJ=1

sx=448579.683456 sy=-2228452.829692 tou=-796595.793624 s1=667686.817671 s2=-2447559.963907 theta=164.620855 NJ=2

sx=-471105.115634 sy=-3323385.659933 tou=-332788.181540 s1=-432791.889164 s2=-3361698.886403 theta=173.432568 NJ=3

sx=-380008.521484 sy=-1171980.561176 tou=-389915.418341 s1=-220261.726594 s2=-1331727.356065 theta=157.721283 NJ=4

sx=-174817.042307 sy=-196368.115360 tou=-113186.429863 s1=-71894.381431 s2=-299290.776236 theta=137.719132 NJ=5

sx=2250254.946492 sy=608991.337238 tou=-940398.915924 s1=2677736.389866 s2=181509.893863 theta=155.554663 NJ=6

sx=252798.799483 sy=25086.773687 tou=-1112048.633437 s1=1256804.743538 s2=-978919.170367 theta=137.922902 NJ=7

sx=-1092918.137680 sy=-517937.687407 tou=-1162821.119077 s1=392404.957485 s2=-2003260.782572 theta=128.056475 NJ=8

sx=-853332.938708 sy=-227597.572178 tou=-337658.474657 s1=-80139.900135 s2=-1000790.610751 theta=113.591210 NJ=9

sx=2978343.620407 sy=191835.446746 tou=-246028.998973 s1=2999899.492124 s2=170279.575029 theta=174.992808

NJ=10

sx=1092941.786794 sy=-50630.492118 tou=-1205166.021063 s1=1855083.879140 s2=-812772.584463 theta=147.690906

NJ=11

sx=-1701535.284748 sy=158394.548145 tou=-1282690.328703 s1=812768.366051 s2=-2355909.102654 theta=117.028733

NJ=12

sx=-2211315.124569 sy=865.147546 tou=-584568.256203 s1=145836.734683 s2=-2356286.711706 theta=103.928218

NJ=13

sx=3579786.645542 sy=169460.350932 tou=-223054.573477 s1=3594313.790609 s2=154933.205866 theta=176.273692

NJ=14

sx=2139336.650683 sy=-395244.610328 tou=-760570.381856 s1=2350049.013383 s2=-605956.973028 theta=164.514865

NJ=15

sx=-2207968.432309 sy=-1408646.941484 tou=-842287.184148 s1=-876011.375629 s2=-2740603.998164 theta=122.307956

NJ=16

sx=-3764178.598901 sy=-1344384.227186 tou=-270068.717065 s1=-1314608.749684 s2=-3793954.076404 theta=96.291535

NJ=17

sx=4112813.455675 sy=192429.224322 tou=-138499.091119 s1=4117700.251544 s2=187542.428453 theta=177.979217

NJ=18

sx=2632386.856938 sy=-195827.868942 tou=-424335.791550 s1=2694680.692152 s2=-258121.704157 theta=171.648453

NJ=19

sx=-2542544.945691 sy=-58043.406734 tou=-406342.838121 s1=6725.898753 s2=-2607314.251178 theta=99.056515

NJ=20

sx=-4100340.167973 sy=-177169.357579 tou=45199.810486 s1=-176648.668614 s2=-4100860.856939 theta=89.339998

NJ=21

sx=4470869.900781 sy=257652.480755 tou=-86026.318615 s1=4472625.671733 s2=255896.709802 theta=178.830774

NJ=22

sx=2866138.245397 sy=23606.783978 tou=-285626.789429 s1=2894554.873043 s2=-4809.843669 theta=174.318416

NJ=23

sx=-2984293.349300 sy=12029.540853 tou=-267868.482925 s1=35788.343246 s2=-3008052.151693 theta=95.068630

NJ=24

sx=-4338251.882825 sy=-248026.023918 tou=-96570.380451 s1=-245747.263294 s2=-4340530.643449 theta=91.351751

NJ=25

sx=4691023.222574 sy=270674.389954 tou=-59406.755348 s1=4691821.468486 s2=269876.144042 theta=179.230166

NJ=26

sx=3018074.086028 sy=-18592.447447 tou=-203143.353180 s1=3031603.453741 s2=-32121.815160 theta=176.189723

NJ=27

sx=-3056553.768618 sy=4600.569223 tou=-224889.255166 s1=21033.952015 s2=-3072987.151410 theta=94.179359

NJ=28

sx=-4629326.528832 sy=-248168.150134 tou=-95492.245568 s1=-246087.777724 s2=-4631406.901242 theta=91.248035

NJ=29

sx=4808948.735861 sy=255563.234763 tou=-21764.002393 s1=4809052.759774 s2=255459.210849 theta=179.726150

NJ=30

sx=3125009.644278 sy=-112493.460083 tou=-81921.250706 s1=3127081.240687 s2=-114565.056492 theta=178.551434

NJ=31

sx=-3094676.805306 sy=-256359.995174 tou=-88188.956336 s1=-253622.528282 s2=-3097414.272197 theta=91.777943

NJ=32

sx=-4864139.635507 sy=-465021.421266 tou=-57056.914380 s1=-464281.512981 s2=-4864879.543793 theta=90.742964

NJ=33

sx=4808948.735861 sy=255563.234763 tou=21764.002393 s1=4809052.759774 s2=255459.210849 theta=0.273850

NJ=34

sx=3125009.644278 sy=-112493.460083 tou=81921.250706 s1=3127081.240687 s2=-114565.056492 theta=1.448566

NJ=35

sx=-3094676.805306 sy=-256359.995174 tou=88188.956336 s1=-253622.528282 s2=-3097414.272197 theta=88.222057

NJ=36

sx=-4864139.635507 sy=-465021.421266 tou=57056.914380 s1=-464281.512981 s2=-4864879.543793 theta=89.257036

NJ=37

sx=4691023.222574 sy=270674.389954 tou=59406.755348 s1=4691821.468486 s2=269876.144042 theta=0.769834

NJ=38

sx=3018074.086028 sy=-18592.447447 tou=203143.353180 s1=3031603.453741 s2=-32121.815160 theta=3.810277

NJ=39

sx=-3056553.768618 sy=4600.569223 tou=224889.255166 s1=21033.952015 s2=-3072987.151410 theta=85.820641

NJ=40

sx=-4629326.528832 sy=-248168.150134 tou=95492.245568 s1=-246087.777724 s2=-4631406.901242 theta=88.751965 Press any key to continuePress any key to continue

32.521.510.50-0.5

第一主应力等值图

051015

第二主应力等值图

5

1015

有限元分析课程设计

题目：

如图所示简支梁，高3米，长15米，承受图示载荷P=2000KN,Q=600KN,E=83Gpa,μ=0.167,厚度t=1米，ρ=1567kg/m3，按平面应力问题分析。用有限元方法计算该梁的变形及应力分布情况。要求用矩形单元。

二、分析过程

一 划分单元

划分单元，标出单元号，和节点号选取坐标，见图。

二 输入参数 1. 基本参数

(1) 单元数 NE=45; (2) 节点数 NJ=64; (3) 支承数 NZ=3；

(4) 节点载荷数 NPJ=4； (5) 半带宽 DD=12；

(6) 节点位移数 NJ2=128； 2. 其他参数

(1) 问题类型码LXM，平面应力问题LXM=0；

(2) 弹性常数E，μ，弹性模量E=83GP 泊松比μ=0.167； (3) 容重ρ，LOU=1567； (4) 板厚t，TE=1m； (5) 节点坐标组AJZ

（1）节点坐标数组：AJZ

AJZ[NJ+1][3]={{0,0,0},{0,0,0},{0,0,1},{0,0,2},{0,0,3},

{0,1,0},{0,1,1},{0,1,2},{0,1,3}, {0,2,0},{0,2,1},{0,2,2},{0,2,3}, {0,3,0},{0,3,1},{0,3,2},{0,3,3}, {0,4,0},{0,4,1},{0,4,2},{0,4,3},

{0,5,0},{0,5,1},{0,5,2},{0,5,3}, {0,6,0},{0,6,1},{0,6,2},{0,6,3}, {0,7,0},{0,7,1},{0,7,2},{0,7,3}, {0,8,0},{0,8,1},{0,8,2},{0,8,3}, {0,9,0},{0,9,1},{0,9,2},{0,9,3}, {0,10,0},{0,10,1},{0,10,2},{0,10,3}, {0,11,0},{0,11,1},{0,11,2},{0,11,3}, {0,12,0},{0,12,1},{0,12,2},{0,12,3}, {0,13,0},{0,13,1},{0,13,2},{0,13,3}, {0,14,0},{0,14,1},{0,14,2},{0,14,3}, {0,15,0},{0,15,1},{0,15,2},{0,15,3}};（2）节点码数组：JM

JM[NE+1][5]={{0,0,0,0,0},{0,1,5,6,2},{0,5,9,10,6},{0,9,13,14,10},{0,13,17,18,14},{0,17,21,22,18}, {0,21,25,26,22},{0,25,29,30,26},{0,29,33,34,30},{0,33,37,38,34},{0,37,41,42,38},

{0,41,45,46,42},{0,45,49,50,46},{0,49,53,54,50},{0,53,57,58,54},{0,57,61,62,58},

{0,2,6,7,3},{0,6,10,11,7},{0,10,14,15,11},{0,14,18,19,15},{0,18,22,23,19},

{0,22,26,27,23},{0,26,30,31,27},{0,30,34,35,31},{0,34,38,39,35},{0,38,42,43,39},

{0,42,46,47,43},{0,46,50,51,47},{0,50,54,55,51},{0,54,58,59,55},{0,58,62,63,59},

{0,3,7,8,4},{0,7,11,12,8},{0,11,15,16,12},{0,15,19,20,16},{0,19,23,24,20},

{0,23,27,28,24},{0,27,31,32,28},{0,31,35,36,32},{0,35,39,40,36},{0,39,43,44,40},

{0,43,47,48,44},{0,47,51,52,48},{0,51,55,56,52},{0,55,59,60,56},{0,59,63,64,60}}; 支撑数组：NZC

NZC[NZ+1]={0,1,2,122}

节点载荷数组PJ

(6) PJ[NPJ+1][2+1]={{0,0,0},{0,-600000,32},{0,-100000,64},{0,-100000,72},{0,-600000,104}}; 等效载荷图：

由上图可知：受外载荷力的节点有16、32、36、52号节点所受力的大小分别为-600000N，-100000N，-100000N和-6000N.,由节点号可知位移数依次为，16,32,36,52可得：

(7) PJ[NPJ+1][2+1]={{0,0,0},{0,-600000,32},{0,-100000,64},{0,-100000,72},{0,-600000,104}};

PJ(NPJ,2)中的元素列排列原则为：一个节点载荷存一行，同一行中第一列世界点

在和值，第二列是载荷对应的位移。 程序框图及程序

三、程序设计

#include #include

#define NE 45 #define NJ 64 #define NZ 3 #define NPJ 4 #define NJ2 128 #define DD 12

int LXM=0; double E0=[1**********]; double MU=0.167; double LOU=1567; double TE=1;

double AJZ[NJ+1][3]={{0,0,0},{0,0,0},{0,0,1},{0,0,2},{0,0,3},

{0,1,0},{0,1,1},{0,1,2},{0,1,3}, {0,2,0},{0,2,1},{0,2,2},{0,2,3}, {0,3,0},{0,3,1},{0,3,2},{0,3,3}, {0,4,0},{0,4,1},{0,4,2},{0,4,3}, {0,5,0},{0,5,1},{0,5,2},{0,5,3}, {0,6,0},{0,6,1},{0,6,2},{0,6,3}, {0,7,0},{0,7,1},{0,7,2},{0,7,3},

{0,8,0},{0,8,1},{0,8,2},{0,8,3}, {0,9,0},{0,9,1},{0,9,2},{0,9,3}, {0,10,0},{0,10,1},{0,10,2},{0,10,3}, {0,11,0},{0,11,1},{0,11,2},{0,11,3}, {0,12,0},{0,12,1},{0,12,2},{0,12,3}, {0,13,0},{0,13,1},{0,13,2},{0,13,3}, {0,14,0},{0,14,1},{0,14,2},{0,14,3}, {0,15,0},{0,15,1},{0,15,2},{0,15,3}}; int

JM[NE+1][5]={{0,0,0,0,0},{0,1,5,6,2},{0,5,9,10,6},{0,9,13,14,10},{0,13,17,18,14},{0,17,21,22,18},

{0,21,25,26,22},{0,25,29,30,26},{0,29,33,34,30},{0,33,37,38,34},{0,37,41,42,38},

{0,41,45,46,42},{0,45,49,50,46},{0,49,53,54,50},{0,53,57,58,54},{0,57,61,62,58},

{0,2,6,7,3},{0,6,10,11,7},{0,10,14,15,11},{0,14,18,19,15},{0,18,22,23,19},

{0,22,26,27,23},{0,26,30,31,27},{0,30,34,35,31},{0,34,38,39,35},{0,38,42,43,39},

{0,42,46,47,43},{0,46,50,51,47},{0,50,54,55,51},{0,54,58,59,55},{0,58,62,63,59},

{0,3,7,8,4},{0,7,11,12,8},{0,11,15,16,12},{0,15,19,20,16},{0,19,23,24,20},

{0,23,27,28,24},{0,27,31,32,28},{0,31,35,36,32},{0,35,39,40,36},{0,39,43,44,40},

{0,43,47,48,44},{0,47,51,52,48},{0,51,55,56,52},{0,55,59,60,56},{0,59,63,64,60}}; int NZC[NZ+1]={0,1,2,122}; double

PJ[NPJ+1][2+1]={{0,0,0},{0,-600000,32},{0,-100000,64},{0,-100000,72},{0,-600000,104}};

double

AE,KZ[NJ2+1][DD+1],P[NJ2+1],S[3+1][8+1],KE[8+1][8+1],SA[7+1][3+1][8+1],a=0.5,b=0.25,jhyl[NJ][3+1]; int v=4;

double xrr[4+1]={0,-1,1,1,-1},yrr[4+1]={0,-1,-1,1,1};

void DUGD(int,int);

void main() {

int NJ1,k,IN,IM,jn,m,n,i,j,z,J0,ii,jj,h,dh,E,l,zl,dl;

double WY[6+1],YL[3+1]; if(LXM!=0) { E0=E0/(1.0-MU*MU); MU=MU/(1.0-MU); }

for(i=0;i

for(E=1;E0) { KZ[dh][dl]=KZ[dh][dl]+KE[h][l]; } } } } } }

//**********************生成p*************************** for(i=1;i0) {

{ j=(int)PJ[i][2]; P[j]=PJ[i][1]; } }

if(LOU>0) { for(E=1;E

//**********************边界条件*************************** for(i=1;iDD) J0=DD; else J0=z; for(j=2;j

//************************高斯消元******************************* NJ1=NJ2-1; for(k=1;kk+DD-1)

IM=k+DD-1; else IM=NJ2; IN=k+1; for(i=IN;i

}

//*************************带回矩********************************** P[NJ2]=P[NJ2]/KZ[NJ2][1]; for(i=NJ1;i>=1;i--) { if(DD>NJ2-i+1) J0=NJ2-i+1; else J0=DD; for(j=2;j

printf("\n");

printf("JD U V\n"); for(i=1;i

// printf("%d\n",n); for(E=1;E

阵

应力

{ DUGD(E,2); for(i=1;i

for(n=1;n

for(n=1;n

ls=(AJZ[JM[E][1]][1]+AJZ[JM[E][2]][1]+AJZ[JM[E][3]][1]+AJZ[JM[E][4]][1])/4+xrr[n]*a;

lss=(AJZ[JM[E][1]][2]+AJZ[JM[E][2]][2]+AJZ[JM[E][3]][2]+AJZ[JM[E][4]][2])/4+yrr[n]*b; for(i=1;i

jhyl[i][3]=jhyl[i][3]+SIG[E][3][n]; } } } }

for(i=1;i

void DUGD(int E,int ASK) {

double B[3+1][8+1],D[3+1][3+1],AEC; int i,j,k,m,p,q;

double xr[5]={0,-1,1,1,-1},yr[5]={0,-1,-1,1,1};

AE=4*a*b;

if(ASK>1) { for (m=1;m

sy=%-9.6f s2=%-9.6f

{ p=i/2+1; B[1][i]=b*xr[p]*(1+yr[p]*yrr[m])/AE; }

for(i=2;i

B[3][1]=B[2][2]; B[3][2]=B[1][1]; B[3][3]=B[2][4]; B[3][4]=B[1][3]; B[3][5]=B[2][6]; B[3][6]=B[1][5]; B[3][7]=B[2][8]; B[3][8]=B[1][7];

D[1][1]=E0/(1-MU*MU);

D[1][2]=E0*MU/(1-MU*MU); D[1][3]=0;

D[2][1]=D[1][2]; D[2][2]=D[1][1]; D[2][3]=0; D[3][1]=0; D[3][2]=0;

D[3][3]=E0/(2*(1+MU));

for(i=1;i

if(ASK>2) { for(i=1;i

for(j=1;j

KE[i][j]=(b*b*xr[p]*xr[q]*(1.0+(yr[p]*yr[q])/3)+((1-MU)/2)*a*a*yr[p]*yr[q]*(1+(xr[p]*xr[q])/3))*AEC; } } for(i=1;i

KE[i][j]=a*b*(MU*xr[p]*yr[q]+(1-MU)/2*yr[p]*xr[q])*AEC; } } for(i=2;i

KE[i][j]=a*b*(MU*yr[p]*xr[q]+(1-MU)/2*xr[p]*yr[q])*AEC; } } for(i=2;i

KE[i][j]=(a*a*yr[p]*yr[q]*(1+(xr[p]*xr[q])/3)+(1-MU)/2*b*b*xr[p]*xr[q]*(1+(y

r[p]*yr[q])/3))*AEC; } } } } }

四、程序结果：

JD U V 1 0.000000 0.000000 2 0.000119 -0.000028 3 0.000215 -0.000039 4 0.000312 -0.000041 5 0.000010 -0.000141 6 0.000119 -0.000140 7 0.000214 -0.000141 8 0.000311 -0.000142 9 0.000026 -0.000245 10 0.000120 -0.000247 11 0.000209 -0.000247 12 0.000302 -0.000244 13 0.000045 -0.000337 14 0.000126 -0.000340 15 0.000203 -0.000341 16 0.000284 -0.000346 17 0.000069 -0.000413 18 0.000134 -0.000416 19 0.000197 -0.000417 20 0.000260 -0.000413 21 0.000095 -0.000471 22 0.000142 -0.000474 23 0.000188 -0.000473 24 0.000235 -0.000471 25 0.000122 -0.000510 26 0.000151 -0.000513 27 0.000179 -0.000513 28 0.000208 -0.000510 29 0.000151 -0.000530 30 0.000160 -0.000533

31 0.000170 -0.000534 32 0.000180 -0.000532 33 0.000179 -0.000530 34 0.000170 -0.000533 35 0.000160 -0.000534 36 0.000150 -0.000532 37 0.000208 -0.000510 38 0.000179 -0.000513 39 0.000151 -0.000513 40 0.000122 -0.000510 41 0.000235 -0.000471 42 0.000188 -0.000474 43 0.000142 -0.000473 44 0.000095 -0.000471 45 0.000261 -0.000413 46 0.000196 -0.000416 47 0.000133 -0.000417 48 0.000070 -0.000413 49 0.000285 -0.000337 50 0.000204 -0.000340 51 0.000127 -0.000341 52 0.000046 -0.000346 53 0.000304 -0.000245 54 0.000210 -0.000247 55 0.000121 -0.000247 56 0.000028 -0.000244 57 0.000320 -0.000141 58 0.000211 -0.000140 59 0.000116 -0.000141 60 0.000019 -0.000142 61 0.000330 0.000000 62 0.000211 -0.000028 63 0.000115 -0.000039 64 0.000018 -0.000041 NJ=1

sx=448579.683456 sy=-2228452.829692 tou=-796595.793624 s1=667686.817671 s2=-2447559.963907 theta=164.620855 NJ=2

sx=-471105.115634 sy=-3323385.659933 tou=-332788.181540 s1=-432791.889164 s2=-3361698.886403 theta=173.432568 NJ=3

sx=-380008.521484 sy=-1171980.561176 tou=-389915.418341 s1=-220261.726594 s2=-1331727.356065 theta=157.721283 NJ=4

sx=-174817.042307 sy=-196368.115360 tou=-113186.429863 s1=-71894.381431 s2=-299290.776236 theta=137.719132 NJ=5

sx=2250254.946492 sy=608991.337238 tou=-940398.915924 s1=2677736.389866 s2=181509.893863 theta=155.554663 NJ=6

sx=252798.799483 sy=25086.773687 tou=-1112048.633437 s1=1256804.743538 s2=-978919.170367 theta=137.922902 NJ=7

sx=-1092918.137680 sy=-517937.687407 tou=-1162821.119077 s1=392404.957485 s2=-2003260.782572 theta=128.056475 NJ=8

sx=-853332.938708 sy=-227597.572178 tou=-337658.474657 s1=-80139.900135 s2=-1000790.610751 theta=113.591210 NJ=9

sx=2978343.620407 sy=191835.446746 tou=-246028.998973 s1=2999899.492124 s2=170279.575029 theta=174.992808

NJ=10

sx=1092941.786794 sy=-50630.492118 tou=-1205166.021063 s1=1855083.879140 s2=-812772.584463 theta=147.690906

NJ=11

sx=-1701535.284748 sy=158394.548145 tou=-1282690.328703 s1=812768.366051 s2=-2355909.102654 theta=117.028733

NJ=12

sx=-2211315.124569 sy=865.147546 tou=-584568.256203 s1=145836.734683 s2=-2356286.711706 theta=103.928218

NJ=13

sx=3579786.645542 sy=169460.350932 tou=-223054.573477 s1=3594313.790609 s2=154933.205866 theta=176.273692

NJ=14

sx=2139336.650683 sy=-395244.610328 tou=-760570.381856 s1=2350049.013383 s2=-605956.973028 theta=164.514865

NJ=15

sx=-2207968.432309 sy=-1408646.941484 tou=-842287.184148 s1=-876011.375629 s2=-2740603.998164 theta=122.307956

NJ=16

sx=-3764178.598901 sy=-1344384.227186 tou=-270068.717065 s1=-1314608.749684 s2=-3793954.076404 theta=96.291535

NJ=17

sx=4112813.455675 sy=192429.224322 tou=-138499.091119 s1=4117700.251544 s2=187542.428453 theta=177.979217

NJ=18

sx=2632386.856938 sy=-195827.868942 tou=-424335.791550 s1=2694680.692152 s2=-258121.704157 theta=171.648453

NJ=19

sx=-2542544.945691 sy=-58043.406734 tou=-406342.838121 s1=6725.898753 s2=-2607314.251178 theta=99.056515

NJ=20

sx=-4100340.167973 sy=-177169.357579 tou=45199.810486 s1=-176648.668614 s2=-4100860.856939 theta=89.339998

NJ=21

sx=4470869.900781 sy=257652.480755 tou=-86026.318615 s1=4472625.671733 s2=255896.709802 theta=178.830774

NJ=22

sx=2866138.245397 sy=23606.783978 tou=-285626.789429 s1=2894554.873043 s2=-4809.843669 theta=174.318416

NJ=23

sx=-2984293.349300 sy=12029.540853 tou=-267868.482925 s1=35788.343246 s2=-3008052.151693 theta=95.068630

NJ=24

sx=-4338251.882825 sy=-248026.023918 tou=-96570.380451 s1=-245747.263294 s2=-4340530.643449 theta=91.351751

NJ=25

sx=4691023.222574 sy=270674.389954 tou=-59406.755348 s1=4691821.468486 s2=269876.144042 theta=179.230166

NJ=26

sx=3018074.086028 sy=-18592.447447 tou=-203143.353180 s1=3031603.453741 s2=-32121.815160 theta=176.189723

NJ=27

sx=-3056553.768618 sy=4600.569223 tou=-224889.255166 s1=21033.952015 s2=-3072987.151410 theta=94.179359

NJ=28

sx=-4629326.528832 sy=-248168.150134 tou=-95492.245568 s1=-246087.777724 s2=-4631406.901242 theta=91.248035

NJ=29

sx=4808948.735861 sy=255563.234763 tou=-21764.002393 s1=4809052.759774 s2=255459.210849 theta=179.726150

NJ=30

sx=3125009.644278 sy=-112493.460083 tou=-81921.250706 s1=3127081.240687 s2=-114565.056492 theta=178.551434

NJ=31

sx=-3094676.805306 sy=-256359.995174 tou=-88188.956336 s1=-253622.528282 s2=-3097414.272197 theta=91.777943

NJ=32

sx=-4864139.635507 sy=-465021.421266 tou=-57056.914380 s1=-464281.512981 s2=-4864879.543793 theta=90.742964

NJ=33

sx=4808948.735861 sy=255563.234763 tou=21764.002393 s1=4809052.759774 s2=255459.210849 theta=0.273850

NJ=34

sx=3125009.644278 sy=-112493.460083 tou=81921.250706 s1=3127081.240687 s2=-114565.056492 theta=1.448566

NJ=35

sx=-3094676.805306 sy=-256359.995174 tou=88188.956336 s1=-253622.528282 s2=-3097414.272197 theta=88.222057

NJ=36

sx=-4864139.635507 sy=-465021.421266 tou=57056.914380 s1=-464281.512981 s2=-4864879.543793 theta=89.257036

NJ=37

sx=4691023.222574 sy=270674.389954 tou=59406.755348 s1=4691821.468486 s2=269876.144042 theta=0.769834

NJ=38

sx=3018074.086028 sy=-18592.447447 tou=203143.353180 s1=3031603.453741 s2=-32121.815160 theta=3.810277

NJ=39

sx=-3056553.768618 sy=4600.569223 tou=224889.255166 s1=21033.952015 s2=-3072987.151410 theta=85.820641

NJ=40

sx=-4629326.528832 sy=-248168.150134 tou=95492.245568 s1=-246087.777724 s2=-4631406.901242 theta=88.751965 Press any key to continuePress any key to continue

32.521.510.50-0.5

第一主应力等值图

051015

第二主应力等值图

5

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