固支梁有限元課程設(shè)計(jì)

1、.一 題目 如圖所示固支梁，高3米，長15m，承受均布載荷q=10kN/，E=20GPa，u=0.167，厚度t=1m，忽略自重，按平面應(yīng)力問題分析。用有限元方法計(jì)算梁的變形及應(yīng)力分布，要求用矩形單元。q=10kN/要求：1.單元數(shù)目不得少于20個(gè)。2.采用矩形單元計(jì)算求解。3.計(jì)算結(jié)果并給出變形圖、應(yīng)力分布圖、單元?jiǎng)澐謭D。二、力學(xué)分析1.題目可以看做是平面應(yīng)力問題故有LXM=02.單元?jiǎng)澐謭D三程序框圖及程序程序框圖：開始插入基本參數(shù)插入其他參數(shù)形成整體剛度矩陣形成荷載列陣引入支承條件解方程輸出位移求應(yīng)力輸出應(yīng)力結(jié)束子程序單元?jiǎng)偠染仃嚕ˋSK=3）計(jì)算單元?jiǎng)偠染仃嚕ˋSK=1）計(jì)算單元面積（A

2、SK=2）計(jì)算S矩陣四源程序#include<stdio.h>#include<math.h>#define NE 30 /單元數(shù)#define NJ 44 /節(jié)點(diǎn)數(shù)#define NZ 16 /支承數(shù)#define NPJ 11 /節(jié)點(diǎn)載荷作用數(shù)#define DD 26 /半帶寬#define NJ2 88 /節(jié)點(diǎn)位移數(shù)int LXM=0;double E0=2e7;double MU=0.167;double LOU=0.0;double TE=1 ;double AJZNJ+13=0,0,0,0,0,3,0,1.5,3,0,3,3,0,4.5,3,0,6,3,0

3、,7.5,3,0,9,3,0,10.5,3,0,12,3,0,13.5,3,0,15,3,0,0,2,0,1.5,2,0,3,2,0,4.5,2,0,6,2,0,7.5,2,0,9,2,0,10.5,2,0,12,2,0,13.5,2,0,15,2,0,0,1,0,1.5,1,0,3,1,0,4.5,1,0,6,1,0,7.5,1,0,9,1,0,10.5,1,0,12,1,0,13.5,1,0,15,1,0,0,0,0,1.5,0,0,3,0,0,4.5,0,0,6,0,0,7.5,0,0,9,0,0,10.5,0,0,12,0,0,13.5,0,0,15,0; /節(jié)點(diǎn)坐標(biāo)int JMNE+

4、15=0,0,0,0,0,0,10,11,22,21,0,9,10,21,20,0,8,9,20,19,0,7,8,19,18,0,6,7,18,17,0,5,6,17,16,0,4,5,16,15,0,3,4,15,14,0,2,3,14,13,0,1,2,13,12,0,21,22,33,32,0,20,21,32,31,0,19,20,31,30,0,18,19,30,29,0,17,18,29,28,0,16,17,28,27,0,15,16,27,26,0,14,15,26,25,0,13,14,25,24,0,12,13,24,23,0,32,33,44,43,0,31,32,43

5、,42,0,30,31,42,41,0,29,30,41,40,0,28,29,40,39,0,27,28,39,38,0,26,27,38,37,0,25,26,37,36,0,24,25,36,35,0,23,24,35,34;int NZCNZ+1=0,1,2,21,22,23,24,43,44,45,46,65,66,67,68,87,88 ; /支撐數(shù)組 double PJNPJ+12+1=0,0,0,0,-7500,68,0,-15000,70,0,-15000,72,0,-15000,74,0,-15000,76,0,-15000,78,0,-15000,80,0,-15000,

6、82,0,-15000,84,0,-15000,86,0,-7500,88; /節(jié)點(diǎn)載荷數(shù)組 /節(jié)點(diǎn)載荷數(shù)組double AE,KZNJ2+1DD+1,PNJ2+1,S3+18+1,KE8+18+1,SZ3+15*8+1;double JDYLNJ6; /節(jié)點(diǎn)應(yīng)力矩陣double DYYL4NE4; /單元應(yīng)力矩陣int IE,JE,ME,PE;void DUGD(int,int);FILE *fp1,*fp2,*ab;void main()int NJ1,k,IN,IM,jn,m,i,j,z,JO,ii,jj,h,dh,E,l,zl,dl,r,n,o,f;double F,c,SIG1,SI

7、G2,SIG3,PYL,RYL,MAYL,MIYL,CETA;double WY8+1,YL3+1;ab=fopen("節(jié)點(diǎn)應(yīng)力.txt","w");fp1=fopen("節(jié)點(diǎn)位移.txt","w");fp2=fopen("單元應(yīng)力.txt","w");if(LXM!=0)E0=E0/(1.0-MU*MU);MU=MU/(1.0-MU); for(i=0;i<=NJ2;i+)for(j=0;j<=DD;j+)KZij=0.0;for(E=1;E<=NE;E+

8、)DUGD(E,3);for(i=1;i<=4;i+)for(ii=1;ii<=2;ii+)h=2*(i-1)+ii;dh=2*(JMEi-1)+ii;for(j=1;j<=4;j+)for(jj=1;jj<=2;jj+)l=2*(j-1)+jj;zl=2*(JMEj-1)+jj;dl=zl-dh+1;if(dl>0)KZdhdl=KZdhdl+KEhl;for(i=1;i<=NJ2;i+)Pi=0.0; if(NPJ>0)for(i=1;i<=NPJ;i+)j=(int)PJi2;Pj=PJi1;if(LOU>0)for(E=1;E<

9、;=NE;E+)DUGD(E,1);F=-LOU*(AE)*TE/4;P2*IE=P2*IE+F;P2*JE=P2*JE+F;P2*ME=P2*ME+F;P2*PE=P2*PE+F;for(i=1;i<=NZ;i+)z=NZCi;KZz1=1.0;for(j=2;j<=DD;j+)KZzj=0.0;if(z!=1)if(z>DD)JO=DD;elseJO=z;for(j=2;j<=JO;j+)KZz-j+1j=0.0;Pz=0.0;NJ1=NJ2-1;for(k=1;k<=NJ1;k+)if(NJ2>k+DD-1)IM=k+DD-1;elseIM=NJ2;I

10、N=k+1;for(i=IN;i<=IM;i+)l=i-k+1;c=KZkl/KZk1;jn=DD-l+1;for(j=1;j<=jn;j+)m=j+i-k;KZij=KZij-c*KZkm;Pi=Pi-c*Pk;PNJ2=PNJ2/KZNJ21; for(i=NJ1;i>=1;i-)if(DD>=NJ2-i+1)JO=NJ2-i+1;elseJO=DD;for(j=2;j<=JO;j+)h=j+i-1;Pi=Pi-KZij*Ph;Pi=Pi/KZi1;printf("n");printf("JD U Vn");fprint

11、f(fp1,"JD U Vn");for(i=1;i<=NJ;i+)printf("%d %-9.6f %-9.6fn",i,P2*i-1,P2*i);fprintf(fp1,"%d %-9.6f %-9.6fn",i,P2*i-1,P2*i);for(i=1;i<=NJ;i+)fprintf(fp1,"a%d=%-9.6f;b%d=%-9.6f;n",i,AJZi1+P2*i-1,i,AJZi2+P2*i);for(E=1;E<=NE;E+)DUGD(E,2);for(i=1;i<=4;i

12、+)for(j=1;j<=2;j+)h=2*(i-1)+j;dh=2*(JMEi-1)+j;WYh=Pdh; for(n=1;n<=5;n+) for(i=1;i<=3;i+) YLi=0; for(j=1;j<=8;j+) YLi=YLi+SZi8*(n-1)+j*WYj; SIG1=YL1; SIG2=YL2; SIG3=YL3; PYL=(SIG1+SIG2)/2; RYL=sqrt(pow(SIG1-SIG2)/2.0,2)+pow(SIG3,2); MAYL=PYL+RYL; MIYL=PYL-RYL; if(SIG2=MIYL) CETA=0; else C

13、ETA=90-57.29578*atan2(SIG3,(SIG2-MIYL); printf("n"); printf("E=%d(%d)n",E,n); printf("sx=%-9.6f sy=%-9.6f tou=%-9.6fn",SIG1,SIG2,SIG3); printf("s1=%-9.6f s2=%-9.6f theta=%-9.6fn",MAYL,MIYL,CETA); fprintf(fp2,"n"); fprintf(fp2,"E=%d(%d)n",E,

14、n); fprintf(fp2,"sx=%-9.6f sy=%-9.6f tou=%-9.6fn",SIG1,SIG2,SIG3); fprintf(fp2,"s1=%-9.6f s2=%-9.6f theta=%-9.6fn",MAYL,MIYL,CETA); if(n<5) DYYLn-1E-10=SIG1; /將各單元應(yīng)力記錄到單元應(yīng)力矩陣中 DYYLn-1E-11=SIG2; DYYLn-1E-12=SIG3; fprintf(ab,"各節(jié)點(diǎn)應(yīng)力：n");for(r=0;r<NJ;r+) /計(jì)算節(jié)點(diǎn)應(yīng)力（始）o=0

15、;for(n=0;n<NE;n+)if(JMn+11=r+1|JMn+12=r+1|JMn+13=r+1|JMn+14=r+1)o=o+1; for(f=0;f<5;f+)if(JMn+1f+1=r+1) JDYLr0=JDYLr0+DYYLfn0; JDYLr1=JDYLr1+DYYLfn1; JDYLr2=JDYLr2+DYYLfn2;/printf("%fn%fn%fnnn",JDYLr0,JDYLr1,JDYLr2); /檢查單元應(yīng)力各項(xiàng)是否正確求和JDYLr0=JDYLr0*1.0/o; JDYLr1=JDYLr1*1.0/o; JDYLr2=JDYL

16、r2*1.0/o;JDYLr3=(JDYLr0+JDYLr1)*0.5;JDYLr4=(float)sqrt(pow(JDYLr0-JDYLr1)*0.5,2)+pow(JDYLr2,2); JDYLr5=JDYLr3+JDYLr4; /計(jì)算節(jié)點(diǎn)應(yīng)力（終）fprintf(ab,"%2dt%fn",r+1,JDYLr5/1000000); /輸出節(jié)點(diǎn)應(yīng)力至文件fclose(ab); /關(guān)閉文件fclose(fp1);fclose(fp2);/*DUGD子程序*/void DUGD(int E,int ASK)double B3+18+1,D3+13+1,x,y,a,b,C;i

17、nt i, j, k,n,w;double xy63=0,0,0,0,-1,-1,0,1,-1,0,1,1,0,-1,1,0,0,0;a=0.75;b=0.5;AE=4*a*b;D11=E0/(1-MU*MU);D12=MU*E0/(1-MU*MU);D13=0;D21=D12;D22=D11;D23=0;D31=0;D32=0;D33=E0/(2*(1+MU);if(ASK>1)for(w=1;w<=5;w+)for(i=0;i<=3;i+) for(j=0;j<=8;j+) Bij=0.0;x=xyw1*a;y=xyw2*b; B11=(y-b)/AE; B13=(

18、b-y)/AE; B15=(b+y)/AE; B17=-(b+y)/AE; B22=(x-a)/AE; B24=-(a+x)/AE; B26=(a+x)/AE; B28=(a-x)/AE; B31=(x-a)/AE; B32=(y-b)/AE; B33=-(a+x)/AE; B34=(b-y)/AE; B35=(a+x)/AE; B36=(b+y)/AE; B37=(a-x)/AE; B38=-(b+y)/AE; for(i=1;i<=3;i+) for(j=1;j<=8;j+) Sij=0.0; for(k=1;k<=3;k+) Sij=Sij+Dik*Bkj; n=8*(

19、w-1)+j; SZin=Sij; if(ASK>2)C=E0*TE/(1-MU*MU);KE11=C*(b/(3*a)+(1-MU)*a/(6*b);KE12=C*(1+MU)/8;KE13=C*(-b)/(3*a)+(1-MU)*a/(12*b);KE14=C*(3*MU-1)/8);KE15=C*(-b)/(6*a)-(1-MU)*a/(12*b);KE16=(-C)*(1+MU)/8;KE17=C*(b/(6*a)-(1-MU)*a/(6*b);KE18=C*(1-3*MU)/8);KE21=KE12;KE22=C*(a/(3*b)+(1-MU)*b/(6*a);KE23=KE1

20、8;KE24=C*(a/(6*b)-(1-MU)*b/(6*a);KE25=KE16; KE26=C*(-a)/(6*b)-(1-MU)*b/(12*a); KE27=KE14; KE28=C*(-a)/(3*b)+(1-MU)*b/(12*a);KE31=KE13;KE32=KE23;KE33=KE11;KE34=KE16;KE35=KE17;KE36=KE14; KE37=KE15; KE38=KE12;KE41=KE14;KE42=KE24;KE43=KE34;KE44=KE22;KE45=KE23;KE46=KE28;KE47=KE12; KE48=KE26; KE51=KE15;KE

21、52=KE25;KE53=KE35;KE54=KE45;KE55=KE11;KE56=KE12;KE57=KE13;KE58=KE14; KE61=KE16;KE62=KE26;KE63=KE36;KE64=KE46;KE65=KE56;KE66=KE22;KE67=KE18;KE68=KE24;KE71=KE17;KE72=KE27;KE73=KE37;KE74=KE47;KE75=KE57;KE76=KE67;KE77=KE11;KE78=KE16; KE81=KE18;KE82=KE28;KE83=KE38;KE84=KE48;KE85=KE58;KE86=KE68;KE87=KE78;

22、KE88=KE22;節(jié)點(diǎn)位移JD U V1 0.000000 0.000000 2 -0.006277 -0.0070923 -0.008254 -0.0171874 -0.007199 -0.0269765 -0.004104 -0.0338576 -0.000000 -0.0363197 0.004104 -0.0338578 0.007199 -0.0269769 0.008254 -0.01718710 0.006277 -0.00709211 0.000000 0.000000 12 0.000000 0.000000 13 -0.001628 -0.00679114 -0.0024

23、51 -0.01723115 -0.002187 -0.02720216 -0.001263 -0.03419417 -0.000000 -0.03669418 0.001263 -0.03419419 0.002187 -0.02720220 0.002451 -0.01723121 0.001628 -0.00679122 0.000000 0.000000 23 0.000000 0.000000 24 0.001524 -0.00701925 0.002416 -0.01749426 0.002168 -0.02744427 0.001253 -0.03443728 -0.000000

24、 -0.03693729 -0.001253 -0.03443730 -0.002168 -0.02744431 -0.002416 -0.01749432 -0.001524 -0.00701933 0.000000 0.000000 34 0.000000 0.000000 35 0.006339 -0.00784436 0.008222 -0.01793837 0.007173 -0.02770838 0.004094 -0.03458739 -0.000000 -0.03705040 -0.004094 -0.03458741 -0.007173 -0.02770842 -0.0082

25、22 -0.01793843 -0.006339 -0.00784444 0.000000 0.000000 a1=0.000000 ;b1=3.000000 ;a2=1.493723 ;b2=2.992908 ;a3=2.991746 ;b3=2.982813 ;a4=4.492801 ;b4=2.973024 ;a5=5.995896 ;b5=2.966143 ;a6=7.500000 ;b6=2.963681 ;a7=9.004104 ;b7=2.966143 ;a8=10.507199;b8=2.973024 ;a9=12.008254;b9=2.982813 ;a10=13.5062

26、77;b10=2.992908 ;a11=15.000000;b11=3.000000 ;a12=0.000000 ;b12=2.000000 ;a13=1.498372 ;b13=1.993209 ;a14=2.997549 ;b14=1.982769 ;a15=4.497813 ;b15=1.972798 ;a16=5.998737 ;b16=1.965806 ;a17=7.500000 ;b17=1.963306 ;a18=9.001263 ;b18=1.965806 ;a19=10.502187;b19=1.972798 ;a20=12.002451;b20=1.982769 ;a21

27、=13.501628;b21=1.993209 ;a22=15.000000;b22=2.000000 ;a23=0.000000 ;b23=1.000000 ;a24=1.501524 ;b24=0.992981 ;a25=3.002416 ;b25=0.982506 ;a26=4.502168 ;b26=0.972556 ;a27=6.001253 ;b27=0.965563 ;a28=7.500000 ;b28=0.963063 ;a29=8.998747 ;b29=0.965563 ;a30=10.497832;b30=0.972556 ;a31=11.997584;b31=0.982

28、506 ;a32=13.498476;b32=0.992981 ;a33=15.000000;b33=1.000000 ;a34=0.000000 ;b34=0.000000 ;a35=1.506339 ;b35=-0.007844;a36=3.008222 ;b36=-0.017938;a37=4.507173 ;b37=-0.027708;a38=6.004094 ;b38=-0.034587;a39=7.500000 ;b39=-0.037050;a40=8.995906 ;b40=-0.034587;a41=10.492827;b41=-0.027708;a42=11.991778;b

29、42=-0.017938;a43=13.493661;b43=-0.007844;a44=15.000000;b44=0.000000 ;單元應(yīng)力E=1(1)sx=-85064.031346 sy=-8193.343396 tou=677.803472s1=-8187.367362 s2=-85070.007380 theta=89.494850E=1(2)sx=-86096.899427 sy=-14378.182204 tou=40514.594572s1=3867.227674 s2=-104342.309305 theta=65.755977E=1(3)sx=-22332.527918

30、 sy=-3729.532162 tou=38797.270996s1=26865.662799 s2=-52927.722879 theta=51.740991E=1(4)sx=-21299.659837 sy=2455.306646 tou=-1039.520104s1=2500.709389 s2=-21345.062580 theta=92.500898E=1(5)sx=-53698.279632 sy=-5961.437779 tou=19737.537234s1=1142.256069 s2=-60801.973479 theta=70.205800E=2(1)sx=-27269.

31、006981 sy=-5449.113903 tou=7939.760809s1=-2865.849735 s2=-29852.271149 theta=71.977291E=2(2)sx=-26082.353287 sy=1656.596840 tou=17830.315154s1=10376.554639 s2=-34802.311085 theta=63.938945E=2(3)sx=-10251.133847 sy=4300.410487 tou=19803.334170s1=18122.242565 s2=-24072.965925 theta=55.086700E=2(4)sx=-

32、11437.787541 sy=-2805.300257 tou=9912.779825s1=3690.170259 s2=-17933.258057 theta=56.764687E=2(5)sx=-18760.070414 sy=-574.351708 tou=13871.547489s1=6918.925347 s2=-26253.347470 theta=61.622507E=3(1)sx=13694.205180 sy=-2231.600468 tou=12968.910655s1=20949.727536 s2=-9487.122824 theta=29.225050E=3(2)s

33、x=14316.663192 sy=1495.693016 tou=6193.920153s1=16820.153980 s2=-1007.797773 theta=22.007829E=3(3)sx=3472.340660 sy=-315.308847 tou=7228.865310s1=9051.337721 s2=-5894.305908 theta=37.659761E=3(4)sx=2849.882648 sy=-4042.602331 tou=14003.855812s1=13825.310135 s2=-15018.029818 theta=38.087334E=3(5)sx=8

34、583.272920 sy=-1273.454658 tou=10098.887982s1=14892.182293 s2=-7582.364031 theta=31.993568E=4(1)sx=41289.050815 sy=161.234221 tou=14967.650151s1=46159.467268 s2=-4709.182231 theta=18.024690E=4(2)sx=41669.654734 sy=2440.299607 tou=-3639.739687s1=42004.495483 s2=2105.458858 theta=174.743825E=4(3)sx=11

35、885.917500 sy=-2533.584511 tou=-3006.919198s1=12487.829097 s2=-3135.496109 theta=168.680399E=4(4)sx=11505.313580 sy=-4812.649897 tou=15600.470639s1=20951.548886 s2=-14258.885203 theta=31.195309E=4(5)sx=26587.484157 sy=-1186.175145 tou=5980.365476s1=27820.469617 s2=-2419.160605 theta=11.649567E=5(1)s

36、x=55006.774539 sy=1682.836761 tou=14060.005700s1=58486.875010 s2=-1797.263710 theta=13.902306E=5(2)sx=55138.926086 sy=2474.163392 tou=-10284.959406s1=57076.222795 s2=536.866683 theta=169.332635E=5(3)sx=16171.394904 sy=-4033.414316 tou=-10065.234378s1=20329.688804 s2=-8191.708215 theta=157.552800E=5(

37、4)sx=16039.243357 sy=-4824.740946 tou=14279.730728s1=23291.627641 s2=-12077.125230 theta=26.925087E=5(5)sx=35589.084722 sy=-1175.288777 tou=1997.385661s1=35697.283019 s2=-1283.487074 theta=3.100679 E=6(1)sx=55138.926086 sy=2474.163392 tou=10284.959406s1=57076.222795 s2=536.866683 theta=10.667365E=6(

38、2)sx=55006.774539 sy=1682.836761 tou=-14060.005700s1=58486.875010 s2=-1797.263710 theta=166.097694E=6(3)sx=16039.243357 sy=-4824.740946 tou=-14279.730728s1=23291.627641 s2=-12077.125230 theta=153.074913E=6(4)sx=16171.394904 sy=-4033.414316 tou=10065.234378s1=20329.688804 s2=-8191.708215 theta=22.447

39、200E=6(5)sx=35589.084722 sy=-1175.288777 tou=-1997.385661s1=35697.283019 s2=-1283.487074 theta=176.899321E=7(1)sx=41669.654734 sy=2440.299607 tou=3639.739687s1=42004.495483 s2=2105.458858 theta=5.256175 E=7(2)sx=41289.050815 sy=161.234221 tou=-14967.650151s1=46159.467268 s2=-4709.182231 theta=161.97

40、5310E=7(3)sx=11505.313580 sy=-4812.649897 tou=-15600.470639s1=20951.548886 s2=-14258.885203 theta=148.804691E=7(4)sx=11885.917500 sy=-2533.584511 tou=3006.919198s1=12487.829097 s2=-3135.496109 theta=11.319601E=7(5)sx=26587.484157 sy=-1186.175145 tou=-5980.365476s1=27820.469617 s2=-2419.160605 theta=

41、168.350433E=8(1)sx=14316.663192 sy=1495.693016 tou=-6193.920153s1=16820.153980 s2=-1007.797773 theta=157.992171E=8(2)sx=13694.205180 sy=-2231.600468 tou=-12968.910655s1=20949.727536 s2=-9487.122824 theta=150.774950E=8(3)sx=2849.882648 sy=-4042.602331 tou=-14003.855812s1=13825.310135 s2=-15018.029818

42、 theta=141.912666E=8(4)sx=3472.340660 sy=-315.308847 tou=-7228.865310s1=9051.337721 s2=-5894.305908 theta=142.340239E=8(5)sx=8583.272920 sy=-1273.454658 tou=-10098.887982s1=14892.182293 s2=-7582.364031 theta=148.006432E=9(1)sx=-26082.353287 sy=1656.596840 tou=-17830.315154s1=10376.554639 s2=-34802.3

43、11085 theta=116.061055E=9(2)sx=-27269.006981 sy=-5449.113903 tou=-7939.760809s1=-2865.849735 s2=-29852.271149 theta=108.022709E=9(3)sx=-11437.787541 sy=-2805.300257 tou=-9912.779825s1=3690.170259 s2=-17933.258057 theta=123.235313E=9(4)sx=-10251.133847 sy=4300.410487 tou=-19803.334170s1=18122.242565

44、s2=-24072.965925 theta=124.913300E=9(5)sx=-18760.070414 sy=-574.351708 tou=-13871.547489s1=6918.925347 s2=-26253.347470 theta=118.377493E=10(1)sx=-86096.899427 sy=-14378.182204 tou=-40514.594572s1=3867.227674 s2=-104342.309305 theta=114.244023E=10(2)sx=-85064.031346 sy=-8193.343396 tou=-677.803472s1

45、=-8187.367362 s2=-85070.007380 theta=90.505150E=10(3)sx=-21299.659837 sy=2455.306646 tou=1039.520104s1=2500.709389 s2=-21345.062580 theta=87.499102E=10(4)sx=-22332.527918 sy=-3729.532162 tou=-38797.270996s1=26865.662799 s2=-52927.722879 theta=128.259009E=10(5)sx=-53698.279632 sy=-5961.437779 tou=-19737.537234s1=1142.256069 s2=-60801.973479 theta=109.794200E=11(1)sx=-23113.069101 sy=-8403.431460 tou=11782.191726s1=-186