悬臂梁受载荷的 矩形单元有限元课程设计

1、有限元课程设计姓名：XXX专业：工程力学081学号：XXXXXXXXX指导老师：XXX2011年6月29日一、题目已知：悬臂梁的材料参数为E=190GPa =0.25 t=10 cm =0 尺寸参数如图所示。要求：1.单元数目不得少于20个。2.采用矩形单元计算求解。3.计算结果并给出变形图、应力分布图、单元划分图。二、力学分析1.题目可以看做是平面应力问题故有LXM=02.单元划分图3.简化成力学模型根据力学模型可以写出支承数组NZC、节点载荷数组PJ 三、程序代码#include <stdio.h>#include <math.h>#define NE 40#def

2、ine NJ 55#define NZ 10#define NPJ 14#define NJ2 110#define DD 26int LXM=0;double MU=0.25;double LOU=0.0;double TE=0.1;double AJZNJ+13=0,0,0,0,0,0,0,0.5,0,0,1,0,0,1.5,0,0,2,0,0,2.5,0,0,3,0,0,3.5,0,0,4,0,0,4.5,0,0,5,0,0,0,0.25,0,0.5,0.25,0,1,0.25,0,1.5,0.25,0,2,0.25,0,2.5,0.25,0,3,0.25,0,3.5,0.25,0,4,

3、0.25,0,4.5,0.25,0,5,0.25,0,0,0.5,0,0.5,0.5,0,1,0.5,0,1.5,0.5,0,2,0.5,0,2.5,0.5,0,3,0.5,0,3.5,0.5,0,4,0.5,0,4.5,0.5,0,5,0.5,0,0,0.75,0,0.5,0.75,0,1,0.75,0,1.5,0.75,0,2,0.75,0,2.5,0.75,0,3,0.75,0,3.5,0.75,0,4,0.75,0,4.5,0.75,0,5,0.75,0,0,1,0,0.5,1,0,1,1,0,1.5,1,0,2,1,0,2.5,1,0,3,1,0,3.5,1,0,4,1,0,4.5,

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

5、,35,34,0,24,25,36,35,0,25,26,37,36,0,26,27,38,37,0,27,28,39,38,0,28,29,40,39,0,29,30,41,40,0,30,31,42,41,0,31,32,43,42,0,32,33,44,43,0,43,44,55,54,0,42,43,54,53,0,41,42,53,52,0,40,41,52,51,0,39,40,51,50,0,38,39,50,49,0,37,38,49,48,0,36,37,48,47,0,35,36,47,46,0,34,35,46,45;int NZCNZ+1=0,1,2,23,24,45,

6、46,67,68,89,90;double PJNPJ+12+1=0,0,0,0,-104166.7,21,0,-125000,43,0,125000,87,0,250000,89,0,500000,91,0,500000,93,0,500000,95,0,500000,97,0,500000,99,0,500000,101,0,500000,103,0,500000,105,0,500000,107,0,354166.7,109;double AE,KZNJ2+1DD+1,PNJ2+1,S3+18+1,KE8+18+1,SZ3+132+1;int IE,JE,ME,PE;void DUGD(

7、int,int);FILE *fp1,*fp2;void main()int NJ1,k,IN,IM,jn,m,i,j,z,JO,ii,jj,h,dh,E,l,zl,dl,n;double F,c,SIG1,SIG2,SIG3,PYL,RYL,MAYL,MIYL,CETA;double WY8+1,YL3+1;fp1=fopen("data1.doc","wb");fp2=fopen("data2.doc","wb");if(LXM!=0)E0=E0/(1.0-MU*MU);MU=MU/(1.0-MU); for(

8、i=0;i<=NJ2;i+)for(j=0;j<=DD;j+)KZij=0.0;for(E=1;E<=NE;E+)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)

9、for(i=1;i<=NPJ;i+)j=(int)PJi2;Pj=PJi1;if(LOU>0)for(E=1;E<=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=N

10、J2-1;for(k=1;k<=NJ1;k+)if(NJ2>k+DD-1)IM=k+DD-1;elseIM=NJ2;IN=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

11、=Pi/KZi1;printf("n");printf("JD U Vn");fprintf(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 %-11.10f %-11.10fn",i,P2*i-1,P2*i);for(E=1;E<=NE;E+)DUGD(E,2);for(i=1;i<=4;i+)for(j=1;j<=2;j+)h=2*(i-

12、1)+j;dh=2*(JMEi-1)+j;WYh=Pdh; for(n=1;n<=4;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 CETA=90-57.29578*atan2(SIG3,(

13、SIG2-MIYL); printf("n"); printf("E=%dn",E); 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,"E= %d n= %dn sx= %-9.6f sy= %-9.6f tou= %-9.6fn sl= %-9.6f s2= %-9.6f theta= %-9

14、.6fn",E,n,SIG1,SIG2,SIG3,MAYL,MIYL,CETA);/*DUGD子程序*/void DUGD(int E,int ASK)double B3+18+1,D3+13+1,x,y,a,b,C;int i, j, k,n,w;double xy53=0,0,0,0,-1,-1,0,1,-1,0,1,1,0,-1,1;a=0.25;b=0.125;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

15、>1)for(w=1;w<=4;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=(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)

16、/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*(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=(-

17、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=KE18;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

18、=KE15; KE38=KE12;KE41=KE14;KE42=KE24;KE43=KE34;KE44=KE22;KE45=KE23;KE46=KE28;KE47=KE12; KE48=KE26; KE51=KE15;KE52=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;

19、KE75=KE57;KE76=KE67;KE77=KE11;KE78=KE16; KE81=KE18;KE82=KE28;KE83=KE38;KE84=KE48;KE85=KE58;KE86=KE68;KE87=KE78;KE88=KE22;四、计算结果I.位移JD U V1 0.0000000000 0.00000000002 -0.0002259887 -0.00018394513 -0.0004448528 -0.00070125424 -0.0006390595 -0.00153658955 -0.0008095061 -0.00264487206 -0.0009575557 -0.0

20、0399131257 -0.0010830612 -0.00554033338 -0.0011860719 -0.00725622109 -0.0012664607 -0.009103719210 -0.0013220882 -0.011046161111 -0.0013541695 -0.013038363312 0.0000000000 0.000000000013 -0.0000542483 -0.000161300914 -0.0001083947 -0.000686138715 -0.0001550339 -0.001522355916 -0.0001976708 -0.002632

21、410417 -0.0002355506 -0.003980535918 -0.0002686865 -0.005531279419 -0.0002970898 -0.007248861420 -0.0003208406 -0.009097952121 -0.0003401072 -0.011042431822 -0.0003543703 -0.013037482323 0.0000000000 0.000000000024 0.0001133227 -0.000161997225 0.0002263054 -0.000690342126 0.0003261282 -0.00152553672

22、7 0.0004114825 -0.002634739028 0.0004838244 -0.003982436229 0.0005430406 -0.005532663530 0.0005891895 -0.007249730531 0.0006219283 -0.009097839732 0.0006399326 -0.011041745433 0.0006470210 -0.013042675534 0.0000000000 0.000000000035 0.0002888781 -0.000186329236 0.0005704587 -0.000714688237 0.0008143

23、055 -0.001545438438 0.0010280250 -0.002652083139 0.0012106056 -0.003996971040 0.0013621718 -0.005544474541 0.0014827101 -0.007258806642 0.0015723161 -0.009103713743 0.0016297494 -0.011044171144 0.0016587587 -0.013053124145 0.0000000000 0.000000000046 0.0004965828 -0.000241943047 0.0009295406 -0.0007

24、55480248 0.0013201152 -0.001582957449 0.0016620002 -0.002684233850 0.0019548509 -0.004024197751 0.0021987670 -0.005566697552 0.0023936836 -0.007276015053 0.0025396019 -0.009115939254 0.0026392930 -0.011050699255 0.0026910605 -0.0130618521II应力E= 1 n= 1 sx= -91600747.038557 sy= -22900186.759639 tou= -

25、27959659.271743 sl= -12959561.599575 s2= -101541372.198620 theta= 109.572058E= 1 n= 2 sx= -87011515.298802 sy= -4543259.800620 tou= 24249405.011048 sl= 2058654.663438 s2= -93613429.762860 theta= 74.770306E= 1 n= 3 sx= -17399429.588414 sy= 12859761.626977 tou= 27691328.815864 sl= 29285107.864271 s2=

26、-33824775.825708 theta= 59.325342E= 1 n= 4 sx= -21988661.328169 sy= -5497165.332042 tou= -24517735.466927 sl= 12124280.419387 s2= -39610107.079598 theta= 125.705649E= 2 n= 1 sx= -84123694.776919 sy= -3821304.670149 tou= -26421908.406934 sl= 4092411.678438 s2= -92037411.125505 theta= 106.673664E= 2 n

27、= 2 sx= -85649534.179315 sy= -9924662.279736 tou= 23652307.139230 sl= -3144117.940791 s2= -92430078.518261 theta= 74.003683E= 2 n= 3 sx= -18883913.451097 sy= 6766742.902318 tou= 22507927.587432 sl= 19846932.422066 s2= -31964102.970844 theta= 59.837544E= 2 n= 4 sx= -17358074.048700 sy= 12870100.51190

28、5 tou= -27566287.958732 sl= 29193822.731317 s2= -33681796.268112 theta= 120.632427E= 3 n= 1 sx= -75655050.353517 sy= -7426041.323287 tou= -24687697.851873 sl= 569807.324891 s2= -83650899.001694 theta= 107.946096E= 3 n= 2 sx= -75833749.945674 sy= -8140839.691917 tou= 20172791.902704 sl= -2585212.9219

29、52 s2= -81389376.715640 theta= 74.602339E= 3 n= 3 sx= -16019763.606238 sy= 6812656.892942 tou= 20038767.208586 sl= 18459014.750628 s2= -27666121.463924 theta= 59.835217E= 3 n= 4 sx= -15841064.014080 sy= 7527455.261572 tou= -24821722.545992 sl= 23277477.707197 s2= -31591086.459704 theta= 122.396180E=

30、 4 n= 1 sx= -66202993.446308 sy= -5733150.567075 tou= -21315171.454291 sl= 1024995.027357 s2= -72961139.040740 theta= 107.591635E= 4 n= 2 sx= -66562123.895291 sy= -7169672.363009 tou= 17538979.439997 sl= -2377035.803027 s2= -71354760.455273 theta= 74.716673E= 4 n= 3 sx= -14756589.369573 sy= 5781711.

31、268421 tou= 17269631.603259 sl= 15604739.128667 s2= -24579617.229820 theta= 60.368627E= 4 n= 4 sx= -14397458.920590 sy= 7218233.064354 tou= -21584519.291029 sl= 20549587.721899 s2= -27728813.578135 theta= 121.700930E= 5 n= 1 sx= -57483868.969439 sy= -4900108.631546 tou= -18661034.933377 sl= 1049245.

32、474934 s2= -63433223.075919 theta= 107.682884E= 5 n= 2 sx= -57825367.468371 sy= -6266102.627274 tou= 14830593.982133 sl= -2304585.681978 s2= -61786884.413667 theta= 75.044449E= 5 n= 3 sx= -13169862.247692 sy= 4897773.677896 tou= 14574470.107934 sl= 13011114.252654 s2= -21283202.822450 theta= 60.8961

33、14E= 5 n= 4 sx= -12828363.748760 sy= 6263767.673624 tou= -18917158.807576 sl= 17906998.031755 s2= -24471594.106891 theta= 121.611680E= 6 n= 1 sx= -48687493.703055 sy= -3981634.185946 tou= -15961610.451903 sl= 1132261.081505 s2= -53801388.970506 theta= 107.764792E= 6 n= 2 sx= -49036638.112660 sy= -53

34、78211.824363 tou= 12118734.992512 sl= -2239880.349318 s2= -52174969.587705 theta= 75.481329E= 6 n= 3 sx= -11596177.520105 sy= 3981903.323775 tou= 11856876.685309 sl= 10379288.647076 s2= -17993562.843406 theta= 61.650891E= 6 n= 4 sx= -11247033.110501 sy= 5378480.962193 tou= -16223468.759107 sl= 15294

35、900.213409 s2= -21163452.361717 theta= 121.434907E= 7 n= 1 sx= -39918748.344176 sy= -3098739.382242 tou= -13245029.959340 sl= 1170742.101271 s2= -44188229.827689 theta= 107.866515E= 7 n= 2 sx= -40262122.278421 sy= -4472235.119221 tou= 9435628.770561 sl= -2137000.844612 s2= -42597356.553029 theta= 76

36、.099129E= 7 n= 3 sx= -10021243.971886 sy= 3087984.457413 tou= 9178098.319878 sl= 7811688.214528 s2= -14744947.729000 theta= 62.766420E= 7 n= 4 sx= -9677870.037641 sy= 4461480.194392 tou= -13502560.410024 sl= 12633177.847007 s2= -17849567.690255 theta= 121.182165E= 8 n= 1 sx= -31092723.270191 sy= -21

37、79885.367163 tou= -10569178.557469 sl= 1271671.119138 s2= -34544279.756492 theta= 108.085386E= 8 n= 2 sx= -31415457.777034 sy= -3470823.394535 tou= 6648782.677684 sl= -1969551.513176 s2= -32916729.658394 theta= 77.276187E= 8 n= 3 sx= -8458176.130164 sy= 2268497.017183 tou= 6406731.797552 sl= 5260493

38、.562438 s2= -11450172.675419 theta= 64.967038E= 8 n= 4 sx= -8135441.623321 sy= 3559435.044555 tou= -10811229.437602 sl= 10003262.594230 s2= -14579269.172996 theta= 120.796252E= 9 n= 1 sx= -21378869.845606 sy= -961676.411678 tou= -7782648.833354 sl= 1666590.576832 s2= -24007136.834116 theta= 108.6602

39、65E= 9 n= 2 sx= -21791872.859591 sy= -2613688.467615 tou= 3271047.054651 sl= -2071125.419918 s2= -22334435.907288 theta= 80.582190E= 9 n= 3 sx= -7053611.675584 sy= 1070876.828387 tou= 2961294.794163 sl= 2035669.001644 s2= -8018403.848842 theta= 71.954350E= 9 n= 4 sx= -6640608.661600 sy= 2722888.8843

40、24 tou= -8092401.093843 sl= 7390243.118429 s2= -11307962.895705 theta= 119.974528E= 10 n= 1 sx= -12247815.450387 sy= -227674.115314 tou= -4292527.878079 sl= 1147832.040449 s2= -13623321.606150 theta= 107.767640E= 10 n= 2 sx= -12825072.044602 sy= -2536700.492176 tou= 1124223.883037 sl= -2415287.85611

41、1 s2= -12946484.680667 theta= 83.836126E= 10 n= 3 sx= -5602736.363114 sy= -731116.571804 tou= 691281.437376 sl= -634923.332897 s2= -5698929.602021 theta= 82.078044E= 10 n= 4 sx= -5025479.768899 sy= 1577909.805058 tou= -4725470.323740 sl= 4040870.970251 s2= -7488440.934092 theta= 117.528965E= 11 n= 1

42、 sx= -5642176.958466 sy= -888878.953209 tou= -5315565.894964 sl= 2557160.535350 s2= -9088216.447024 theta= 122.955024E= 11 n= 2 sx= -6833766.649600 sy= -5655237.717747 tou= 1175275.100877 sl= -4929776.290742 s2= -7559228.076605 theta= 58.314233E= 11 n= 3 sx= 1820688.011521 sy= -3491624.052466 tou= 2

43、81582.832525 sl= 1835571.806612 s2= -3506507.847556 theta= 3.025701 E= 11 n= 4 sx= 3012277.702656 sy= 1274734.712072 tou= -6209258.163316 sl= 8413247.099118 s2= -4126234.684390 theta= 138.982432E= 12 n= 1 sx= -7786640.642310 sy= -1861239.038518 tou= -8959172.062971 sl= 4612392.079113 s2= -14260271.7

44、59941 theta= 125.850756E= 12 n= 2 sx= -7670308.865151 sy= -1395911.929880 tou= 2371199.222938 sl= -600604.837418 s2= -8465615.957613 theta= 71.458398E= 12 n= 3 sx= 7436852.849395 sy= 2380878.498756 tou= 2458448.055808 sl= 8435150.688320 s2= 1382580.659831 theta= 22.100512E= 12 n= 4 sx= 7320521.07223

45、6 sy= 1915551.390119 tou= -8871923.230102 sl= 13892433.576394 s2= -4656361.114040 theta= 143.470655E= 13 n= 1 sx= -9803133.399768 sy= -3111332.061235 tou= -11632881.247566 sl= 5647269.630544 s2= -18561735.091548 theta= 126.976737E= 13 n= 2 sx= -9604208.110874 sy= -2315630.905659 tou= 5539960.828423

46、sl= 671219.564288 s2= -12591058.580820 theta= 61.668829E= 13 n= 3 sx= 13292914.657110 sy= 3408649.786337 tou= 5689154.795093 sl= 15886772.885959 s2= 814791.557489 theta= 24.509681E= 13 n= 4 sx= 13093989.368217 sy= 2612948.630760 tou= -11483687.280895 sl= 20476389.711449 s2= -4769451.712472 theta= 14

47、7.264668E= 14 n= 1 sx= -11793293.671104 sy= -4000214.339460 tou= -14307412.389268 sl= 6931768.194987 s2= -22725276.205552 theta= 127.382659E= 14 n= 2 sx= -11688935.748333 sy= -3582782.648376 tou= 8356446.509913 sl= 1651639.269641 s2= -16923357.666350 theta= 57.937247E= 14 n= 3 sx= 18529542.783908 sy= 3971836.984683 tou= 8434714.951991 sl= 22391879.9399