固支梁有限元课程设计.doc

一 题目 如图所示固支梁，高3米，长15m，承受均布载荷q=10kN/，E=20GPa，u=0.167，厚度t=1m，忽略自重，按平面应力问题分析。用有限元方法计算梁的变形及应力分布，要求用矩形单元。q=10kN/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.单元划分图三程序框图及程序程序框图：开始插入基本参数插入其他参数形成整体刚度矩阵形成荷载列阵引入支承条件解方程输出位移求应力输出应力结束子程序单元刚度矩阵（ASK=3）计算单元刚度矩阵（ASK=1）计算单元面积（ASK=2）计算S矩阵四源程序#include#include#define NE 30 /单元数#define NJ 44 /节点数#define NZ 16 /支承数#define NPJ 11 /节点载荷作用数#define DD 26 /半带宽#define NJ2 88 /节点位移数int LXM=0;double E0=2e7;double MU=0.167;double LOU=0.0;double TE=1 ;double AJZNJ+13=0,0,0,0,0,3,0,1.5,3,0,3,3,0,4.5,3,0,6,3,0,7.5,3,0,9,3,0,10.5,3,0,12,3,0,13.5,3,0,15,3,0,0,2,0,1.5,2,0,3,2,0,4.5,2,0,6,2,0,7.5,2,0,9,2,0,10.5,2,0,12,2,0,13.5,2,0,15,2,0,0,1,0,1.5,1,0,3,1,0,4.5,1,0,6,1,0,7.5,1,0,9,1,0,10.5,1,0,12,1,0,13.5,1,0,15,1,0,0,0,0,1.5,0,0,3,0,0,4.5,0,0,6,0,0,7.5,0,0,9,0,0,10.5,0,0,12,0,0,13.5,0,0,15,0; /节点坐标int JMNE+15=0,0,0,0,0,0,10,11,22,21,0,9,10,21,20,0,8,9,20,19,0,7,8,19,18,0,6,7,18,17,0,5,6,17,16,0,4,5,16,15,0,3,4,15,14,0,2,3,14,13,0,1,2,13,12,0,21,22,33,32,0,20,21,32,31,0,19,20,31,30,0,18,19,30,29,0,17,18,29,28,0,16,17,28,27,0,15,16,27,26,0,14,15,26,25,0,13,14,25,24,0,12,13,24,23,0,32,33,44,43,0,31,32,43,42,0,30,31,42,41,0,29,30,41,40,0,28,29,40,39,0,27,28,39,38,0,26,27,38,37,0,25,26,37,36,0,24,25,36,35,0,23,24,35,34;int NZCNZ+1=0,1,2,21,22,23,24,43,44,45,46,65,66,67,68,87,88 ; /支撑数组 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,-15000,82,0,-15000,84,0,-15000,86,0,-7500,88; /节点载荷数组 /节点载荷数组double AE,KZNJ2+1DD+1,PNJ2+1,S3+18+1,KE8+18+1,SZ3+15*8+1;double JDYLNJ6; /节点应力矩阵double DYYL4NE4; /单元应力矩阵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,SIG2,SIG3,PYL,RYL,MAYL,MIYL,CETA;double WY8+1,YL3+1;ab=fopen(节点应力.txt,w);fp1=fopen(节点位移.txt,w);fp2=fopen(单元应力.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+)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;jj0)KZdhdl=KZdhdl+KEhl;for(i=1;i0)for(i=1;i0)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;jDD)JO=DD;elseJO=z;for(j=2;j=JO;j+)KZz-j+1j=0.0;Pz=0.0;NJ1=NJ2-1;for(k=1;kk+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=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);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 %-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+)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 CETA=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,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(n5) DYYLn-1E-10=SIG1; /将各单元应力记录到单元应力矩阵中 DYYLn-1E-11=SIG2; DYYLn-1E-12=SIG3; fprintf(ab,各节点应力：n);for(r=0;rNJ;r+) /计算节点应力（始）o=0;for(n=0;nNE;n+)if(JMn+11=r+1|JMn+12=r+1|JMn+13=r+1|JMn+14=r+1)o=o+1; for(f=0;f1)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=(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;k2)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=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=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;KE75=KE57;KE76=KE67;KE77=KE11;KE78=KE16; KE81=KE18;KE82=KE28;KE83=KE38;KE84=KE48;KE85=KE58;KE86=KE68;KE87=KE78;KE88=KE22;节点位移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 -0.002451 -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 -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 -0.008222 -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=13.506277;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=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=0.982506 ;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;b42=-0.017938;a43=13.493661;b43=-0.007844;a44=15.000000;b44=0.000000 ;单元应力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 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=-27269.006981 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=-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)sx=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=8583.272920 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=11885.917500 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)sx=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(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(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=22.447200E=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=161.975310E=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=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 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=-34802.311085 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 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=-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=-1868.923380 s2=-29647.577181 theta=60.986861E=11(2)sx=-22332.527918 sy=-3729.532162 tou=38797.270996s1=26865.662799 s2=-52927.722879 theta=51.740991E