有限元报告——温度场.doc

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1、精选优质文档-倾情为你奉上有限元上机报告温度场的有限元计算一问题 如图一平面结构在无热源情况下，给定热边界条件，用有限元分析温度分布。xy10000100ABDC二解决步骤1 对问题的分析采用简单的三角形单元，单元内温度假定为线性分布，即与平面结构一样，可用单元3个顶点的温度插值单元内部温度场，有其中为单元的节点温度列阵，而形状函数矩阵为简单三角形单元内假定的温度场是线性分布的，其形状函数应为对任一个单元，如面积域为，则单元泛函数为而所以，泛函数单元刚度矩阵所以所以2.数据准备 如图所示，划分单元格 7 1 2 3 4 5 6 xy13 每节点有一个自由度，边界约束为1,2,3,4,5,6,7

2、,12,13,18,19,24,25,30,31,33,34,35,36，温度相当于载荷分布，所以只有边界处有载荷。和之前分析步骤相同，可得数据文件INP.DAT。3.程序运行结果三 改变边界条件 单元格不变，边界条件改变如下，则程序的运行结果为四 思考与讨论1.分析采用该种单元分析平面温度场时是否可以收敛于真实解。 对同样的三角形单元，用节点温度插值单元内部温度的形状函数，与用节点位移插值单元内部位移的形状函数是完全一样的。与位移单元的分析一样，这种单元在单元交界处温度也是连续的，满足本问题的相容性要求。这种单元内部温度T(x,y)为完全的一次多项式，可以实现任意的常温度导数的温度状态，满足

3、插值函数的完备性要求。因而，采用这种单元分析平面温度场时，有限元分析是可以收敛于真实解的。附录：1. input.TXT1,3,36,8,20,50,22.1,0.3,10.,0.,0.,20.,0.,40.,0.,60.,0.,80.,0.,100.,0.,0.,20.,20.,20.,40.,20.,60.,20.,80.,20.,100.,20.,0.,40.,20.,40.,40.,40.,60.,40.,80.,40.,100.,40.,0.,60.,20.,60.,40.,60.,60.,60.,80.,60.,100.,60.,0.,80.,20.,80.,40.,80.,60.

4、,80.,80.,80.,100.,80.,0.,100.,20.,100.,40.,100.,60.,100.,80.,100.,100.,100.,0.,20.,40.,60.,80.,100.,20.,0.,0.,0.,0.,80.,40.,0.,0.,0.,0.,60.,60.,0.,0.,0.,0.,40.,80.,0.,0.,0.,0.,20.,100.,80.,60.,40.,20.,0.,1,2,8,2,3,9,3,4,10,4,5,11,5,6,12,1,8,7,2,9,8,3,10,9,4,11,10,5,12,11,7,8,14,8,9,15,9,10,16,10,11,

5、17,11,12,18,7,14,13,8,15,14,9,16,15,10,17,16,11,18,17,13,14,20,14,15,21,15,16,22,16,17,23,17,18,24,13,20,19,14,21,20,15,22,21,16,23,22,17,24,23,19,20,26,20,21,27,21,22,28,22,23,29,23,24,30,19,26,25,20,27,26,21,28,27,22,29,28,23,30,29,25,26,32,26,27,33,27,28,34,28,29,35,29,30,36,25,32,31,26,33,32,27,

6、34,33,28,35,34,29,36,35,1,2,3,4,5,6,7,12,13,18,19,24,25,30,31,32,33,34,35,36,2. PLANE.FORPROGRAM MAINDIMENSION SK(300,30),EK(12,12),Q(300),MC(55),XY(2,100),XYE(2,4),QE *(12),NX(4,100) OPEN (7,FILE=input.TXT)REWIND 7READ (7,*) NF,NE,NN,MB,ND,LE,LSREAD (7,*) E,UM,T10FORMAT (7I5)12 FORMAT (3F15.2)WRITE

7、(*,600) NF,NE,NN,MB,ND,LE,LS,E,UM,TME=NE*NFMS=NN*NFCALL INPUT (XY,Q,NX,MC,LS,NN,MS,NE,LE,ND)WRITE(*,102)(XY(I,J),I=1,LS),J=1,NN)102FORMAT (10X,XY/,(2X,6F12.3) WRITE (*,101)(Q(I),I=1,MS)101FORMAT(10X,Q/,(2X,6F12.3)WRITE(*,500)(NX(I,J),I=1,NE),J=1,LE)WRITE(*,400)(MC(I),I=1,ND)500 FORMAT(10X,NX/,(2X,12

8、I6)600 FORMAT(10X,NF NE NN MB ND LE LS E UM T/7(2X,I4),3(2X,F8.4)400 FORMAT(10X,MC/,(2X,10I6)CALL STIFS(SK,EK,Q,NX,XY,XYE,MC,MS,MB,ME,ND,LE,NE,NF,NN,LS,E,UM,T *) CALL SOLVE(SK,Q,MS,MB)OPEN (9,FILE=OUT.DAT)REWIND 9WRITE (9,200)WRITE (9,250) (Q(I),I=1,MS,3)200 FORMAT(5X,DISPLACEMENT)250FORMAT(2X,5E14.

9、5)WRITE(9,222) (Q(I),I=1,13,3)222FORMAT(2X,E14.5)cCALL STRES(Q,QE,NX,XY,XYE,MS,ME,NE,LE,NF,NN,LS,E,UM,T)STOP 1000ENDSUBROUTINE INPUT(XY,Q,NX,MC,LS,NN,MS,NE,LE,ND)DIMENSION XY(LS,NN),Q(MS),NX(NE,LE),MC(ND)READ(7,*)XYREAD(7,*)QREAD(7,*)NXREAD(7,*)MCCLOSE(7)10FORMAT(6F11.2)20FORMAT(12I5)RETURN ENDSUBRO

10、UTINE STIFS(SK,EK,Q,NX,XY,XYE,MC,MS,MB,ME,ND,LE,NE,NF,NN,LS,E *,UM,T)DIMENSION SK(MS,MB),EK(ME,ME),Q(MS),NX(NE,LE),MC(ND),XY(LS,NN),XYE *(LS,NE)DO 35 I=1,MSDO 35 J=1,MB35SK(I,J)=0.DO 200 L=1,LEDO 40 J=1,NELJ=NX(J,L)DO 40 I=1,LS40XYE(I,J)=XY(I,LJ)DO 50 I=1,MEDO 50 J=1,ME50EK(I,J)=0.0CALL STIFE(EK,XYE

11、,ME,NE,NF,LS,E,UM,T)IF(L.EQ.1) WRITE(*,70)EK70FORMAT(10X,EK/,(6E14.5)DO 200 I=1,NEDO 200 II=1,NFM=NF*(I-1)+IIM1=NF*(NX(I,L)-1)+IIDO 200 J=1,NEDO 200 JJ=1,NFN=NF*(J-1)+JJN1=NF*(NX(J,L)-1)+JJMN=N1-M1+1IF(MN)200,200,150150SK(M1,MN)=SK(M1,MN)+EK(M,N)200CONTINUE DO 220 I=1,NDM=MC(I)Q(M)=SK(M,1)*Q(M)*1E82

12、20SK(M,1)=SK(M,1)*1E8RETURNENDSUBROUTINE SOLVE(SK,Q,MS,MB)DIMENSION SK(MS,MB),Q(MS)K1=MS-1DO 125 K=1,K1IF(K+MB-1-MS) 105,106,106105N=K+MB-1GOTO 110106N=MS110I1=K+1DO 125 I=I1,NL=I-K+1C=SK(K,L)/SK(K,1)J1=MB-L+1DO 122 J=1,J1M=J+I-K122SK(I,J)=SK(I,J)-C*SK(K,M)125Q(I)=Q(I)-C*Q(K)Q(MS)=Q(MS)/SK(MS,1)M=MS

13、-1DO 145 I1=1,MI=MS-I1IF(MS-I+1-MB) 135,136,136135N=MS-I+1GOTO 140136N=MB140DO 142 J=2,NL=J+I-1142Q(I)=Q(I)-SK(I,J)*Q(L)145Q(I)=Q(I)/SK(I,1)WRITE(*,147)147FORMAT(5X,DISPLACEMENT)WRITE(*,150)(Q(I),I=1,MS)150FORMAT(2X,15E14.5)RETURNENDSUBROUTINE STRES(Q,QE,NX,XY,XYE,MS,ME,NE,LE,NF,NN, *LS,E,UM,T)DIMEN

14、SION Q(MS),QE(ME),NX(NE,LE),XY(LS,NN),XYE(LS, *NE)DO 400L=1,LEDO 160I=1,NEDO 160J=1,NFN=NF*(I-1)+JN1=NF*(NX(I,L)-1)+J160QE(N)=Q(N1)WRITE(*,165)LWRITE(*,170)(QE(I),I=1,ME)165FORMAT(4X,L=,I4)170FORMAT(6E14.5)DO 200 J=1,NELJ=NX(J,L)DO 200 I=1,LS200XYE(I,J)=XY(I,LJ)CALL STE(XYE,QE,NE,LS,ME,E,UM,T)400CON

15、TINUERETURNENDSUBROUTINE STIFE(EK,XYE,ME,NE,NF,LS,E,UM,T)DIMENSION EK(ME,ME),XYE(LS,NE)B(1)=XYE(2,2)-XYE(2,3)B(2)=XYE(2,3)-XYE(2,1)B(3)=XYE(2,1)-XYE(2,2)C(1)=XYE(1,3)-XYE(1,2)C(2)=XYE(1,1)-XYE(1,3)C(3)=XYE(1,2)-XYE(1,1)AE=(B(2)*C(3)-B(3)*C(2)/2DO 30 I=1,3DO 30 J=1,330EK(I,J)=B(I)*B(J)+C(I)*C(J)RETUR

16、NENDSUBROUTINE STE(XYE,QE,NE,LS,ME,E,UM,T)DIMENSION QE(ME),XYE(LS,NE)A=(XYE(1,2)-XYE(1,1)/2B=(XYE(2,4)-XYE(2,1)/2CALL STR(QE,ME,A,B,E,UM,-A,-B,T)CALL STR(QE,ME,A,B,E,UM,A,-B,T)CALL STR(QE,ME,A,B,E,UM,A,B,T)CALL STR(QE,ME,A,B,E,UM,-A,B,T)RETURNENDSUBROUTINE STR(QE,ME,A,B,E,UM,X,Y,T)DIMENSION QE(ME),S

17、(3,12),SG(3)D=E*T*T*T/96./(1.-UM*UM)A1=X/AB1=Y/BC1=1.-B1C2=1.-A1A2=(1.-UM)/AB2=(1.-UM)/BD1=1.+B1D2=1.+A1S(1,1)=-6*A1*C1/A/A-6*UM*B1*C2/B/BS(2,1)=-6*UM*A1*C1/A/A-6*B1*C2/B/BS(3,1)=-A2/B*(4-3*A1*A1-3*B1*B1)S(1,2)=2*UM/B*C2*(1.-3*B1)S(2,2)=S(1,2)/UMS(3,2)=-A2*(1.+2*B1-3*B1*B1)S(1,3)=-2/A*(1.-3*A1)*C1S(

18、2,3)=UM*S(1,3)S(3,3)=B2*(1.+2*A1-3*A1*A1)S(1,4)=6*A1*C1/A/A-6*UM*B1*D2/B/BS(2,4)=6*UM*A1*C1/A/A-6*B1*D2/B/BS(3,4)=-S(3,1)S(1,5)=2*UM/B*D2*(1.-3*B1)S(2,5)=S(1,5)/UMS(3,5)=-S(3,2)S(1,6)=2/A*(1.+3*A1)*C1S(2,6)=UM*S(1,6)S(3,6)=B2*(1.-2*A1-3*A1*A1)S(1,7)=6*A1*D1/A/A+6*UM*B1*D2/B/BS(2,7)=6*UM*A1*D1/A/A+6*

19、B1*D2/B/BS(3,7)=-S(3,4)S(1,8)=-2*UM/B*D2*(1.+3*B1)S(2,8)=S(1,8)/UMS(3,8)=A2*(1.-2*B1-3*B1*B1)S(1,9)=2/A*(1.+3*A1)*D1S(2,9)=UM*S(1,9)S(3,9)=-S(3,6)S(1,10)=-6*A1*D1/A/A+6*UM*B1*C2/B/BS(2,10)=-6*UM*A1*D1/A/A+6*B1*C2/B/BS(3,10)=S(3,4)S(1,11)=-2*UM/B*C2*(1.+3*B1)S(2,11)=S(1,11)/UMS(3,11)=-S(3,8)S(1,12)=-2/A*(1.-3*A1)*D1S(2,12)=UM*S(1,12)S(3,12)=-S(3,3)DO 100 I=1,3SG(I)=0.DO 100 K=1,ME100SG(I)=SG(I)+S(I,K)*QE(K)*DWRITE (*,102)SG102FORMAT(5X,SEGMA,3E20.4)WRITE(9,102) SGRETURNEND专心-专注-专业