BC가 global coordinate system에 평행하지 않을 때?

[아니소]

시료 모양은 직사각형에 가운데 크랙이 있으며 BC은 3-point bending을 따릅니다.

한 쪽 끝에는 UX’ = UY’ = 0이고 다른 한 끝은UX’ = 0입니다 (여기서 ’은 transformed된 좌표계를 의미). 시료 한 가운데서 하중이 X’방향으로 주어지고요 (아래 코드를 참조해 주세요).

문제는 이 시료가 global coordinate system으로부터 45도 회전을 했기때문에 위와 같은 BC을 바로 적용시킬 수 없다는 것입니다.

제 짧은 생각으론 local coordinate system을 시료와 평행하게 만들어서 할 수 있지 않을까 해서 인터넷에서 유사한 문제를 찾아 따라 해 봤는데 안 되더군요. 이 방법에 의하면 먼저 local coordinate system를 설정한 후 (예를 들어 KP를 3개 이용해서) “nrotat,all” 명령어를 쓰고 그리고 “esys”로 새로 설정한 local coordinate system를 activate해서 문제를 푼다는 건데 그대로 따라 해보니 “Node 407 on 2D element 1 (PLANE2) has invalid node rotation angle. Only THXY is valid for 2D elements.” 이 비슷한 에러메시지가 여러 개 나오면서 아예 프로그램이 꺼져 버리더군요.

두 번째 생각해 본 방법은 양쪽 끝 constraint를 둘 다 UX = UY = 0로 설정하고 하중을 decomposition을 써서 (즉 X와 Y 방향의 두 하중으로 나누어서 (하중)x(루트2)로 설정) 했습니다. 이 방법으로는 결과가 실제값과는 틀리겠지만 적어도 크랙을 중심으로 시료의 양쪽이 symmetric한지를 보는데는 무리가 없겠기에 해봤습니다.

하지만 결과는 여전히 global coordinate system에 의한 값으로 나오지요. 당연히 symmetric하지도 않고요. 이 결과값만이라도 local coordinate system에 의한 값으로 나오게끔 할 수 는 없을까요?

간단한 문제인 것 같은데 선뜻 안 떠오르네요.

많은 도움 부탁드립니다.

참고로 아래는 제가 했던 모델링 코드입니다.

/PREP7 
!* 
ET,1,PLANE2
!* 
KEYOPT,1,1,0
KEYOPT,1,2,0
KEYOPT,1,3,0
KEYOPT,1,5,0
KEYOPT,1,6,0
!* 
!* 
MPTEMP,,,,,,,, 
MPTEMP,1,0 
MPDATA,EX,1,,171.611E+9
MPDATA,EY,1,,8.25303E+9
MPDATA,EZ,1,,8.25303E+9
MPDATA,PRXY,1,,.344
MPDATA,PRYZ,1,,.302
MPDATA,PRXZ,1,,.344
MPDATA,GXY,1,,6.20528E+9
MPDATA,GYZ,1,,4E+9 
MPDATA,GXZ,1,,6.20528E+9

BTOL,1e-014,

K,1 , 0 , 0
K,2 , 0.0226628 , 0.0228749
K,3 , 0.0222385 , 0.0232992
K,4 , 0.0211778 , 0.0243598
K,5 , 0.0169352 , 0.0286025
K,6 , 0.00632861 , 0.0392091
K,7 , 0.00420729 , 0.0413304
K,8 , -3.54E-05 , 0.045573
K,9 , -0.00852064 , 0.0540583
K,10 , -0.0170059 , 0.0625436
K,11 , -0.0254912 , 0.0710289
K,12 , -0.0311127 , 0.0766504
K,13 , -0.00449013 , -0.004278
K,14 , -0.00491439 , -0.00385373
K,15 , -0.00597505 , -0.00279307
K,16 , -0.0102177 , 0.00144957
K,17 , -0.0208243 , 0.0120562
K,18 , -0.0229456 , 0.0141775
K,19 , -0.0271883 , 0.0184201
K,20 , -0.0356735 , 0.0269054
K,21 , -0.0441588 , 0.0353907
K,22 , -0.0526441 , 0.043876
K,23 , -0.0582656 , 0.0494975
K,24 , 0.0228749 , 0.0226628
K,25 , 0.0232992 , 0.0222385
K,26 , 0.0243598 , 0.0211778
K,27 , 0.0286025 , 0.0169352
K,28 , 0.0392091 , 0.00632861
K,29 , 0.0413304 , 0.00420729
K,30 , 0.045573 , -3.53553E-05
K,31 , 0.0540583 , -0.00852064
K,32 , 0.0625436 , -0.0170059
K,33 , 0.0710289 , -0.0254912
K,34 , 0.0766504 , -0.0311127
K,35 , -0.004278 , -0.00449013
K,36 , -0.00385373 , -0.00491439
K,37 , -0.00279307 , -0.00597505
K,38 , 0.00144957 , -0.0102177
K,39 , 0.0120562 , -0.0208243
K,40 , 0.0141775 , -0.0229456
K,41 , 0.0184201 , -0.0271883
K,42 , 0.0269054 , -0.0356735
K,43 , 0.0353907 , -0.0441588
K,44 , 0.043876 , -0.0526441
K,45 , 0.0494975 , -0.0582656
K,46 , -0.000212132 , 0
K,47 , 0 , -0.000212132
K,48 , -0.000106066 , -0.000106066
K,49 , -0.000564085 , 0.0323164
K,50 , 0.0323164 , -0.000564085
K,51 , 0.0227688 , 0.0227688
K,52 , -0.00159099 , 0.00159099
K,53 , 0.00159099 , 0.00159099

LSTR, 2 , 46
LSTR, 3 , 14
LSTR, 4 , 15
LSTR, 5 , 16
LSTR, 6 , 17
LSTR, 7 , 18
LSTR, 8 , 19
LSTR, 9 , 20
LSTR, 10 , 21
LSTR, 11 , 22
LSTR, 12 , 23
LSTR, 24 , 47
LSTR, 25 , 36
LSTR, 26 , 37
LSTR, 27 , 38
LSTR, 28 , 39
LSTR, 29 , 40
LSTR, 30 , 41
LSTR, 31 , 42
LSTR, 32 , 43
LSTR, 33 , 44
LSTR, 34 , 45
LSTR, 12 , 23
LSTR, 34 , 45
LSTR, 1 , 49
LSTR, 1 , 50
LSTR, 12 , 34
LSTR, 23 , 45
LSTR, 13 , 46
LSTR, 46 , 47
LSTR, 47 , 35
LSTR, 35 , 13

FLST,2,4,4 
FITEM,2,29 
FITEM,2,27 
FITEM,2,30 
FITEM,2,28 
AL,P51X
CYL4,-0.000106066,-0.000106066,0.00015 
FLST,2,2,5,ORDE,2  
FITEM,2,1  
FITEM,2,-2 
AADD,P51X  

FLST,2,4,4 
FITEM,2,11 
FITEM,2,25 
FITEM,2,26 
FITEM,2,22 
AL,P51X
ASBA,       1,       3 

FLST,3,22,4,ORDE,6 
FITEM,3,1  
FITEM,3,-10
FITEM,3,12 
FITEM,3,-21
FITEM,3,23 
FITEM,3,-24
ASBL,       2,P51X

FLST,2,2,4,ORDE,2  
FITEM,2,57 
FITEM,2,59 
LCOMB,P51X, ,0 
FLST,2,2,4,ORDE,2  
FITEM,2,53 
FITEM,2,55 
LCOMB,P51X, ,0 

FLST,2,2,4,ORDE,2  
FITEM,2,27 
FITEM,2,107
LCOMB,P51X, ,0 
FLST,2,2,4,ORDE,2  
FITEM,2,29 
FITEM,2,109
LCOMB,P51X, ,0 

!* First 7 Areas

FLST,5,6,4,ORDE,5  
FITEM,5,53 
FITEM,5,-54
FITEM,5,56 
FITEM,5,-58
FITEM,5,60 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,4, , , , ,1 

FLST,5,2,4,ORDE,2  
FITEM,5,27 
FITEM,5,29 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,28, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,106
FITEM,5,108
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,3, , , , ,1 
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,64 
FITEM,5,84 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,4, , , , ,1 
 
FLST,5,2,4,ORDE,2  
FITEM,5,75 
FITEM,5,95 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,32, , , , ,1
!* 
MSHKEY,0
FLST,5,2,5,ORDE,2  
FITEM,5,31 
FITEM,5,-32
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 
!* 
MSHKEY,0
FLST,5,2,5,ORDE,2  
FITEM,5,12 
FITEM,5,-13
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 

FLST,5,2,4,ORDE,2  
FITEM,5,62 
FITEM,5,82 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,150, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,63 
FITEM,5,83 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,148, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,61 
FITEM,5,81 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,3, , , , ,1 
!* 
FLST,5,1,4,ORDE,1  
FITEM,5,105
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,2, , , , ,1 
!* 
MSHKEY,0
FLST,5,3,5,ORDE,3  
FITEM,5,14 
FITEM,5,21 
FITEM,5,30 
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 

!* Next 8 Areas

FLST,5,4,4,ORDE,4  
FITEM,5,65 
FITEM,5,74 
FITEM,5,85 
FITEM,5,94 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,6, , , , ,1 
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,76 
FITEM,5,96 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,38, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,66 
FITEM,5,86 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,120, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,67 
FITEM,5,87 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,10, , , , ,1
!* 
MSHKEY,0
FLST,5,4,5,ORDE,4  
FITEM,5,15 
FITEM,5,18 
FITEM,5,22 
FITEM,5,25 
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 
!* 
LPLOT  
FLST,5,4,4,ORDE,4  
FITEM,5,68 
FITEM,5,77 
FITEM,5,88 
FITEM,5,97 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,24, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,78 
FITEM,5,98 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,64, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,69 
FITEM,5,89 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,100, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,70 
FITEM,5,90 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,36, , , , ,1
!* 
MSHKEY,0
FLST,5,4,5,ORDE,4  
FITEM,5,16 
FITEM,5,19 
FITEM,5,23 
FITEM,5,26 
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 

!* Next 6 Areas

FLST,5,4,4,ORDE,4  
FITEM,5,71 
FITEM,5,79 
FITEM,5,91 
FITEM,5,99 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,36, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,80 
FITEM,5,100
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,68, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,72 
FITEM,5,92 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,24, , , , ,1
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,73 
FITEM,5,93 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,50, , , , ,1
!* 
MSHKEY,0
FLST,5,4,5,ORDE,4  
FITEM,5,17 
FITEM,5,20 
FITEM,5,24 
FITEM,5,27 
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 
!* 
LPLOT  
FLST,5,4,4,ORDE,2  
FITEM,5,101
FITEM,5,-104
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,7, , , , ,1 
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,6  
FITEM,5,17 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,92, , , , ,1
!* 
MSHKEY,0
FLST,5,2,5,ORDE,2  
FITEM,5,28 
FITEM,5,-29
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 

!* Next 4 Areas

FLST,5,2,4,ORDE,2  
FITEM,5,7  
FITEM,5,18 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,46, , , , ,1
!* 
FLST,5,4,4,ORDE,4  
FITEM,5,26 
FITEM,5,30 
FITEM,5,43 
FITEM,5,-44
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,7, , , , ,1 
!* 
FLST,5,4,4,ORDE,4  
FITEM,5,33 
FITEM,5,-34
FITEM,5,45 
FITEM,5,-46
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,8, , , , ,1 
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,8  
FITEM,5,19 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,24, , , , ,1
!* 
MSHKEY,0
FLST,5,4,5,ORDE,4  
FITEM,5,1  
FITEM,5,3  
FITEM,5,7  
FITEM,5,-8 
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 

!* Last 6 Areas

FLST,5,4,4,ORDE,4  
FITEM,5,37 
FITEM,5,-38
FITEM,5,47 
FITEM,5,-48
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,5, , , , ,1 
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,9  
FITEM,5,20 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,16, , , , ,1
!* 
FLST,5,4,4,ORDE,4  
FITEM,5,39 
FITEM,5,-40
FITEM,5,49 
FITEM,5,-50
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,4, , , , ,1 
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,10 
FITEM,5,21 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,12, , , , ,1
!* 
FLST,5,4,4,ORDE,4  
FITEM,5,41 
FITEM,5,-42
FITEM,5,51 
FITEM,5,-52
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
FLST,5,4,4,ORDE,4  
FITEM,5,41 
FITEM,5,-42
FITEM,5,51 
FITEM,5,-52
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,2, , , , ,1 
!* 
FLST,5,2,4,ORDE,2  
FITEM,5,11 
FITEM,5,22 
CM,_Y,LINE 
LSEL, , , ,P51X
CM,_Y1,LINE
CMSEL,,_Y  
!* 
LESIZE,_Y1, , ,8, , , , ,1 
  
MSHKEY,0
FLST,5,6,5,ORDE,4  
FITEM,5,4  
FITEM,5,-6 
FITEM,5,9  
FITEM,5,-11
CM,_Y,AREA 
ASEL, , , ,P51X
CM,_Y1,AREA
CHKMSH,'AREA'  
CMSEL,S,_Y 
!* 
AMESH,_Y1  
!* 
CMDELE,_Y  
CMDELE,_Y1 
CMDELE,_Y2 

NUMMRG,ALL,1E-10, , ,LOW

[김서형]

그림을 올려 주시면 더 이해하기 좋을듯 한데요 ^^

[아니소]

Pre Q&A에 그림 올렸습니다.

[졸린지니]

결과값은 RSYS를 쓰면 간단하지요. 하지만, 구속도 해결방법이 있을 것 같네요. NROTAT명령을 쓰실 때 좌표계를 조금 잘못 쓰신 것 같네요. 2차원이라면 굳이 NROTAT명령을 쓰지 않고 직접 NODE를 회전시키실 수도 있으실텐데요. NODE를 정하실 때, N,[node 번호],[x 좌표],[y좌표],[z좌표]... 이렇게만 하시잖아요. 바로 다음 파라메터가 THXY인데, 여기다가 node의 회전각을 지정하시면, 역시 절점이 돌아갑니다. 다만, 조금 헷갈리실 수 있으니, 45도 혹은 -45도를 쓰신 후에 D명령으로 구속을 주시고 PLOT을 하셔서 구속이 올바르게 들어갔는지 확인하시면 됩니다.