1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
|
!
! CalculiX - A 3-dimensional finite element program
! Copyright (C) 1998-2015 Guido Dhondt
!
! This program is free software; you can redistribute it and/or
! modify it under the terms of the GNU General Public License as
! published by the Free Software Foundation(version 2);
!
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program; if not, write to the Free Software
! Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
!
subroutine shape20h_ax(xi,et,ze,xl,xsj,shp,iflag)
!
! shape functions and derivatives for a 20-node quadratic
! isoparametric brick element. -1<=xi,et,ze<=1
! special case: axisymmetric elements
!
! iflag=1: calculate only the value of the shape functions
! iflag=2: calculate the value of the shape functions and
! the Jacobian determinant
! iflag=3: calculate the value of the shape functions, the
! value of their derivatives w.r.t. the global
! coordinates and the Jacobian determinant
!
implicit none
!
integer j,k,iflag
!
real*8 shp(4,20),xs(3,3),xsi(3,3),xl(3,20),shpe(4,20),dd,
& dd1,dd2,dd3
!
real*8 xi,et,ze,xsj,omg,omh,omr,opg,oph,opr,
& tpgphpr,tmgphpr,tmgmhpr,tpgmhpr,tpgphmr,tmgphmr,tmgmhmr,tpgmhmr,
& omgopg,omhoph,omropr,omgmopg,omhmoph,omrmopr
!
intent(in) xi,et,ze,xl,iflag
!
intent(out) shp,xsj
!
! shape functions and their glocal derivatives
!
omg=1.d0-xi
omh=1.d0-et
omr=1.d0-ze
opg=1.d0+xi
oph=1.d0+et
opr=1.d0+ze
tpgphpr=opg+oph+ze
tmgphpr=omg+oph+ze
tmgmhpr=omg+omh+ze
tpgmhpr=opg+omh+ze
tpgphmr=opg+oph-ze
tmgphmr=omg+oph-ze
tmgmhmr=omg+omh-ze
tpgmhmr=opg+omh-ze
omgopg=omg*opg/4.d0
omhoph=omh*oph/4.d0
omropr=omr*opr/4.d0
omgmopg=(omg-opg)/4.d0
omhmoph=(omh-oph)/4.d0
omrmopr=(omr-opr)/4.d0
!
! shape functions
!
shp(4, 1)=-omg*omh*omr*tpgphpr/8.d0
shp(4, 2)=-opg*omh*omr*tmgphpr/8.d0
shp(4, 3)=-opg*oph*omr*tmgmhpr/8.d0
shp(4, 4)=-omg*oph*omr*tpgmhpr/8.d0
shp(4, 5)=-omg*omh*opr*tpgphmr/8.d0
shp(4, 6)=-opg*omh*opr*tmgphmr/8.d0
shp(4, 7)=-opg*oph*opr*tmgmhmr/8.d0
shp(4, 8)=-omg*oph*opr*tpgmhmr/8.d0
shp(4, 9)=omgopg*omh*omr
shp(4,10)=omhoph*opg*omr
shp(4,11)=omgopg*oph*omr
shp(4,12)=omhoph*omg*omr
shp(4,13)=omgopg*omh*opr
shp(4,14)=omhoph*opg*opr
shp(4,15)=omgopg*oph*opr
shp(4,16)=omhoph*omg*opr
shp(4,17)=omropr*omg*omh
shp(4,18)=omropr*opg*omh
shp(4,19)=omropr*opg*oph
shp(4,20)=omropr*omg*oph
!
if(iflag.eq.1) return
!
! local derivatives of the shape functions: xi-derivative
!
shpe(1, 1)=omh*omr*(tpgphpr-omg)/8.d0
shpe(1, 2)=(opg-tmgphpr)*omh*omr/8.d0
shpe(1, 3)=(opg-tmgmhpr)*oph*omr/8.d0
shpe(1, 4)=oph*omr*(tpgmhpr-omg)/8.d0
shpe(1, 5)=omh*opr*(tpgphmr-omg)/8.d0
shpe(1, 6)=(opg-tmgphmr)*omh*opr/8.d0
shpe(1, 7)=(opg-tmgmhmr)*oph*opr/8.d0
shpe(1, 8)=oph*opr*(tpgmhmr-omg)/8.d0
shpe(1, 9)=omgmopg*omh*omr
shpe(1,10)=omhoph*omr
shpe(1,11)=omgmopg*oph*omr
shpe(1,12)=-omhoph*omr
shpe(1,13)=omgmopg*omh*opr
shpe(1,14)=omhoph*opr
shpe(1,15)=omgmopg*oph*opr
shpe(1,16)=-omhoph*opr
shpe(1,17)=-omropr*omh
shpe(1,18)=omropr*omh
shpe(1,19)=omropr*oph
shpe(1,20)=-omropr*oph
!
! local derivatives of the shape functions: eta-derivative
!
shpe(2, 1)=omg*omr*(tpgphpr-omh)/8.d0
shpe(2, 2)=opg*omr*(tmgphpr-omh)/8.d0
shpe(2, 3)=opg*(oph-tmgmhpr)*omr/8.d0
shpe(2, 4)=omg*(oph-tpgmhpr)*omr/8.d0
shpe(2, 5)=omg*opr*(tpgphmr-omh)/8.d0
shpe(2, 6)=opg*opr*(tmgphmr-omh)/8.d0
shpe(2, 7)=opg*(oph-tmgmhmr)*opr/8.d0
shpe(2, 8)=omg*(oph-tpgmhmr)*opr/8.d0
shpe(2, 9)=-omgopg*omr
shpe(2,10)=omhmoph*opg*omr
shpe(2,11)=omgopg*omr
shpe(2,12)=omhmoph*omg*omr
shpe(2,13)=-omgopg*opr
shpe(2,14)=omhmoph*opg*opr
shpe(2,15)=omgopg*opr
shpe(2,16)=omhmoph*omg*opr
shpe(2,17)=-omropr*omg
shpe(2,18)=-omropr*opg
shpe(2,19)=omropr*opg
shpe(2,20)=omropr*omg
!
! local derivatives of the shape functions: zeta-derivative
!
shpe(3, 1)=omg*omh*(tpgphpr-omr)/8.d0
shpe(3, 2)=opg*omh*(tmgphpr-omr)/8.d0
shpe(3, 3)=opg*oph*(tmgmhpr-omr)/8.d0
shpe(3, 4)=omg*oph*(tpgmhpr-omr)/8.d0
shpe(3, 5)=omg*omh*(opr-tpgphmr)/8.d0
shpe(3, 6)=opg*omh*(opr-tmgphmr)/8.d0
shpe(3, 7)=opg*oph*(opr-tmgmhmr)/8.d0
shpe(3, 8)=omg*oph*(opr-tpgmhmr)/8.d0
shpe(3, 9)=-omgopg*omh
shpe(3,10)=-omhoph*opg
shpe(3,11)=-omgopg*oph
shpe(3,12)=-omhoph*omg
shpe(3,13)=omgopg*omh
shpe(3,14)=omhoph*opg
shpe(3,15)=omgopg*oph
shpe(3,16)=omhoph*omg
shpe(3,17)=omrmopr*omg*omh
shpe(3,18)=omrmopr*opg*omh
shpe(3,19)=omrmopr*opg*oph
shpe(3,20)=omrmopr*omg*oph
!
! computation of the local derivative of the global coordinates
! (xs)
!
c do i=1,3
c do j=1,3
c xs(i,j)=0.d0
c do k=1,20
c xs(i,j)=xs(i,j)+xl(i,k)*shpe(j,k)
c enddo
c enddo
c enddo
do j=1,3
xs(1,j)=xl(1,1)*(shpe(j,1)+shpe(j,5))
& +xl(1,2)*(shpe(j,2)+shpe(j,6))
& +xl(1,3)*(shpe(j,3)+shpe(j,7))
& +xl(1,4)*(shpe(j,4)+shpe(j,8))
& +xl(1,9)*(shpe(j,9)+shpe(j,13))
& +xl(1,10)*(shpe(j,10)+shpe(j,14))
& +xl(1,11)*(shpe(j,11)+shpe(j,15))
& +xl(1,12)*(shpe(j,12)+shpe(j,16))
& +xl(1,17)*shpe(j,17)+xl(1,18)*shpe(j,18)
& +xl(1,19)*shpe(j,19)+xl(1,20)*shpe(j,20)
xs(2,j)=xl(2,1)*(shpe(j,1)+shpe(j,5)+shpe(j,17))
& +xl(2,2)*(shpe(j,2)+shpe(j,6)+shpe(j,18))
& +xl(2,3)*(shpe(j,3)+shpe(j,7)+shpe(j,19))
& +xl(2,4)*(shpe(j,4)+shpe(j,8)+shpe(j,20))
& +xl(2,9)*(shpe(j,9)+shpe(j,13))
& +xl(2,10)*(shpe(j,10)+shpe(j,14))
& +xl(2,11)*(shpe(j,11)+shpe(j,15))
& +xl(2,12)*(shpe(j,12)+shpe(j,16))
xs(3,j)=xl(3,1)*(shpe(j,1)-shpe(j,5))
& +xl(3,2)*(shpe(j,2)-shpe(j,6))
& +xl(3,3)*(shpe(j,3)-shpe(j,7))
& +xl(3,4)*(shpe(j,4)-shpe(j,8))
& +xl(3,9)*(shpe(j,9)-shpe(j,13))
& +xl(3,10)*(shpe(j,10)-shpe(j,14))
& +xl(3,11)*(shpe(j,11)-shpe(j,15))
& +xl(3,12)*(shpe(j,12)-shpe(j,16))
enddo
!
! computation of the jacobian determinant
!
dd1=xs(2,2)*xs(3,3)-xs(2,3)*xs(3,2)
dd2=xs(2,3)*xs(3,1)-xs(2,1)*xs(3,3)
dd3=xs(2,1)*xs(3,2)-xs(2,2)*xs(3,1)
xsj=xs(1,1)*dd1+xs(1,2)*dd2+xs(1,3)*dd3
c xsj=xs(1,1)*(xs(2,2)*xs(3,3)-xs(2,3)*xs(3,2))
c & -xs(1,2)*(xs(2,1)*xs(3,3)-xs(2,3)*xs(3,1))
c & +xs(1,3)*(xs(2,1)*xs(3,2)-xs(2,2)*xs(3,1))
!
if(iflag.eq.2) return
!
dd=1.d0/xsj
!
! computation of the global derivative of the local coordinates
! (xsi) (inversion of xs)
!
xsi(1,1)=dd1*dd
xsi(1,2)=(xs(1,3)*xs(3,2)-xs(1,2)*xs(3,3))*dd
xsi(1,3)=(xs(1,2)*xs(2,3)-xs(2,2)*xs(1,3))*dd
xsi(2,1)=dd2*dd
xsi(2,2)=(xs(1,1)*xs(3,3)-xs(3,1)*xs(1,3))*dd
xsi(2,3)=(xs(1,3)*xs(2,1)-xs(1,1)*xs(2,3))*dd
xsi(3,1)=dd3*dd
xsi(3,2)=(xs(1,2)*xs(3,1)-xs(1,1)*xs(3,2))*dd
xsi(3,3)=(xs(1,1)*xs(2,2)-xs(2,1)*xs(1,2))*dd
c xsi(1,1)=(xs(2,2)*xs(3,3)-xs(3,2)*xs(2,3))*dd
c xsi(1,2)=(xs(1,3)*xs(3,2)-xs(1,2)*xs(3,3))*dd
c xsi(1,3)=(xs(1,2)*xs(2,3)-xs(2,2)*xs(1,3))*dd
c xsi(2,1)=(xs(2,3)*xs(3,1)-xs(2,1)*xs(3,3))*dd
c xsi(2,2)=(xs(1,1)*xs(3,3)-xs(3,1)*xs(1,3))*dd
c xsi(2,3)=(xs(1,3)*xs(2,1)-xs(1,1)*xs(2,3))*dd
c xsi(3,1)=(xs(2,1)*xs(3,2)-xs(3,1)*xs(2,2))*dd
c xsi(3,2)=(xs(1,2)*xs(3,1)-xs(1,1)*xs(3,2))*dd
c xsi(3,3)=(xs(1,1)*xs(2,2)-xs(2,1)*xs(1,2))*dd
!
! computation of the global derivatives of the shape functions
!
do k=1,20
do j=1,3
shp(j,k)=shpe(1,k)*xsi(1,j)+shpe(2,k)*xsi(2,j)
& +shpe(3,k)*xsi(3,j)
enddo
enddo
!
return
end
|
