FrontISTR 5.2.0
Large-scale structural analysis program with finit element method
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quadrature.f90
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1!-------------------------------------------------------------------------------
2! Copyright (c) 2019 FrontISTR Commons
3! This software is released under the MIT License, see LICENSE.txt
4!-------------------------------------------------------------------------------
29
30 integer, parameter, private :: kreal = kind(0.0d0)
31
32 real(kind=kreal) :: &
33 gauss1d1(1,1),gauss1d2(1,2), &
34 gauss2d1(2,1),gauss2d2(2,4),gauss2d3(2,9),gauss2d4(2,1), &
35 gauss2d5(2,3),gauss2d6(2,4),gauss3d1(3,1),gauss3d2(3,8), &
36 gauss3d3(3,27),gauss3d4(3,1),gauss3d5(3,4),gauss3d6(3,15), &
37 gauss3d7(3,2),gauss3d8(3,9),gauss3d9(3,18),gauss3d10(3,6), &
38 gauss3d12(3,5), &
44
45
46 data gauss1d1 /0.d0/
47 data gauss1d2 /-0.577350269189626d0, 0.577350269189626d0/
48 !
49 data gauss2d1 /0.d0,0.d0/
50 !
51 data gauss2d2 / &
52 -0.577350269189626d0,-0.577350269189626d0, &
53 0.577350269189626d0,-0.577350269189626d0, &
54 -0.577350269189626d0,0.577350269189626d0, &
55 0.577350269189626d0,0.577350269189626d0/
56 !
57 data gauss2d3 / &
58 -0.774596669241483d0,-0.774596669241483d0, &
59 -0.d0,-0.774596669241483d0, &
60 0.774596669241483d0,-0.774596669241483d0, &
61 -0.774596669241483d0,0.d0, &
62 -0.d0,0.d0, &
63 0.774596669241483d0,0.d0, &
64 -0.774596669241483d0,0.774596669241483d0, &
65 -0.d0,0.774596669241483d0, &
66 0.774596669241483d0,0.774596669241483d0/
67 !
68 data gauss2d4 /0.333333333333333d0,0.333333333333333d0/
69 !
70 data gauss2d5 / &
71 0.166666666666667d0,0.166666666666667d0, &
72 0.666666666666667d0,0.166666666666667d0, &
73 0.166666666666667d0,0.666666666666667d0/
74
75 data gauss2d6 / &
76 0.166666666666667d0,0.166666666666667d0, &
77 0.666666666666667d0,0.166666666666667d0, &
78 0.166666666666667d0,0.666666666666667d0, &
79 0.333333333333333d0,0.333333333333333d0/
80 !
81 data gauss3d1 /0.,0.,0./
82 !
83 data gauss3d2 / &
84 -0.577350269189626d0,-0.577350269189626d0,-0.577350269189626d0, &
85 0.577350269189626d0,-0.577350269189626d0,-0.577350269189626d0, &
86 -0.577350269189626d0,0.577350269189626d0,-0.577350269189626d0, &
87 0.577350269189626d0,0.577350269189626d0,-0.577350269189626d0, &
88 -0.577350269189626d0,-0.577350269189626d0,0.577350269189626d0, &
89 0.577350269189626d0,-0.577350269189626d0,0.577350269189626d0, &
90 -0.577350269189626d0,0.577350269189626d0,0.577350269189626d0, &
91 0.577350269189626d0,0.577350269189626d0,0.577350269189626d0/
92 !
93 data gauss3d3 / &
94 -0.774596669241483d0,-0.774596669241483d0,-0.774596669241483d0, &
95 0.d0,-0.774596669241483d0,-0.774596669241483d0, &
96 0.774596669241483d0,-0.774596669241483d0,-0.774596669241483d0, &
97 -0.774596669241483d0,0.d0,-0.774596669241483d0, &
98 0.d0,0.d0,-0.774596669241483d0, &
99 0.774596669241483d0,0.d0,-0.774596669241483d0, &
100 -0.774596669241483d0,0.774596669241483d0,-0.774596669241483d0, &
101 0.d0,0.774596669241483d0,-0.774596669241483d0, &
102 0.774596669241483d0,0.774596669241483d0,-0.774596669241483d0, &
103 -0.774596669241483d0,-0.774596669241483d0,0.d0, &
104 0.d0,-0.774596669241483d0,0.d0, &
105 0.774596669241483d0,-0.774596669241483d0,0.d0, &
106 -0.774596669241483d0,0.d0,0.d0, &
107 0.d0,0.d0,0.d0, &
108 0.774596669241483d0,0.d0,0.d0, &
109 -0.774596669241483d0,0.774596669241483d0,0.d0, &
110 0.d0,0.774596669241483d0,0.d0, &
111 0.774596669241483d0,0.774596669241483d0,0.d0, &
112 -0.774596669241483d0,-0.774596669241483d0,0.774596669241483d0, &
113 0.d0,-0.774596669241483d0,0.774596669241483d0, &
114 0.774596669241483d0,-0.774596669241483d0,0.774596669241483d0, &
115 -0.774596669241483d0,0.d0,0.774596669241483d0, &
116 0.d0,0.d0,0.774596669241483d0, &
117 0.774596669241483d0,0.d0,0.774596669241483d0, &
118 -0.774596669241483d0,0.774596669241483d0,0.774596669241483d0, &
119 0.d0,0.774596669241483d0,0.774596669241483d0, &
120 0.774596669241483d0,0.774596669241483d0,0.774596669241483d0/
121 !
122 data gauss3d4 /0.25d0,0.25d0,0.25d0/
123 !
124 data gauss3d5 / &
125 0.138196601125011d0,0.138196601125011d0,0.138196601125011d0, &
126 0.585410196624968d0,0.138196601125011d0,0.138196601125011d0, &
127 0.138196601125011d0,0.585410196624968d0,0.138196601125011d0, &
128 0.138196601125011d0,0.138196601125011d0,0.585410196624968d0/
129 !
130 data gauss3d6 / &
131 0.25,0.25,0.25d0, &
132 0.091971078052723d0,0.091971078052723d0,0.091971078052723d0, &
133 0.724086765841831d0,0.091971078052723d0,0.091971078052723d0, &
134 0.091971078052723d0,0.724086765841831d0,0.091971078052723d0, &
135 0.091971078052723d0,0.091971078052723d0,0.724086765841831d0, &
136 0.319793627829630d0,0.319793627829630d0,0.319793627829630d0, &
137 0.040619116511110d0,0.319793627829630d0,0.319793627829630d0, &
138 0.319793627829630d0,0.040619116511110d0,0.319793627829630d0, &
139 0.319793627829630d0,0.319793627829630d0,0.040619116511110d0, &
140 0.056350832689629d0,0.056350832689629d0,0.443649167310371d0, &
141 0.443649167310371d0,0.056350832689629d0,0.056350832689629d0, &
142 0.443649167310371d0,0.443649167310371d0,0.056350832689629d0, &
143 0.056350832689629d0,0.443649167310371d0,0.443649167310371d0, &
144 0.056350832689629d0,0.443649167310371d0,0.056350832689629d0, &
145 0.443649167310371d0,0.056350832689629d0,0.443649167310371d0/
146 !
147 data gauss3d7 / &
148 0.333333333333333d0,0.333333333333333d0,-0.577350269189626d0, &
149 0.333333333333333d0,0.333333333333333d0,0.577350269189626d0/
150 !
151 data gauss3d8 / &
152 0.166666666666667d0,0.166666666666667d0,-0.774596669241483d0, &
153 0.666666666666667d0,0.166666666666667d0,-0.774596669241483d0, &
154 0.166666666666667d0,0.666666666666667d0,-0.774596669241483d0, &
155 0.166666666666667d0,0.166666666666667d0,0.d0, &
156 0.666666666666667d0,0.166666666666667d0,0.d0, &
157 0.166666666666667d0,0.666666666666667d0,0.d0, &
158 0.166666666666667d0,0.166666666666667d0,0.774596669241483d0, &
159 0.666666666666667d0,0.166666666666667d0,0.774596669241483d0, &
160 0.166666666666667d0,0.666666666666667d0,0.774596669241483d0/
161 !
162 data gauss3d9 / &
163 0.166666666666667d0,0.166666666666667d0,-0.774596669241483d0, &
164 0.166666666666667d0,0.666666666666667d0,-0.774596669241483d0, &
165 0.666666666666667d0,0.166666666666667d0,-0.774596669241483d0, &
166 0.000000000000000d0,0.500000000000000d0,-0.774596669241483d0, &
167 0.500000000000000d0,0.000000000000000d0,-0.774596669241483d0, &
168 0.500000000000000d0,0.500000000000000d0,-0.774596669241483d0, &
169 0.166666666666667d0,0.166666666666667d0,0.d0, &
170 0.166666666666667d0,0.666666666666667d0,0.d0, &
171 0.666666666666667d0,0.166666666666667d0,0.d0, &
172 0.000000000000000d0,0.500000000000000d0,0.d0, &
173 0.500000000000000d0,0.000000000000000d0,0.d0, &
174 0.500000000000000d0,0.500000000000000d0,0.d0, &
175 0.166666666666667d0,0.166666666666667d0,0.774596669241483d0, &
176 0.166666666666667d0,0.666666666666667d0,0.774596669241483d0, &
177 0.666666666666667d0,0.166666666666667d0,0.774596669241483d0, &
178 0.000000000000000d0,0.500000000000000d0,0.774596669241483d0, &
179 0.500000000000000d0,0.000000000000000d0,0.774596669241483d0, &
180 0.500000000000000d0,0.500000000000000d0,0.774596669241483d0/
181 !
182 data gauss3d10 / &
183 0.166666666666667d0,0.166666666666667d0,-0.577350269189626d0, &
184 0.666666666666667d0,0.166666666666667d0,-0.577350269189626d0, &
185 0.166666666666667d0,0.666666666666667d0,-0.577350269189626d0, &
186 0.166666666666667d0,0.166666666666667d0,0.577350269189626d0, &
187 0.666666666666667d0,0.166666666666667d0,0.577350269189626d0, &
188 0.166666666666667d0,0.666666666666667d0,0.577350269189626d0/
189
190 !
191 data gauss3d12 / &
192 0.25d0,0.25d0,0.25d0, &
193 0.5d0 ,0.166666666666667d0,0.166666666666667d0, &
194 0.166666666666667d0,0.5d0,0.166666666666667d0, &
195 0.166666666666667d0,0.166666666666667d0,0.5d0, &
196 0.166666666666667d0,0.666666666666667d0,0.166666666666667d0/
197
198 !
199 data weight1d1 /2.d0/
200 data weight1d2 /1.d0,1.d0/
201 !
202 data weight2d1 /4.d0/
203 !
204 data weight2d2 /1.d0,1.d0,1.d0,1.d0/
205 !
206 data weight2d3 / &
207 0.308641975308642d0,0.493827160493827d0,0.308641975308642d0, &
208 0.493827160493827d0,0.790123456790123d0,0.493827160493827d0, &
209 0.308641975308642d0,0.493827160493827d0,0.308641975308642d0/
210 !
211 data weight2d4 /0.5d0/
212 !
213 data weight2d5 / &
214 0.166666666666666d0,0.166666666666666d0,0.166666666666666d0/
215
216 data weight2d6 / &
217 0.5d0,0.5d0,0.5d0,0.5d0/
218 !
219 data weight3d1 /8.d0/
220 !
221 data weight3d2 /1.d0,1.d0,1.d0,1.d0,1.d0,1.d0,1.d0,1.d0/
222 !
223 data weight3d3 / &
224 0.171467764060357d0,0.274348422496571d0,0.171467764060357d0, &
225 0.274348422496571d0,0.438957475994513d0,0.274348422496571d0, &
226 0.171467764060357d0,0.274348422496571d0,0.171467764060357d0, &
227 0.274348422496571d0,0.438957475994513d0,0.274348422496571d0, &
228 0.438957475994513d0,0.702331961591221d0,0.438957475994513d0, &
229 0.274348422496571d0,0.438957475994513d0,0.274348422496571d0, &
230 0.171467764060357d0,0.274348422496571d0,0.171467764060357d0, &
231 0.274348422496571d0,0.438957475994513d0,0.274348422496571d0, &
232 0.171467764060357d0,0.274348422496571d0,0.171467764060357d0/
233 !
234 data weight3d4 /0.166666666666667d0/
235 !
236 data weight3d5 / &
237 0.041666666666667d0,0.041666666666667d0,0.041666666666667d0, &
238 0.041666666666667d0/
239 !
240 data weight3d6 / &
241 0.019753086419753d0,0.011989513963170d0,0.011989513963170d0, &
242 0.011989513963170d0,0.011989513963170d0,0.011511367871045d0, &
243 0.011511367871045d0,0.011511367871045d0,0.011511367871045d0, &
244 0.008818342151675d0,0.008818342151675d0,0.008818342151675d0, &
245 0.008818342151675d0,0.008818342151675d0,0.008818342151675d0/
246 !
247 data weight3d7 /0.5d0,0.5d0/
248 !
249 data weight3d8 / &
250 0.092592592592593d0,0.092592592592593d0,0.092592592592593d0, &
251 0.148148148148148d0,0.148148148148148d0,0.148148148148148d0, &
252 0.092592592592593d0,0.092592592592593d0,0.092592592592593d0/
253 !
254 data weight3d9 / &
255 0.083333333333333d0,0.083333333333333d0,0.083333333333333d0, &
256 0.009259259259259d0,0.009259259259259d0,0.009259259259259d0, &
257 0.133333333333333d0,0.133333333333333d0,0.133333333333333d0, &
258 0.014814814814815d0,0.014814814814815d0,0.014814814814815d0, &
259 0.083333333333333d0,0.083333333333333d0,0.083333333333333d0, &
260 0.009259259259259d0,0.009259259259259d0,0.009259259259259d0/
261 !
262 data weight3d10 / &
263 0.166666666666666d0,0.166666666666666d0,0.166666666666666d0, &
264 0.166666666666666d0,0.166666666666666d0,0.166666666666666d0/
265
266 data weight3d12 / &
267 -0.80000000000000d0,0.450000000000000d0,0.450000000000000d0, &
268 0.450000000000000d0,0.450000000000000d0/
269
270end module
271
272
This module contains Gauss point information.
Definition: quadrature.f90:28
real(kind=kreal), dimension(3, 9) gauss3d8
Definition: quadrature.f90:32
real(kind=kreal), dimension(2, 1) gauss2d4
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 4) gauss3d5
Definition: quadrature.f90:32
real(kind=kreal), dimension(6) weight3d10
Definition: quadrature.f90:32
real(kind=kreal), dimension(1) weight2d4
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 8) gauss3d2
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 2) gauss3d7
Definition: quadrature.f90:32
real(kind=kreal), dimension(2, 9) gauss2d3
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 1) gauss3d1
Definition: quadrature.f90:32
real(kind=kreal), dimension(2, 4) gauss2d2
Definition: quadrature.f90:32
real(kind=kreal), dimension(9) weight3d8
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 1) gauss3d4
Definition: quadrature.f90:32
real(kind=kreal), dimension(2) weight1d2
Definition: quadrature.f90:32
real(kind=kreal), dimension(1) weight3d1
Definition: quadrature.f90:32
real(kind=kreal), dimension(4) weight3d5
Definition: quadrature.f90:32
real(kind=kreal), dimension(2, 3) gauss2d5
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 6) gauss3d10
Definition: quadrature.f90:32
real(kind=kreal), dimension(1, 2) gauss1d2
Definition: quadrature.f90:32
real(kind=kreal), dimension(2, 4) gauss2d6
Definition: quadrature.f90:32
real(kind=kreal), dimension(27) weight3d3
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 27) gauss3d3
Definition: quadrature.f90:32
real(kind=kreal), dimension(1) weight2d1
Definition: quadrature.f90:32
real(kind=kreal), dimension(2, 1) gauss2d1
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 15) gauss3d6
Definition: quadrature.f90:32
real(kind=kreal), dimension(8) weight3d2
Definition: quadrature.f90:32
real(kind=kreal), dimension(9) weight2d3
Definition: quadrature.f90:32
real(kind=kreal), dimension(4) weight2d2
Definition: quadrature.f90:32
real(kind=kreal), dimension(2) weight3d7
Definition: quadrature.f90:32
real(kind=kreal), dimension(1) weight3d4
Definition: quadrature.f90:32
real(kind=kreal), dimension(18) weight3d9
Definition: quadrature.f90:32
real(kind=kreal), dimension(3) weight2d5
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 5) gauss3d12
Definition: quadrature.f90:32
real(kind=kreal), dimension(15) weight3d6
Definition: quadrature.f90:32
real(kind=kreal), dimension(5) weight3d12
Definition: quadrature.f90:32
real(kind=kreal), dimension(1) weight1d1
Definition: quadrature.f90:32
real(kind=kreal), dimension(3, 18) gauss3d9
Definition: quadrature.f90:32
real(kind=kreal), dimension(4) weight2d6
Definition: quadrature.f90:32
real(kind=kreal), dimension(1, 1) gauss1d1
Definition: quadrature.f90:32