FrontISTR  5.7.0
Large-scale structural analysis program with finit element method
quad9n.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 !-------------------------------------------------------------------------------
7 module shape_quad9n
8  !####################################################################
9 
10  implicit none
11 
12  !--------------------------------------------------------------------
13 
14  integer, parameter, private :: kreal = kind( 0.0d0 )
15 
16  !--------------------------------------------------------------------
17 
18 contains
19 
20 
21  !####################################################################
22  subroutine shapefunc_quad9n(lcoord, func)
23  !####################################################################
24 
25  real(kind = kreal), intent(in) :: lcoord(2)
26  real(kind = kreal), intent(out) :: func(9)
27 
28  !--------------------------------------------------------------------
29 
30  real(kind = kreal) :: xi(9), eta(9)
31  real(kind = kreal) :: n_xi(9), n_eta(9)
32 
33  integer :: na
34 
35  !--------------------------------------------------------------------
36 
37  ! xi-coordinate at a node in a local element
38  xi(1) = -1.0d0
39  xi(2) = 1.0d0
40  xi(3) = 1.0d0
41  xi(4) = -1.0d0
42  xi(5) = 0.0d0
43  xi(6) = 1.0d0
44  xi(7) = 0.0d0
45  xi(8) = -1.0d0
46  xi(9) = 0.0d0
47  ! eta-coordinate at a node in a local element
48  eta(1) = -1.0d0
49  eta(2) = -1.0d0
50  eta(3) = 1.0d0
51  eta(4) = 1.0d0
52  eta(5) = -1.0d0
53  eta(6) = 0.0d0
54  eta(7) = 1.0d0
55  eta(8) = 0.0d0
56  eta(9) = 0.0d0
57 
58  !--------------------------------------------------------------------
59 
60  do na = 1, 9
61 
62  n_xi(na) = ( 0.5d0*xi(na) *lcoord(1) ) &
63  *( 1.0d0+xi(na) *lcoord(1) ) &
64  +( 1.0d0-xi(na) *xi(na) ) &
65  *( 1.0d0-lcoord(1)*lcoord(1) )
66  n_eta(na) = ( 0.5d0*eta(na)*lcoord(2) ) &
67  *( 1.0d0+eta(na)*lcoord(2) ) &
68  +( 1.0d0-eta(na)*eta(na) ) &
69  *( 1.0d0-lcoord(2)*lcoord(2) )
70 
71  end do
72 
73  !--------------------------------------------------------------------
74 
75  do na = 1, 9
76 
77  func(na) = n_xi(na)*n_eta(na)
78 
79  end do
80 
81  !--------------------------------------------------------------------
82 
83  return
84 
85  !####################################################################
86  end subroutine shapefunc_quad9n
87  !####################################################################
88 
89  !####################################################################
90  subroutine shapederiv_quad9n(lcoord, func)
91  !####################################################################
92 
93  real(kind = kreal), intent(in) :: lcoord(2)
94  real(kind = kreal), intent(out) :: func(9, 2)
95 
96  !--------------------------------------------------------------------
97 
98  real(kind = kreal) :: xi(9), eta(9)
99  real(kind = kreal) :: n_xi(9), n_eta(9)
100  real(kind = kreal) :: dn_xi(9), dn_eta(9)
101 
102  integer :: na
103 
104  !--------------------------------------------------------------------
105 
106  ! xi-coordinate at a node in a local element
107  xi(1) = -1.0d0
108  xi(2) = 1.0d0
109  xi(3) = 1.0d0
110  xi(4) = -1.0d0
111  xi(5) = 0.0d0
112  xi(6) = 1.0d0
113  xi(7) = 0.0d0
114  xi(8) = -1.0d0
115  xi(9) = 0.0d0
116  ! eta-coordinate at a node in a local element
117  eta(1) = -1.0d0
118  eta(2) = -1.0d0
119  eta(3) = 1.0d0
120  eta(4) = 1.0d0
121  eta(5) = -1.0d0
122  eta(6) = 0.0d0
123  eta(7) = 1.0d0
124  eta(8) = 0.0d0
125  eta(9) = 0.0d0
126 
127  !--------------------------------------------------------------------
128 
129  do na = 1, 9
130 
131  n_xi(na) = ( 0.5d0*xi(na) *lcoord(1) ) &
132  *( 1.0d0+xi(na) *lcoord(1) ) &
133  +( 1.0d0-xi(na) *xi(na) ) &
134  *( 1.0d0-lcoord(1)*lcoord(1) )
135  n_eta(na) = ( 0.5d0*eta(na)*lcoord(2) ) &
136  *( 1.0d0+eta(na)*lcoord(2) ) &
137  +( 1.0d0-eta(na)*eta(na) ) &
138  *( 1.0d0-lcoord(2)*lcoord(2) )
139 
140  dn_xi(na) = ( 0.5d0*xi(na) ) &
141  *( 1.0d0+xi(na) *lcoord(1) ) &
142  +( 0.5d0*xi(na) *lcoord(1) ) &
143  *xi(na) &
144  +( 1.0d0-xi(na) *xi(na) ) &
145  *( -2.0d0*lcoord(1) )
146  dn_eta(na) = ( 0.5d0*eta(na) ) &
147  *( 1.0d0+eta(na)*lcoord(2) ) &
148  +( 0.5d0*eta(na)*lcoord(2) ) &
149  *eta(na) &
150  +( 1.0d0-eta(na)*eta(na) ) &
151  *( -2.0d0*lcoord(2) )
152 
153  end do
154 
155  !--------------------------------------------------------------------
156 
157  do na = 1, 9
158 
159  func(na, 1) = dn_xi(na)*n_eta(na)
160  func(na, 2) = n_xi(na) *dn_eta(na)
161 
162  end do
163 
164  !--------------------------------------------------------------------
165 
166  return
167 
168  !####################################################################
169  end subroutine shapederiv_quad9n
170  !####################################################################
171 
172  !####################################################################
173  subroutine nodalnaturalcoord_quad9n(nncoord)
174  !####################################################################
175 
176  real(kind = kreal), intent(out) :: nncoord(9, 2)
177 
178  !--------------------------------------------------------------------
179 
180  ! xi-coordinate at a node in a local element
181  nncoord(1, 1) = -1.0d0
182  nncoord(2, 1) = 1.0d0
183  nncoord(3, 1) = 1.0d0
184  nncoord(4, 1) = -1.0d0
185  nncoord(5, 1) = 0.0d0
186  nncoord(6, 1) = 1.0d0
187  nncoord(7, 1) = 0.0d0
188  nncoord(8, 1) = -1.0d0
189  nncoord(9, 1) = 0.0d0
190  ! eta-coordinate at a node in a local element
191  nncoord(1, 2) = -1.0d0
192  nncoord(2, 2) = -1.0d0
193  nncoord(3, 2) = 1.0d0
194  nncoord(4, 2) = 1.0d0
195  nncoord(5, 2) = -1.0d0
196  nncoord(6, 2) = 0.0d0
197  nncoord(7, 2) = 1.0d0
198  nncoord(8, 2) = 0.0d0
199  nncoord(9, 2) = 0.0d0
200 
201  !--------------------------------------------------------------------
202 
203  return
204 
205  !####################################################################
206  end subroutine nodalnaturalcoord_quad9n
207  !####################################################################
208 
209 end module shape_quad9n
shape_quad9n::nodalnaturalcoord_quad9n
subroutine nodalnaturalcoord_quad9n(nncoord)
Definition: quad9n.f90:174
shape_quad9n
This module contains functions for interpolation in 9 node quadrilateral element.
Definition: quad9n.f90:7
shape_quad9n::shapederiv_quad9n
subroutine shapederiv_quad9n(lcoord, func)
Definition: quad9n.f90:91
shape_quad9n::shapefunc_quad9n
subroutine shapefunc_quad9n(lcoord, func)
Definition: quad9n.f90:23