This repository has been archived by the owner on Apr 23, 2022. It is now read-only.
-
Notifications
You must be signed in to change notification settings - Fork 18
/
emat_quad_bend.cpp
286 lines (276 loc) · 11.3 KB
/
emat_quad_bend.cpp
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
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
/*
* emat_quad_bend.cpp
* sensitive couture
*
* Created by Nobuyuki Umetani on 11/30/10.
* Copyright 2010 The University of Tokyo and Columbia University. All rights reserved.
*
*/
#include <iostream>
#include <math.h>
#include "delfem/vector3d.h"
#include "emat_quad_bend.h"
void GetKmatRes_QuadBend
(double Kmat[4][4][3][3], double res[4][3],
const double C[4][3], const double c[4][3],
double stiff,
double& strain_energy)
{
const double A0 = Com::TriArea3D(C[0],C[2],C[3]);
const double A1 = Com::TriArea3D(C[1],C[3],C[2]);
const double L0 = Com::Distance3D(C[2],C[3]);
const double H0 = A0*2.0/L0;
const double H1 = A1*2.0/L0;
const double e23[3] = { C[3][0]-C[2][0], C[3][1]-C[2][1], C[3][2]-C[2][2] };
const double e02[3] = { C[2][0]-C[0][0], C[2][1]-C[0][1], C[2][2]-C[0][2] };
const double e03[3] = { C[3][0]-C[0][0], C[3][1]-C[0][1], C[3][2]-C[0][2] };
const double e12[3] = { C[2][0]-C[1][0], C[2][1]-C[1][1], C[2][2]-C[1][2] };
const double e13[3] = { C[3][0]-C[1][0], C[3][1]-C[1][1], C[3][2]-C[1][2] };
double cot023, cot032;
{
const double r2 = -Com::Dot3D(e02,e23);
const double r3 = +Com::Dot3D(e03,e23);
cot023 = r2/H0;
cot032 = r3/H0;
}
double cot123, cot132;
{
const double r2 = -Com::Dot3D(e12,e23);
const double r3 = +Com::Dot3D(e13,e23);
cot123 = r2/H1;
cot132 = r3/H1;
}
const double tmp0 = stiff/((A0+A1)*L0*L0);
const double K[4] = { -cot023-cot032, -cot123-cot132, cot032+cot132, cot023+cot123 };
for(unsigned int i=0;i<4*4*3*3;i++){ (&Kmat[0][0][0][0])[i] = 0; }
for(unsigned int ino=0;ino<4;ino++){
for(unsigned int jno=0;jno<4;jno++){
const double tmp = K[ino]*K[jno]*tmp0;
Kmat[ino][jno][0][0] = tmp;
Kmat[ino][jno][1][1] = tmp;
Kmat[ino][jno][2][2] = tmp;
}
}
for(unsigned int ino=0;ino<4;ino++){
for(unsigned int idim=0;idim<3;idim++){
res[ino][idim] = 0;
for(unsigned int jno=0;jno<4;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
res[ino][idim] += Kmat[ino][jno][idim][jdim]*c[jno][jdim];
}
}
strain_energy += res[ino][idim]*c[ino][idim];
}
}
}
void GetMatRes_QuadBend_BackwardEular
(double Kmat[4][4][3][3], double Res[4][3],
const double C[4][3],
const double u[4][3], const double v[4][3],
double stiff,
double dt,
double& strain_energy)
{
const double c[4][3] = {
{ C[0][0]+u[0][0], C[0][1]+u[0][1], C[0][2]+u[0][2] },
{ C[1][0]+u[1][0], C[1][1]+u[1][1], C[1][2]+u[1][2] },
{ C[2][0]+u[2][0], C[2][1]+u[2][1], C[2][2]+u[2][2] },
{ C[3][0]+u[3][0], C[3][1]+u[3][1], C[3][2]+u[3][2] }, };
GetKmatRes_QuadBend(Kmat,Res, C,c, stiff, strain_energy);
for(unsigned int i=0;i<4*3; i++){ (&Res[0][0])[i] *= dt; }
////
for(unsigned int ino=0;ino<4;ino++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jno=0;jno<4;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
Res[ino][idim] += Kmat[ino][jno][idim][jdim]*v[jno][jdim]*dt*dt;
}
}
}
}
for(unsigned int i=0;i<4*4*3*3;i++){ (&Kmat[0][0][0][0])[i] *= dt*dt; }
}
static void DerDoubleAreaTri3D
(double dAdC[3][3],
const double c0[3], const double c1[3], const double c2[3],
const double un[3]) // unit normal
{
const double c[3][3] = {
{ c2[0]-c1[0], c2[1]-c1[1], c2[2]-c1[2] },
{ c0[0]-c2[0], c0[1]-c2[1], c0[2]-c2[2] },
{ c1[0]-c0[0], c1[1]-c0[1], c1[2]-c0[2] } };
Com::Cross3D(dAdC[0], un, c[0]);
Com::Cross3D(dAdC[1], un, c[1]);
Com::Cross3D(dAdC[2], un, c[2]);
}
inline void UnitNormalAreaTri3D(double n[3], double& a, const double v1[3], const double v2[3], const double v3[3]){
n[0] = ( v2[1] - v1[1] )*( v3[2] - v1[2] ) - ( v3[1] - v1[1] )*( v2[2] - v1[2] );
n[1] = ( v2[2] - v1[2] )*( v3[0] - v1[0] ) - ( v3[2] - v1[2] )*( v2[0] - v1[0] );
n[2] = ( v2[0] - v1[0] )*( v3[1] - v1[1] ) - ( v3[0] - v1[0] )*( v2[1] - v1[1] );
a = sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2])*0.5;
const double invlen = 0.5/a;
n[0]*=invlen; n[1]*=invlen; n[2]*=invlen;
}
void GetKmatResdRdC_QuadBend
(double Kmat[4][4][3][3], double Res[4][3], double dRdC[4][4][3][3],
const double C[4][3], const double c[4][3],
double stiff)
{
double A0,UN0[3]; UnitNormalAreaTri3D(UN0, A0, C[0], C[2], C[3]);
double A1,UN1[3]; UnitNormalAreaTri3D(UN1, A1, C[1], C[3], C[2]);
const double L0 = Com::Distance3D(C[2],C[3]);
double coeff = stiff/((A0+A1)*L0*L0);
double dcoeffdC[4][3];
{
double dA0dC023[3][3]; DerDoubleAreaTri3D(dA0dC023,C[0],C[2],C[3], UN0); // 023
double dA1dC132[3][3]; DerDoubleAreaTri3D(dA1dC132,C[1],C[3],C[2], UN1); // 132
const double t0 = stiff/((A0+A1)*(A0+A1)*L0*L0*L0*L0);
const double u23[3] = { (C[3][0]-C[2][0])/L0, (C[3][1]-C[2][1])/L0, (C[3][2]-C[2][2])/L0 };
for(unsigned int i=0;i<3;i++){
dcoeffdC[0][i] = -dA0dC023[0][i]*L0*L0*0.5*t0;
dcoeffdC[1][i] = -dA1dC132[0][i]*L0*L0*0.5*t0;
dcoeffdC[2][i] = -((dA0dC023[1][i]+dA1dC132[2][i])*L0*L0*0.5 - (A0+A1)*2.0*L0*u23[i])*t0;
dcoeffdC[3][i] = -((dA0dC023[2][i]+dA1dC132[1][i])*L0*L0*0.5 + (A0+A1)*2.0*L0*u23[i])*t0;
}
} /////////
const double H0 = A0*2.0/L0;
const double H1 = A1*2.0/L0;
////
const double e23[3] = { C[3][0]-C[2][0], C[3][1]-C[2][1], C[3][2]-C[2][2] };
const double e02[3] = { C[2][0]-C[0][0], C[2][1]-C[0][1], C[2][2]-C[0][2] };
const double e03[3] = { C[3][0]-C[0][0], C[3][1]-C[0][1], C[3][2]-C[0][2] };
const double e12[3] = { C[2][0]-C[1][0], C[2][1]-C[1][1], C[2][2]-C[1][2] };
const double e13[3] = { C[3][0]-C[1][0], C[3][1]-C[1][1], C[3][2]-C[1][2] };
double dKdC[4][3][4];
double cot023, cot032, cot123, cot132;
{
const double d02 = -Com::Dot3D(e02,e23);
const double d03 = +Com::Dot3D(e03,e23);
cot023 = d02/H0;
cot032 = d03/H0;
const double r02 = d03/(d02+d03);
const double invH0 = 1.0/H0;
double uvH0[3] = {
( r02*C[2][0]+(1-r02)*C[3][0] - C[0][0] )*invH0,
( r02*C[2][1]+(1-r02)*C[3][1] - C[0][1] )*invH0,
( r02*C[2][2]+(1-r02)*C[3][2] - C[0][2] )*invH0 };
// std::cout << uvH0[0]*uvH0[0] + uvH0[1]*uvH0[1] + uvH0[2]*uvH0[2] << std::endl;
double dcotdC023[3][3] = {
{ +e23[0] *invH0 + d02*uvH0[0]*invH0*invH0,
+e23[1] *invH0 + d02*uvH0[1]*invH0*invH0,
+e23[2] *invH0 + d02*uvH0[2]*invH0*invH0 },
{ (e02[0]-e23[0])*invH0 - r02 *d02*uvH0[0]*invH0*invH0,
(e02[1]-e23[1])*invH0 - r02 *d02*uvH0[1]*invH0*invH0,
(e02[2]-e23[2])*invH0 - r02 *d02*uvH0[2]*invH0*invH0 },
{ -e02[0] *invH0 - (1-r02)*d02*uvH0[0]*invH0*invH0,
-e02[1] *invH0 - (1-r02)*d02*uvH0[1]*invH0*invH0,
-e02[2] *invH0 - (1-r02)*d02*uvH0[2]*invH0*invH0 }
};
double dcotdC032[3][3] = {
{ -e23[0] *invH0 + d03*uvH0[0]*invH0*invH0,
-e23[1] *invH0 + d03*uvH0[1]*invH0*invH0,
-e23[2] *invH0 + d03*uvH0[2]*invH0*invH0 },
{ (e23[0]+e03[0])*invH0 - (1-r02)*d03*uvH0[0]*invH0*invH0,
(e23[1]+e03[1])*invH0 - (1-r02)*d03*uvH0[1]*invH0*invH0,
(e23[2]+e03[2])*invH0 - (1-r02)*d03*uvH0[2]*invH0*invH0 },
{ -e03[0] *invH0 - r02 *d03*uvH0[0]*invH0*invH0,
-e03[1] *invH0 - r02 *d03*uvH0[1]*invH0*invH0,
-e03[2] *invH0 - r02 *d03*uvH0[2]*invH0*invH0 }
};
const double d12 = -Com::Dot3D(e12,e23);
const double d13 = +Com::Dot3D(e13,e23);
cot123 = d12/H1;
cot132 = d13/H1;
const double r12 = d13/(d12+d13);
const double invH1 = 1.0/H1;
double uvH1[3] = {
( r12*C[2][0]+(1-r12)*C[3][0] - C[1][0] )*invH1,
( r12*C[2][1]+(1-r12)*C[3][1] - C[1][1] )*invH1,
( r12*C[2][2]+(1-r12)*C[3][2] - C[1][2] )*invH1 };
// std::cout << uvH0[0]*uvH0[0] + uvH0[1]*uvH0[1] + uvH0[2]*uvH0[2] << std::endl;
double dcotdC123[3][3] = {
{ +e23[0] *invH1 + d12*uvH1[0]*invH1*invH1,
+e23[1] *invH1 + d12*uvH1[1]*invH1*invH1,
+e23[2] *invH1 + d12*uvH1[2]*invH1*invH1 },
{ (e12[0]-e23[0])*invH1 - r12 *d12*uvH1[0]*invH1*invH1,
(e12[1]-e23[1])*invH1 - r12 *d12*uvH1[1]*invH1*invH1,
(e12[2]-e23[2])*invH1 - r12 *d12*uvH1[2]*invH1*invH1 },
{ -e12[0] *invH1 - (1-r12)*d12*uvH1[0]*invH1*invH1,
-e12[1] *invH1 - (1-r12)*d12*uvH1[1]*invH1*invH1,
-e12[2] *invH1 - (1-r12)*d12*uvH1[2]*invH1*invH1 }
};
double dcotdC132[3][3] = {
{ -e23[0] *invH1 + d13*uvH1[0]*invH1*invH1,
-e23[1] *invH1 + d13*uvH1[1]*invH1*invH1,
-e23[2] *invH1 + d13*uvH1[2]*invH1*invH1 },
{ (e23[0]+e13[0])*invH1 - (1-r12)*d13*uvH1[0]*invH1*invH1,
(e23[1]+e13[1])*invH1 - (1-r12)*d13*uvH1[1]*invH1*invH1,
(e23[2]+e13[2])*invH1 - (1-r12)*d13*uvH1[2]*invH1*invH1 },
{ -e13[0] *invH1 - r12 *d13*uvH1[0]*invH1*invH1,
-e13[1] *invH1 - r12 *d13*uvH1[1]*invH1*invH1,
-e13[2] *invH1 - r12 *d13*uvH1[2]*invH1*invH1 }
};
for(unsigned int i=0;i<3;i++){
dKdC[0][i][0] = -dcotdC023[0][i]-dcotdC032[0][i];
dKdC[1][i][0] = 0;
dKdC[2][i][0] = -dcotdC023[1][i]-dcotdC032[2][i];
dKdC[3][i][0] = -dcotdC023[2][i]-dcotdC032[1][i];
///
dKdC[0][i][1] = 0;
dKdC[1][i][1] = -dcotdC123[0][i]-dcotdC132[0][i];
dKdC[2][i][1] = -dcotdC123[1][i]-dcotdC132[2][i];
dKdC[3][i][1] = -dcotdC123[2][i]-dcotdC132[1][i];
///
dKdC[0][i][2] = +dcotdC032[0][i];
dKdC[1][i][2] = +dcotdC132[0][i];
dKdC[2][i][2] = +dcotdC032[2][i]+dcotdC132[2][i];
dKdC[3][i][2] = +dcotdC032[1][i]+dcotdC132[1][i];
///
dKdC[0][i][3] = +dcotdC023[0][i];
dKdC[1][i][3] = +dcotdC123[0][i];
dKdC[2][i][3] = +dcotdC023[1][i]+dcotdC123[1][i];
dKdC[3][i][3] = +dcotdC023[2][i]+dcotdC123[2][i];
}
}
const double K[4] = { -cot023-cot032, -cot123-cot132, cot032+cot132, cot023+cot123 };
for(unsigned int i=0;i<4*4*3*3;i++){ (&Kmat[0][0][0][0])[i] = 0; }
for(unsigned int ino=0;ino<4;ino++){
for(unsigned int jno=0;jno<4;jno++){
const double tmp = K[ino]*K[jno]*coeff;
Kmat[ino][jno][0][0] = tmp;
Kmat[ino][jno][1][1] = tmp;
Kmat[ino][jno][2][2] = tmp;
}
}
for(unsigned int ino=0;ino<4;ino++){
for(unsigned int idim=0;idim<3;idim++){
Res[ino][idim] = 0;
for(unsigned int jno=0;jno<4;jno++){
for(unsigned int jdim=0;jdim<3;jdim++){
Res[ino][idim] += Kmat[ino][jno][idim][jdim]*c[jno][jdim];
}
}
}
}
{
const double Kc[3] = {
K[0]*c[0][0] + K[1]*c[1][0] + K[2]*c[2][0] + K[3]*c[3][0],
K[0]*c[0][1] + K[1]*c[1][1] + K[2]*c[2][1] + K[3]*c[3][1],
K[0]*c[0][2] + K[1]*c[1][2] + K[2]*c[2][2] + K[3]*c[3][2] };
for(unsigned int ino=0;ino<4;ino++){
for(unsigned int jno=0;jno<4;jno++){
for(unsigned int idim=0;idim<3;idim++){
for(unsigned int jdim=0;jdim<3;jdim++){
dRdC[ino][jno][idim][jdim] =
dcoeffdC[jno][jdim]*K[ino]*Kc[idim]
+ coeff*dKdC[jno][jdim][ino]*Kc[idim]
+ coeff*K[ino]*(dKdC[jno][jdim][0]*c[0][idim]+
dKdC[jno][jdim][1]*c[1][idim]+
dKdC[jno][jdim][2]*c[2][idim]+
dKdC[jno][jdim][3]*c[3][idim]);
}
}
}
}
}
}