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
|
/*
This file is part of the FElt finite element analysis package.
Copyright (C) 1993-2000 Jason I. Gobat and Darren C. Atkinson
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; either version 2 of the License, or
(at your option) any later version.
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.
*/
/*****************************************************************************
*
* File: stress.c
*
* Description: contains routines to find principal stresses for solid
* elements
*
******************************************************************************/
# include <math.h>
# include "fe.h"
# include "misc.h"
# include "error.h"
# include "allocate.h"
static int cubic(a, b, c, d, x)
double a, b, c, d;
double *x;
{
int nsol;
double a1 = b/a, a2 = c/a, a3 = d/a;
double Q = (a1*a1 - 3.0*a2)/9.0;
double R = (2.0*a1*a1*a1 - 9.0*a1*a2 + 27.0*a3)/54.0;
double R2_Q3 = R*R - Q*Q*Q;
double theta;
if (R2_Q3 <= 0) {
nsol = 3;
theta = acos(R/sqrt(Q*Q*Q));
x[0] = -2.0*sqrt(Q)*cos(theta/3.0) - a1/3.0;
x[1] = -2.0*sqrt(Q)*cos((theta+2.0*M_PI)/3.0) - a1/3.0;
x[2] = -2.0*sqrt(Q)*cos((theta+4.0*M_PI)/3.0) - a1/3.0;
}
else {
nsol = 1;
x[0] = pow(sqrt(R2_Q3)+fabs(R), 1/3.0);
x[0] += Q/x[0];
x[0] *= (R < 0.0) ? 1 : -1;
x[0] -= a1/3.0;
}
return nsol;
}
void PrincipalStresses3D(stress)
double *stress;
{
double I1, I2, I3;
double sx, sy, sz, txy, tyz, txz;
double s1, s2, s3;
double sVM;
double x [3];
int i1, i2, i3;
int n;
sx = stress [1];
sy = stress [2];
sz = stress [3];
txy = stress [4];
txz = stress [5];
tyz = stress [6];
I1 = sx + sy + sz;
I2 = sx*sy + sx*sz + sy*sz - txy*txy - tyz*tyz - txz*txz;
I3 = sx*sy*sz + 2*txy*tyz*txz - (sx*tyz*tyz + sy*txz*txz + sz*txy*txy);
n = cubic(1.0, -I1, I2, -I3, x);
fprintf (stderr,"%g %g %g\n", x[0], x[1], x[2]);
i1 = 0;
i3 = 2;
if (x [1] > x [i1]) i1 = 1;
if (x [2] > x [i1]) i1 = 2;
if (x [0] < x [i3]) i3 = 0;
if (x [1] < x [i3]) i3 = 1;
i2 = 3 - i1 - i3;
s1 = x [i1];
s2 = x [i2];
s3 = x [i3];
sVM = sqrt(0.5*((s1 - s2)*(s1 - s2)
+ (s1 - s3)*(s1 - s3) + (s2 - s3)*(s2 - s3)));
stress [7] = s1;
stress [8] = s2;
stress [9] = s3;
stress [10] = sVM;
return;
}
void PrincipalStresses2D(stress)
double *stress;
{
double sx, sy, txy;
double s1, s2, s3;
double sVM;
double diameter;
double x [2];
int i1, i2;
sx = stress [1];
sy = stress [2];
txy = stress [4];
diameter = sqrt((sx - sy)*(sx - sy)/4 + txy*txy);
x[0] = (sx + sy)/2 + diameter;
x[1] = (sx + sy)/2 - diameter;
i1 = 0;
i2 = 1;
if (x [i1] < x [i2]) {
i1 = 1;
i2 = 0;
}
s1 = x [i1];
s2 = x [i2];
s3 = 0.0;
sVM = sqrt(0.5*((s1 - s2)*(s1 - s2)
+ (s1 - s3)*(s1 - s3) + (s2 - s3)*(s2 - s3)));
stress [7] = s1;
stress [8] = s2;
stress [9] = s3;
stress [10] = sVM;
return;
}
/*****************************************************************************
*
* Function: SetupStressMemory
*
* Return value: none
*
*****************************************************************************/
void SetupStressMemory (element)
Element element;
{
unsigned i;
element -> stress = Allocate (Stress, element -> ninteg);
if (element -> stress == NULL)
Fatal ("allocation error setting up stress memory\n");
UnitOffset (element -> stress);
for (i = 1 ; i <= element -> ninteg ; i++) {
/*
* now allocate space for each actual stress structure
*/
element -> stress[i] = Allocate (struct stress, 1);
if (element -> stress [i] == NULL)
Fatal ("allocation error setting up stress memory\n");
/*
* followed by space for each actual stress value (fy and mz)
*/
element -> stress[i] -> values =
Allocate (double, element -> definition -> numstresses);
if (element -> stress[i] -> values == NULL)
Fatal ("allocation error setting up stress memory\n");
UnitOffset (element -> stress[i] -> values);
}
return;
}
void AllocateNodalStress(node)
Node node;
{
int j;
if (node -> stress)
return;
node -> stress = Allocate(double, 10);
if (!node -> stress)
Fatal("error allocating memory for nodal stresses");
UnitOffset(node -> stress);
for (j = 1 ; j <= 10 ; j++)
node -> stress [j] = 0.0;
return;
}
|
