3DNLG-4: Lateral torsional buckling of an elastic cantilever subjected to a transverse end load

1

Hello and Happy new year 2025 everybody,

Example of the need of initial imperfections on NL Buckling analysis.

Based on benchmark 3DNLG-4: Lateral torsional buckling of an elastic cantilever subjected to a transverse end load. (Can be found on many software’s nonlinear solvers validation manuals).

Perfect geometry: Analytical Buckling Load. 18.92 KPa
Perfect geometry: Linear Buckling Load. 19.6 KPa (S4) ,19.0 KPa (S8R)
Perfect geometry: Non-Linear Buckling Load. >2000 KPa and it has not buckle yet.
Initial Imperfection 0.01% of plate length: NL_Buckling Load. 18.4 KPa (S4),19 KPa (S8R)

Problem still needs some refinement to reach the benchmark reference value. Actual mesh is just to show the need for imperfections.

By other hand :

-Ccx S4R elements are performing wrong in most benchmarks I’m doing when dealing with Buckling loads no matter what I’m using, linear or nonlinear methods.

-For this particular file , Monitor is warning about *INFO in cascade: linear MPCs and nonlinear MPCs depend on each other on common node: 290 in direction 1.

That node has no BC at all. ¿Any Idea where that error comes from?

3DNLG-4_Lateral_torsional_buckling_S4_NL-Undeformed

*NODE
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3,0.025,0,0.005
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237,0.0775,0,0.003333333333333
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239,0.005,0,0.0008333333333333
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242,0.005,0,0.001666666666667
243,0.0725,0,0.005
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256,0.015,0,0.0008333333333333
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259,0.0125,0,0.005
260,0.0625,0,0.003333333333333
261,0.0175,0,0.0008333333333333
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264,0.085,0,0.0008333333333333
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282,0.0825,0,0.003333333333333
283,0.075,0,0.0025
284,0.0675,0,0.004166666666667
285,0.0325,0,0.0008333333333333
286,0.0675,0,0.005
287,0.0325,0,0
*ELEMENT,TYPE=S4
1,227,47,11,229
2,244,79,83,246
3,261,84,88,263
4,278,89,93,280
5,107,94,98,134
6,13,99,103,274
7,265,104,108,202
8,4,109,113,204
9,185,114,118,105
10,181,132,6,50
11,155,61,142,208
12,208,142,144,20
13,20,144,146,87
14,87,146,148,59
15,59,148,47,227
16,171,81,168,195
17,195,168,170,216
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19,184,172,174,249
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21,147,86,194,162
22,162,194,196,161
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24,197,198,200,10
25,10,200,84,261
26,131,91,9,92
27,92,9,12,133
28,133,12,14,177
29,177,14,16,90
30,90,16,89,278
31,226,96,37,218
32,218,37,39,267
33,267,39,41,169
34,169,41,43,82
35,82,43,94,107
36,17,101,66,22
37,22,66,69,164
38,164,69,71,255
39,255,71,73,127
40,127,73,99,13
41,257,106,201,138
42,138,201,203,266
43,266,203,205,80
44,80,205,207,58
45,58,207,104,265
46,286,111,49,284
47,284,49,51,25
48,25,51,53,45
49,45,53,55,78
50,78,55,109,4
51,157,116,21,85
52,85,21,23,237
53,237,23,75,68
54,68,75,77,36
55,36,77,114,185
56,42,121,124,271
57,271,124,126,15
58,15,126,128,34
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61,132,217,219,6
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73,89,285,287,93
74,285,145,102,287
75,145,107,134,102
76,94,193,211,98
77,193,277,272,211
78,277,13,274,272
79,99,163,252,103
80,163,5,72,252
81,5,265,202,72
82,104,65,176,108
83,65,141,67,176
84,141,4,204,67
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86,26,44,38,178
87,44,185,105,38
88,114,262,183,118
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90,264,181,50,136
91,121,180,27,124
92,180,95,179,27
93,95,155,208,179
94,124,27,54,126
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96,179,208,20,233
97,126,54,254,128
98,54,233,212,254
99,233,20,87,212
100,128,254,56,130
101,254,212,182,56
102,212,87,59,182
103,130,56,217,132
104,56,182,222,217
105,182,59,227,222
106,62,46,18,150
107,46,64,29,18
108,64,171,195,29
109,150,18,167,152
110,18,29,199,167
111,29,195,216,199
112,152,167,245,154
113,167,199,238,245
114,199,216,184,238
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119,191,242,239,234
120,242,249,244,239
121,81,259,60,168
122,259,19,165,60
123,19,147,162,165
124,168,60,209,170
125,60,165,189,209
126,165,162,161,189
127,170,209,160,172
128,209,189,8,160
129,189,161,197,8
130,172,160,279,174
131,160,8,2,279
132,8,197,10,2
133,174,279,251,79
134,279,2,256,251
135,2,10,261,256
136,86,215,188,194
137,215,3,129,188
138,3,131,92,129
139,194,188,117,196
140,188,129,206,117
141,129,92,133,206
142,196,117,248,198
143,117,206,30,248
144,206,133,177,30
145,198,248,151,200
146,248,30,149,151
147,30,177,90,149
148,200,151,268,84
149,151,149,273,268
150,149,90,278,273
151,91,166,240,9
152,166,235,231,240
153,235,226,218,231
154,9,240,125,12
155,240,231,52,125
156,231,218,267,52
157,12,125,70,14
158,125,52,57,70
159,52,267,169,57
160,14,70,281,16
161,70,57,173,281
162,57,169,82,173
163,16,281,285,89
164,281,173,145,285
165,173,82,107,145
166,96,100,35,37
167,100,159,140,35
168,159,17,22,140
169,37,35,63,39
170,35,140,112,63
171,140,22,164,112
172,39,63,220,41
173,63,112,247,220
174,112,164,255,247
175,41,220,276,43
176,220,247,119,276
177,247,255,127,119
178,43,276,193,94
179,276,119,277,193
180,119,127,13,277
181,101,48,28,66
182,48,213,228,28
183,213,257,138,228
184,66,28,175,69
185,28,228,187,175
186,228,138,266,187
187,69,175,32,71
188,175,187,186,32
189,187,266,80,186
190,71,32,7,73
191,32,186,153,7
192,186,80,58,153
193,73,7,163,99
194,7,153,5,163
195,153,58,265,5
196,106,232,269,201
197,232,210,214,269
198,210,286,284,214
199,201,269,260,203
200,269,214,123,260
201,214,284,25,123
202,203,260,40,205
203,260,123,221,40
204,123,25,45,221
205,205,40,135,207
206,40,221,122,135
207,221,45,78,122
208,207,135,65,104
209,135,122,141,65
210,122,78,4,141
211,111,243,97,49
212,243,137,31,97
213,137,157,85,31
214,49,97,115,51
215,97,31,250,115
216,31,85,237,250
217,51,115,76,53
218,115,250,283,76
219,250,237,68,283
220,53,76,192,55
221,76,283,24,192
222,283,68,36,24
223,55,192,26,109
224,192,24,44,26
225,24,36,185,44
226,116,110,225,21
227,110,120,223,225
228,120,42,271,223
229,21,225,282,23
230,225,223,139,282
231,223,271,15,139
232,23,282,230,75
233,282,139,190,230
234,139,15,34,190
235,75,230,143,77
236,230,190,33,143
237,190,34,74,33
238,77,143,262,114
239,143,33,264,262
240,33,74,181,264
*ELSET,ELSET=DEFAULT
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*MATERIAL,NAME=MATERIAL
*ELASTIC,TYPE=ISOTROPIC
10000000000,0
*SHELL SECTION,ELSET=DEFAULT,MATERIAL=MATERIAL
0.0002
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
1,4,,0
1,5,,0
1,6,,0
62,1,,0
62,2,,0
62,3,,0
62,4,,0
62,5,,0
62,6,,0
150,1,,0
150,2,,0
150,3,,0
150,4,,0
150,5,,0
150,6,,0
152,1,,0
152,2,,0
152,3,,0
152,4,,0
152,5,,0
152,6,,0
154,1,,0
154,2,,0
154,3,,0
154,4,,0
154,5,,0
154,6,,0
156,1,,0
156,2,,0
156,3,,0
156,4,,0
156,5,,0
156,6,,0
158,1,,0
158,2,,0
158,3,,0
158,4,,0
158,5,,0
158,6,,0
*AMPLITUDE,NAME=Az_61_1
0,0
1,-0.1666666666666
*AMPLITUDE,NAME=Az_142_2
0,0
1,-0.3333333333334
*AMPLITUDE,NAME=Az_144_3
0,0
1,-0.3333333333334
*AMPLITUDE,NAME=Az_146_4
0,0
1,-0.3333333333332
*AMPLITUDE,NAME=Az_148_5
0,0
1,-0.3333333333333
*AMPLITUDE,NAME=Az_47_6
0,0
1,-0.3333333333334
*AMPLITUDE,NAME=Az_11_7
0,0
1,-0.1666666666667
*STEP,NLGEOM=YES,INC=110,AMPLITUDE=STEP
*STATIC,SOLVER=PARDISO
0.01,1,0,0.01
*CLOAD,AMPLITUDE=Az_61_1
61,3,1
*CLOAD,AMPLITUDE=Az_142_2
142,3,1
*CLOAD,AMPLITUDE=Az_144_3
144,3,1
*CLOAD,AMPLITUDE=Az_146_4
146,3,1
*CLOAD,AMPLITUDE=Az_148_5
148,3,1
*CLOAD,AMPLITUDE=Az_47_6
47,3,1
*CLOAD,AMPLITUDE=Az_11_7
11,3,1
*NODE FILE,GLOBAL=YES
U,RF
*EL FILE
S,NOE,E
*END STEP

3DNLG-4_Lateral_torsional_buckling_S4_NL-Deformed

*NODE
1,0,0,0
2,0.015,1.066666666667E-07,0.001666666666667
3,0.025,2.5E-07,0.005
4,0.0675,4.108125E-06,0.0008333333333333
5,0.055,2.636944444444E-06,0.0008333333333333
6,0.09,7.2E-06,0
7,0.0525,2.473333333333E-06,0.001666666666667
8,0.015,9.75E-08,0.0025
9,0.03,5.833333333333E-07,0.004166666666667
10,0.0175,1.711111111111E-07,0.001666666666667
11,0.1,9E-06,0
12,0.03,6.533333333333E-07,0.003333333333333
13,0.0475,1.909236111111E-06,0.0008333333333333
14,0.03,6.9E-07,0.0025
15,0.0875,7.607638888889E-06,0.003333333333333
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17,0.0475,1.7575E-06,0.005
18,0.0025,-3.159722222222E-08,0.004166666666667
19,0.015,-3E-08,0.005
20,0.0975,9.582083333333E-06,0.003333333333333
21,0.08,6.222222222222E-06,0.004166666666667
22,0.0475,1.893402777778E-06,0.004166666666667
23,0.08,6.275555555556E-06,0.003333333333333
24,0.075,5.333333333333E-06,0.001666666666667
25,0.0675,4.33875E-06,0.003333333333333
26,0.0725,4.787013888889E-06,0.0008333333333333
27,0.0925,8.543402777778E-06,0.004166666666667
28,0.0525,2.398958333333E-06,0.004166666666667
29,0.005,-4.861111111111E-08,0.004166666666667
30,0.025,4.375E-07,0.0025
31,0.075,5.395833333333E-06,0.004166666666667
32,0.0525,2.506875E-06,0.0025
33,0.085,6.951111111111E-06,0.001666666666667
34,0.0875,7.546875E-06,0.0025
35,0.0425,1.446180555555E-06,0.004166666666667
36,0.0775,5.717777777778E-06,0.001666666666667
37,0.04,1.244444444444E-06,0.004166666666667
38,0.075,4.875E-06,0
39,0.04,1.324444444444E-06,0.003333333333333
40,0.0625,3.671875E-06,0.0025
41,0.04,1.36E-06,0.0025
42,0.0875,7.4375E-06,0.005
43,0.04,1.351111111111E-06,0.001666666666667
44,0.075,5.145833333333E-06,0.0008333333333333
45,0.0675,4.336875E-06,0.0025
46,0.0025,-4.25E-08,0.005
47,0.1,9.444444444444E-06,0.0008333333333333
48,0.0525,2.2575E-06,0.005
49,0.07,4.627777777778E-06,0.004166666666667
50,0.0875,6.78125E-06,0
51,0.07,4.697777777778E-06,0.003333333333333
52,0.035,9.605555555556E-07,0.003333333333333
53,0.07,4.69E-06,0.0025
54,0.0925,8.566527777778E-06,0.003333333333333
55,0.07,4.604444444444E-06,0.001666666666667
56,0.0925,8.304444444444E-06,0.001666666666667
57,0.035,9.975E-07,0.0025
58,0.0575,3.015555555556E-06,0.001666666666667
59,0.0975,9.273333333333E-06,0.001666666666667
60,0.0125,-1.215277777778E-08,0.004166666666667
61,0.1,1E-05,0.005
62,0,0,0.005
63,0.0425,1.527638888889E-06,0.003333333333333
64,0.005,-7E-08,0.005
65,0.0625,3.480902777778E-06,0.0008333333333333
66,0.05,2.138888888889E-06,0.004166666666667
67,0.065,3.575E-06,0
68,0.0775,5.831875E-06,0.0025
69,0.05,2.222222222222E-06,0.003333333333333
70,0.0325,8.36875E-07,0.0025
71,0.05,2.25E-06,0.0025
72,0.055,2.475E-06,0
73,0.05,2.222222222222E-06,0.001666666666667
74,0.0875,7.388888888889E-06,0.001666666666667
75,0.08,6.24E-06,0.0025
76,0.0725,5.056875E-06,0.0025
77,0.08,6.115555555556E-06,0.001666666666667
78,0.0675,4.26E-06,0.001666666666667
79,0.01,1.444444444444E-08,0.0008333333333333
80,0.0575,3.061875E-06,0.0025
81,0.01,-8E-08,0.005
82,0.0375,1.166666666667E-06,0.001666666666667
83,0.01,2.117582368136E-22,0
84,0.02,2.355555555556E-07,0.0008333333333333
85,0.0775,5.801736111111E-06,0.004166666666667
86,0.02,8E-08,0.005
87,0.0975,9.481875E-06,0.0025
88,0.02,2E-07,0
89,0.03,6.633333333333E-07,0.0008333333333333
90,0.0275,5.622222222222E-07,0.001666666666667
91,0.03,4.8E-07,0.005
92,0.0275,4.545138888889E-07,0.004166666666667
93,0.03,6E-07,0
94,0.04,1.297777777778E-06,0.0008333333333333
95,0.095,8.93E-06,0.005
96,0.04,1.12E-06,0.005
97,0.0725,5.004513888889E-06,0.004166666666667
98,0.04,1.2E-06,0
99,0.05,2.138888888889E-06,0.0008333333333333
100,0.0425,1.3175E-06,0.005
101,0.05,2E-06,0.005
102,0.035,8.75E-07,0
103,0.05,2E-06,0
104,0.06,3.186666666667E-06,0.0008333333333333
105,0.0775,5.23125E-06,0
106,0.06,3.12E-06,0.005
107,0.0375,1.119791666667E-06,0.0008333333333333
108,0.06,3E-06,0
109,0.07,4.441111111111E-06,0.0008333333333333
110,0.0825,6.5175E-06,0.005
111,0.07,4.48E-06,0.005
112,0.045,1.745E-06,0.003333333333333
113,0.07,4.2E-06,0
114,0.08,5.902222222222E-06,0.0008333333333333
115,0.0725,5.070972222222E-06,0.003333333333333
116,0.08,6.08E-06,0.005
117,0.0225,2.9875E-07,0.003333333333333
118,0.08,5.6E-06,0
119,0.045,1.76E-06,0.001666666666667
120,0.085,6.97E-06,0.005
121,0.09,7.92E-06,0.005
122,0.065,3.928888888889E-06,0.001666666666667
123,0.065,3.993888888889E-06,0.003333333333333
124,0.09,8.05E-06,0.004166666666667
125,0.0325,7.998611111112E-07,0.003333333333333
126,0.09,8.08E-06,0.003333333333333
127,0.0475,1.984444444444E-06,0.001666666666667
128,0.09,8.01E-06,0.0025
129,0.025,3.402777777778E-07,0.004166666666667
130,0.09,7.84E-06,0.001666666666667
131,0.0275,3.575E-07,0.005
132,0.09,7.57E-06,0.0008333333333333
133,0.0275,5.209722222222E-07,0.003333333333333
134,0.0375,1.03125E-06,0
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139,0.085,7.149444444444E-06,0.003333333333333
140,0.045,1.6625E-06,0.004166666666667
141,0.065,3.788055555556E-06,0.0008333333333333
142,0.1,1.011111111111E-05,0.004166666666667
143,0.0825,6.526666666667E-06,0.001666666666667
144,0.1,1.011111111111E-05,0.003333333333333
145,0.035,9.547222222222E-07,0.0008333333333333
146,0.1,1E-05,0.0025
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148,0.1,9.777777777778E-06,0.001666666666667
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150,0,0,0.004166666666667
151,0.0225,3.4E-07,0.001666666666667
152,0,0,0.003333333333333
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154,0,0,0.0025
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156,0,0,0.001666666666667
157,0.0775,5.6575E-06,0.005
158,0,0,0.0008333333333333
159,0.045,1.53E-06,0.005
160,0.0125,4.6875E-08,0.0025
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162,0.0175,8.506944444446E-08,0.004166666666667
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168,0.01,-3.888888888889E-08,0.004166666666667
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171,0.0075,-8.25E-08,0.005
172,0.01,1E-08,0.0025
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174,0.01,1.777777777778E-08,0.001666666666667
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184,0.0075,-1.3125E-08,0.0025
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187,0.055,2.756111111111E-06,0.003333333333333
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192,0.0725,4.962222222222E-06,0.001666666666667
193,0.0425,1.488680555556E-06,0.0008333333333333
194,0.02,1.555555555556E-07,0.004166666666667
195,0.0075,-5.104166666667E-08,0.004166666666667
196,0.02,2.088888888889E-07,0.003333333333333
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198,0.02,2.4E-07,0.0025
199,0.005,-3.277777777778E-08,0.003333333333333
200,0.02,2.488888888889E-07,0.001666666666667
201,0.06,3.266666666667E-06,0.004166666666667
202,0.0575,2.73125E-06,0
203,0.06,3.346666666667E-06,0.003333333333333
204,0.0675,3.88125E-06,0
205,0.06,3.36E-06,0.0025
206,0.025,4.027777777778E-07,0.003333333333333
207,0.06,3.306666666667E-06,0.001666666666667
208,0.0975,9.573958333333E-06,0.004166666666667
209,0.0125,2.430555555556E-08,0.003333333333333
210,0.065,3.77E-06,0.005
211,0.0425,1.38125E-06,0
212,0.095,8.9775E-06,0.0025
213,0.055,2.53E-06,0.005
214,0.065,3.918055555556E-06,0.004166666666667
215,0.0225,1.575E-07,0.005
216,0.0075,-2.791666666667E-08,0.003333333333333
217,0.0925,8.019236111111E-06,0.0008333333333333
218,0.0375,1.057291666666E-06,0.004166666666667
219,0.0925,7.63125E-06,0
220,0.0425,1.561875E-06,0.0025
221,0.065,3.9975E-06,0.0025
222,0.095,8.481388888889E-06,0.0008333333333333
223,0.085,7.106944444444E-06,0.004166666666667
224,0.095,8.075E-06,0
225,0.0825,6.657291666666E-06,0.004166666666667
226,0.0375,9.375E-07,0.005
227,0.0975,8.956458333333E-06,0.0008333333333333
228,0.055,2.673611111111E-06,0.004166666666667
229,0.0975,8.53125E-06,0
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239,0.005,-1.861111111111E-08,0.0008333333333333
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243,0.0725,4.8575E-06,0.005
244,0.0075,-8.541666666668E-09,0.0008333333333333
245,0.0025,-1.8125E-08,0.0025
246,0.0075,-1.875E-08,0
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251,0.0125,5.034722222222E-08,0.0008333333333333
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255,0.0475,2.006875E-06,0.0025
256,0.015,9.916666666667E-08,0.0008333333333333
257,0.0575,2.8175E-06,0.005
258,0.015,7.5E-08,0
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260,0.0625,3.663194444445E-06,0.003333333333333
261,0.0175,1.609027777778E-07,0.0008333333333333
262,0.0825,6.299791666667E-06,0.0008333333333333
263,0.0175,1.3125E-07,0
264,0.085,6.710277777778E-06,0.0008333333333333
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266,0.0575,3.044305555556E-06,0.003333333333333
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268,0.0225,3.23125E-07,0.0008333333333333
269,0.0625,3.585069444445E-06,0.004166666666667
270,0.0225,2.8125E-07,0
271,0.0875,7.571180555555E-06,0.004166666666667
272,0.045,1.575E-06,0
273,0.025,4.236111111111E-07,0.0008333333333333
274,0.0475,1.78125E-06,0
275,0.025,3.75E-07,0
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277,0.045,1.6925E-06,0.0008333333333333
278,0.0275,5.370138888889E-07,0.0008333333333333
279,0.0125,5.555555555558E-08,0.001666666666667
280,0.0275,4.8125E-07,0
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282,0.0825,6.705416666667E-06,0.003333333333333
283,0.075,5.4375E-06,0.0025
284,0.0675,4.265625E-06,0.004166666666667
285,0.0325,8.025694444444E-07,0.0008333333333333
286,0.0675,4.1175E-06,0.005
287,0.0325,7.3125E-07,0
*ELEMENT,TYPE=S4
1,227,47,11,229
2,244,79,83,246
3,261,84,88,263
4,278,89,93,280
5,107,94,98,134
6,13,99,103,274
7,265,104,108,202
8,4,109,113,204
9,185,114,118,105
10,181,132,6,50
11,155,61,142,208
12,208,142,144,20
13,20,144,146,87
14,87,146,148,59
15,59,148,47,227
16,171,81,168,195
17,195,168,170,216
18,216,170,172,184
19,184,172,174,249
20,249,174,79,244
21,147,86,194,162
22,162,194,196,161
23,161,196,198,197
24,197,198,200,10
25,10,200,84,261
26,131,91,9,92
27,92,9,12,133
28,133,12,14,177
29,177,14,16,90
30,90,16,89,278
31,226,96,37,218
32,218,37,39,267
33,267,39,41,169
34,169,41,43,82
35,82,43,94,107
36,17,101,66,22
37,22,66,69,164
38,164,69,71,255
39,255,71,73,127
40,127,73,99,13
41,257,106,201,138
42,138,201,203,266
43,266,203,205,80
44,80,205,207,58
45,58,207,104,265
46,286,111,49,284
47,284,49,51,25
48,25,51,53,45
49,45,53,55,78
50,78,55,109,4
51,157,116,21,85
52,85,21,23,237
53,237,23,75,68
54,68,75,77,36
55,36,77,114,185
56,42,121,124,271
57,271,124,126,15
58,15,126,128,34
59,34,128,130,74
60,74,130,132,181
61,132,217,219,6
62,217,222,224,219
63,222,227,229,224
64,158,234,236,1
65,234,239,241,236
66,239,244,246,241
67,79,251,253,83
68,251,256,258,253
69,256,261,263,258
70,84,268,270,88
71,268,273,275,270
72,273,278,280,275
73,89,285,287,93
74,285,145,102,287
75,145,107,134,102
76,94,193,211,98
77,193,277,272,211
78,277,13,274,272
79,99,163,252,103
80,163,5,72,252
81,5,265,202,72
82,104,65,176,108
83,65,141,67,176
84,141,4,204,67
85,109,26,178,113
86,26,44,38,178
87,44,185,105,38
88,114,262,183,118
89,262,264,136,183
90,264,181,50,136
91,121,180,27,124
92,180,95,179,27
93,95,155,208,179
94,124,27,54,126
95,27,179,233,54
96,179,208,20,233
97,126,54,254,128
98,54,233,212,254
99,233,20,87,212
100,128,254,56,130
101,254,212,182,56
102,212,87,59,182
103,130,56,217,132
104,56,182,222,217
105,182,59,227,222
106,62,46,18,150
107,46,64,29,18
108,64,171,195,29
109,150,18,167,152
110,18,29,199,167
111,29,195,216,199
112,152,167,245,154
113,167,199,238,245
114,199,216,184,238
115,154,245,191,156
116,245,238,242,191
117,238,184,249,242
118,156,191,234,158
119,191,242,239,234
120,242,249,244,239
121,81,259,60,168
122,259,19,165,60
123,19,147,162,165
124,168,60,209,170
125,60,165,189,209
126,165,162,161,189
127,170,209,160,172
128,209,189,8,160
129,189,161,197,8
130,172,160,279,174
131,160,8,2,279
132,8,197,10,2
133,174,279,251,79
134,279,2,256,251
135,2,10,261,256
136,86,215,188,194
137,215,3,129,188
138,3,131,92,129
139,194,188,117,196
140,188,129,206,117
141,129,92,133,206
142,196,117,248,198
143,117,206,30,248
144,206,133,177,30
145,198,248,151,200
146,248,30,149,151
147,30,177,90,149
148,200,151,268,84
149,151,149,273,268
150,149,90,278,273
151,91,166,240,9
152,166,235,231,240
153,235,226,218,231
154,9,240,125,12
155,240,231,52,125
156,231,218,267,52
157,12,125,70,14
158,125,52,57,70
159,52,267,169,57
160,14,70,281,16
161,70,57,173,281
162,57,169,82,173
163,16,281,285,89
164,281,173,145,285
165,173,82,107,145
166,96,100,35,37
167,100,159,140,35
168,159,17,22,140
169,37,35,63,39
170,35,140,112,63
171,140,22,164,112
172,39,63,220,41
173,63,112,247,220
174,112,164,255,247
175,41,220,276,43
176,220,247,119,276
177,247,255,127,119
178,43,276,193,94
179,276,119,277,193
180,119,127,13,277
181,101,48,28,66
182,48,213,228,28
183,213,257,138,228
184,66,28,175,69
185,28,228,187,175
186,228,138,266,187
187,69,175,32,71
188,175,187,186,32
189,187,266,80,186
190,71,32,7,73
191,32,186,153,7
192,186,80,58,153
193,73,7,163,99
194,7,153,5,163
195,153,58,265,5
196,106,232,269,201
197,232,210,214,269
198,210,286,284,214
199,201,269,260,203
200,269,214,123,260
201,214,284,25,123
202,203,260,40,205
203,260,123,221,40
204,123,25,45,221
205,205,40,135,207
206,40,221,122,135
207,221,45,78,122
208,207,135,65,104
209,135,122,141,65
210,122,78,4,141
211,111,243,97,49
212,243,137,31,97
213,137,157,85,31
214,49,97,115,51
215,97,31,250,115
216,31,85,237,250
217,51,115,76,53
218,115,250,283,76
219,250,237,68,283
220,53,76,192,55
221,76,283,24,192
222,283,68,36,24
223,55,192,26,109
224,192,24,44,26
225,24,36,185,44
226,116,110,225,21
227,110,120,223,225
228,120,42,271,223
229,21,225,282,23
230,225,223,139,282
231,223,271,15,139
232,23,282,230,75
233,282,139,190,230
234,139,15,34,190
235,75,230,143,77
236,230,190,33,143
237,190,34,74,33
238,77,143,262,114
239,143,33,264,262
240,33,74,181,264
*ELSET,ELSET=DEFAULT
1
2
3
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237
238
239
240
*MATERIAL,NAME=MATERIAL
*ELASTIC,TYPE=ISOTROPIC
10000000000,0
*SHELL SECTION,ELSET=DEFAULT,MATERIAL=MATERIAL
0.0002
*BOUNDARY
1,1,,0
1,2,,0
1,3,,0
1,4,,0
1,5,,0
1,6,,0
62,1,,0
62,2,,0
62,3,,0
62,4,,0
62,5,,0
62,6,,0
150,1,,0
150,2,,0
150,3,,0
150,4,,0
150,5,,0
150,6,,0
152,1,,0
152,2,,0
152,3,,0
152,4,,0
152,5,,0
152,6,,0
154,1,,0
154,2,,0
154,3,,0
154,4,,0
154,5,,0
154,6,,0
156,1,,0
156,2,,0
156,3,,0
156,4,,0
156,5,,0
156,6,,0
158,1,,0
158,2,,0
158,3,,0
158,4,,0
158,5,,0
158,6,,0
*AMPLITUDE,NAME=Az_61_1
0,0
1,-0.00166666668148
*AMPLITUDE,NAME=Az_142_2
0,0
1,-0.003333333348147
*AMPLITUDE,NAME=Az_144_3
0,0
1,-0.003333333348145
*AMPLITUDE,NAME=Az_146_4
0,0
1,-0.003333333407399
*AMPLITUDE,NAME=Az_148_5
0,0
1,-0.003333333525916
*AMPLITUDE,NAME=Az_47_6
0,0
1,-0.003333333703691
*AMPLITUDE,NAME=Az_11_7
0,0
1,-0.001666666903696
*STEP,NLGEOM=YES,INC=110,AMPLITUDE=STEP
*STATIC,SOLVER=PARDISO
0.01,1,0,0.01
*CLOAD,AMPLITUDE=Az_61_1
61,3,1
*CLOAD,AMPLITUDE=Az_142_2
142,3,1
*CLOAD,AMPLITUDE=Az_144_3
144,3,1
*CLOAD,AMPLITUDE=Az_146_4
146,3,1
*CLOAD,AMPLITUDE=Az_148_5
148,3,1
*CLOAD,AMPLITUDE=Az_47_6
47,3,1
*CLOAD,AMPLITUDE=Az_11_7
11,3,1
*NODE FILE,GLOBAL=YES
U,RF
*EL FILE
S,NOE,E
*END STEP
1 Like
2

@Disla , *INFO in cascade: linear MPCs

As I read and understand the code, then the info message actual refers to all nodes on the boundary surface in direction 1 & 3. but a flag is raised on the first hit on node 290 in direction 1 causing you doesn’t see all other nodes and directions.

Here is a list of all nodes affected.
Please don’t ask me why all nodes on the upper edge are checked multiple times for MPC in the same direction and this don’t happen for the lower edge.

       common node: 290 in direction 1
       common node: 290 in direction 3
       common node: 290 in direction 1
       common node: 290 in direction 3

       common node: 473 in direction 1
       common node: 473 in direction 3
       common node: 473 in direction 1
       common node: 473 in direction 3

       common node: 737 in direction 1
       common node: 737 in direction 3
       common node: 737 in direction 1
       common node: 737 in direction 3

       common node: 743 in direction 1
       common node: 743 in direction 3
       common node: 743 in direction 1
       common node: 743 in direction 3

       common node: 749 in direction 1
       common node: 749 in direction 3
       common node: 749 in direction 1
       common node: 749 in direction 3

       common node: 755 in direction 1
       common node: 755 in direction 3
       common node: 755 in direction 1
       common node: 755 in direction 3

       common node: 761 in direction 1
       common node: 761 in direction 3
       common node: 761 in direction 1
       common node: 761 in direction 3

       common node: 288 in direction 3
       common node: 288 in direction 1

       common node: 471 in direction 3
       common node: 471 in direction 1

       common node: 735 in direction 3
       common node: 735 in direction 1

       common node: 741 in direction 3
       common node: 741 in direction 1

       common node: 747 in direction 3
       common node: 747 in direction 1

       common node: 753 in direction 3
       common node: 753 in direction 1

       common node: 759 in direction 3
       common node: 759 in direction 1
3

Thank you very much fgr,

:joy:

Sorry. I just wanted to report. I have seen that many times I didn’t know why too.
By the way, How did you know the nodes involved. ¿Are they stored at some file?

4

linear quadrilateral shell element with reduced integration (S4R) in CalculiX expanded to linear hexahedral with reduced integration (C3D8R) also. This element cannot capture bending since only one integration at center, at least there’s some improvement in future to double the number of integrations trough thickness. I hope this also apply to S8R, similar approach to B32R element.

benchmark of beam lateral torsional buckling in Abaqus mentioned the loads assumed follower during deformation, however CalculiX input file attached shown not. Probably, it needed exactly the same assumption of element formulation or limitation and boundary condition, just before going further in verification by hand calculation or referring to another FE code.

*edited (add)
for local buckling as given example below, seems to be usable when the mesh is fine enough. Linear shell element without reduced integration (S4) divergences in this case.

S4R (convergences)

2025-01-03 04_55_56-
2025-01-03 04_55_56-723×533 193 KB

S4 (divergennces)

2025-01-03 05_03_36-
2025-01-03 05_03_36-723×533 176 KB

5

@Disla
I just modified the code in the source file cascade.c
By bypassing to raise the flag for first occurrence, the message will come for every occurrence.


	  /* no expansion if there is a dependence of a
	     nonlinear MPC on another linear or nonlinear MPC
	     and the call is from main */ 

	  if((jmpc[mpc-1]==1)||(nl==1)){
	    *icascade=2;
	    if(idepend==0){
	      printf(" *INFO in cascade: linear MPCs and\n");
	      printf("       nonlinear MPCs depend on each other\n");
	      printf("       common node: %" ITGFORMAT " in direction %" ITGFORMAT "\n\n",nodempc[3*index-3],nodempc[3*index-2]);
//	      idepend=1;   <<<< bypassing flag for first occurrence omitted
		}
6

@xyont
Thanks you

I didn’t understood well that requirement. We are evaluating Buckling initiation and the drawing they have prepared is somewhat exagerated. “Terminate when y-displacement at A exceeds 0.06mm.” (Plate thikness is 0.2mm) Plate doesn’t even have time to start rotating.

imagen
imagen513×417 36.7 KB

@fgr
Uff. Thats bellond my skills.
Thank you.

7

I’m finding S4R buckling loads almost 1/2 the referenced value. It provides kind of cleaner snap but wrong value.
3DNLG-2: Elastic large deflection response of a pear-shaped cylinder under end shortening is a good example.S4R S4 and S8R. Almost all NL benchmarks I have been reviewing discard S8.

screenshot.7
screenshot.71610×869 129 KB

screenshot.8
screenshot.81610×865 114 KB

screenshot.9
screenshot.91612×868 128 KB

8

benchmark of beam lateral torsional buckling has several mentioned about the force follower.

in real case i stick to quadratic shell element with reduced integration (S8R) and layered shell by composite options, another element type found to have problem in locking or plasticity. S4R with only one integration point trough the thickness of shell element is already known to be not sufficient, CalculiX documentation also given notify. Some case of local buckling with less bending mode or multiple curvature may still give usable result, but global buckling as in beam lateral torsional buckling or pear shape model are not due to large bending and single curvature occurs.

*edited (add)
it seems two layer or element trough thickness of linear hexahedral element with reduced integration (C3D8R) still insufficient to capture bending as shown in graph below with incompatible mode.

p.s force did not follower

2025-01-03 17_00_42-
2025-01-03 17_00_42-723×575 54 KB

2025-01-03 17_03_22-Untitled 1 — LibreOffice Calc
2025-01-03 17_03_22-Untitled 1 — LibreOffice Calc869×444 23.2 KB

9

I’m beginning to wonder if it’s a bug instead of a limitation. Your value is again about 1/2 of the expected value.

10

looking of beam with lateral torsional buckling cases by increasing number of element trough thickness to five, reaction force seems not reported properly but deformation and stress shown reasonably well. So, a linear hexahedral element with reduced integration (C3D8R) needed defined properly in the number element trough thickness. This limitation also common and apply to another FE code, recommended to eight elements for accuracy in case of bending dominate. Improperly report of reaction force in CalculiX can be another story.

2025-01-03 18_25_53-Window
2025-01-03 18_25_53-Window891×417 23.1 KB

2025-01-03 18_25_09-Window
2025-01-03 18_25_09-Window713×529 44.9 KB

*edited (add)
refine model by double the nesh shown C3D8R element inconsistency for this case of slender beam, but C3D8I element is not. Interesting to know this problem solved with solid element in Abaqus also.

chart1
chart1549×448 15.5 KB

11

Analytical Buckling load 18.92E-3 [N].

1 Like
12

when i look from benchmark references of Abaqus, it seems related to element response not ultimate capacity of buckling load. The graph response clearly shown not constant at the end steps, it can continue increase probably. If i can understand properly the sentences and graph, P_max is 0.017 for conservative model and 0.032 for nonconservative.

13

I dare someone used Timoshenko formula with the default Poisson Ratio =0.3.

imagen

imagen
imagen508×305 35.9 KB

14

i’m interesting element response in Abaqus or any FE code with solid element, specifically linear hexahedral with reduced integration. Probably, it will lead to similar behavior due to limitation itself, not a bug.

p.s value of P_max (0.017 and 0.032) is only value being assigned or applied. It’s not buckling load capacity, the graph of load and displacement is not constant at ends, can continue increase.

15

*CLOAD
311,3,-1.0

*HEADING
 NAFEMS BENCHMARK EXAMPLE 3DNLG-4, ELEMENT S8R
 LATERAL TORSIONAL BUCKLING OF AN ELASTIC CANTILEVER SUBJECTED TO TRANSVERSE END LOAD
 CONSERVATIVE LOAD CASE 
*NODE
    1,      0.000,      0.000,      0.000
    2,     10.000,      0.000,      0.000
    3,     20.000,      0.000,      0.000
    4,     30.000,      0.000,      0.000
    5,     40.000,      0.001,      0.000
    6,     50.000,      0.002,      0.000
    7,     60.000,      0.003,      0.000
    8,     70.000,      0.004,      0.000
    9,     80.000,      0.006,      0.000
   10,     90.000,      0.008,      0.000
   11,    100.000,      0.009,      0.000
  101,      0.000,      0.000,      0.833
  102,     10.000,      0.000,      0.833
  103,     20.000,      0.000,      0.833
  104,     30.000,      0.000,      0.833
  105,     40.000,      0.001,      0.833
  106,     50.000,      0.002,      0.833
  107,     60.000,      0.003,      0.833
  108,     70.000,      0.005,      0.833
  109,     80.000,      0.006,      0.833
  110,     90.000,      0.008,      0.833
  111,    100.000,      0.010,      0.833
  201,      0.000,      0.000,      1.667
  202,     10.000,      0.000,      1.667
  203,     20.000,      0.000,      1.667
  204,     30.000,      0.000,      1.667
  205,     40.000,      0.001,      1.667
  206,     50.000,      0.002,      1.667
  207,     60.000,      0.003,      1.667
  208,     70.000,      0.005,      1.667
  209,     80.000,      0.006,      1.667
  210,     90.000,      0.008,      1.667
  211,    100.000,      0.010,      1.667
  301,      0.000,      0.000,      2.500
  302,     10.000,      0.000,      2.500
  303,     20.000,      0.000,      2.500
  304,     30.000,      0.001,      2.500
  305,     40.000,      0.001,      2.500
  306,     50.000,      0.002,      2.500
  307,     60.000,      0.003,      2.500
  308,     70.000,      0.005,      2.500
  309,     80.000,      0.006,      2.500
  310,     90.000,      0.008,      2.500
  311,    100.000,      0.010,      2.500
  401,      0.000,      0.000,      3.333
  402,     10.000,      0.000,      3.333
  403,     20.000,      0.000,      3.333
  404,     30.000,      0.001,      3.333
  405,     40.000,      0.001,      3.333
  406,     50.000,      0.002,      3.333
  407,     60.000,      0.003,      3.333
  408,     70.000,      0.005,      3.333
  409,     80.000,      0.006,      3.333
  410,     90.000,      0.008,      3.333
  411,    100.000,      0.010,      3.333
  501,      0.000,      0.000,      4.167
  502,     10.000,      0.000,      4.167
  503,     20.000,      0.000,      4.167
  504,     30.000,      0.001,      4.167
  505,     40.000,      0.001,      4.167
  506,     50.000,      0.002,      4.167
  507,     60.000,      0.003,      4.167
  508,     70.000,      0.005,      4.167
  509,     80.000,      0.006,      4.167
  510,     90.000,      0.008,      4.167
  511,    100.000,      0.010,      4.167
  601,      0.000,      0.000,      5.000
  602,     10.000,      0.000,      5.000
  603,     20.000,      0.000,      5.000
  604,     30.000,      0.001,      5.000
  605,     40.000,      0.001,      5.000
  606,     50.000,      0.002,      5.000
  607,     60.000,      0.004,      5.000
  608,     70.000,      0.005,      5.000
  609,     80.000,      0.007,      5.000
  610,     90.000,      0.008,      5.000
  611,    100.000,      0.010,      5.000
*NSET,NSET=FIX,GEN
1,601,100
*NSET,NSET=N311
311, 
*ELEMENT,TYPE=S8R
1,1,3,203,201,2,103,202,101
*ELGEN,ELSET=SHELL
1,5,2,1,3,200,100
*SHELL SECTION,ELSET=SHELL,MATERIAL=MAT
0.2, 
*MATERIAL,NAME=MAT
*ELASTIC
1.0E4,0.0
*BOUNDARY
FIX,1,6
*RESTART, WRITE
*STEP,NLGEOM,INC=50
*STATIC,RIKS
0.0005,1.0,1E-4,0.001,0.02,311,2,0.065
*CLOAD
311,3,-1.0
*EL PRINT,FREQ=0
*NODE PRINT,FREQ=1,NSET=N311
U2,CF3
*NODE FILE,FREQ=1,NSET=N311
U, 
CF, 
*OUTPUT,FIELD,FREQ=1
*NODE OUTPUT,NSET=N311
U,
CF,
*END STEP
16

try to change the last number by double value in Abaqus.

*STATIC,RIKS
0.0005,1.0,1E-4,0.001,0.02,311,2,0.065
17

I should have said “your value is again about 1/2 of your comparision value”

I don’t really know what your graph means. Reference value 0.06 mentioned on benchmark refers to lateral displacement [mm] not Force RF2[N].

I don’t have ABAQUS sorry. What’s the aim of that change?. Nafems only provides reference values up to 0.06mm lateral displacement. That’s considered the Buckling initiation point. They don’t mention post buckling or asymptotic behavior. I can imagine one can go further, probably much more if one uses Riks as ABAQUS to see Post Buckling behavior but that’s not the aim of the benchmark.

What are you looking for beyond that point?

Regards

18

Abaqus graph P_i vs displacement, my graph is R_i vs time, only different in X_axis, it can be easily modified also.

maybe someone else, here’s open forum not private.

these values are questionable, it seems to be too small since the ratio about 0.3x thickness only.

19

This plate is 5 x 0.2 = 1.mm2 P (KPa) and R (N) are directly comparable as Abaqus Graph has a 1E-3 Scale factor for loads. It’s easaly seen… it’s wrong.

I thought you were asking to me.

I don’t feel so alone anymore.:slight_smile: Now we have more questionable people with me. Abaqus and NAFEMS . Now only you are missing.

20

no, i did several checks of my solid model, different load model including displacement and imperfection value.

did you mean 0.3t lateral movement is large deformation and buckling limit point :slight_smile: i’m questioning the value not authority or developer.