T2 and T3 : One-dimensional with radiation and heat transfer. B32 discrepancy

1

Hi,
B32 is not giving me the right answer on this benchmark. I’m finding that it’s not a refinement issue. The midside nodes on the expanded beam do not satisfy the imposed BC of T=1000K.

imagen
imagen973×524 52 KB

That makes a small difference in the final result. Inp shows the beam with discrepancy beside the solid option C3D20 which delivers exact solution.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test T2 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.
Target solution: Temperature at B=927 K (653.85°C).

C3D20 Result :927.004 K
B32 Result : 924 K

*NODE
1,0,0,0
2,0.1,0,0
3,0.09,0,0
4,0.06,0,0
5,0.01,0,0
6,0.08,0,0
7,0.02,0,0
8,0.05,0,0
9,0.03,0,0
10,0.07,0,0
11,0.04,0,0
12,0.095,0,0
13,0.005,0,0
14,0.015,0,0
15,0.025,0,0
16,0.035,0,0
17,0.045,0,0
18,0.055,0,0
19,0.065,0,0
20,0.075,0,0
21,0.085,0,0
22,0.09,0,0.005
23,0.09,0,0.01
24,0.1,0,0.005
25,0.1,0,0.01
26,0,0,0.005
27,0,0,0.01
28,0.01,0,0.005
29,0.01,0,0.01
30,0.02,0,0.005
31,0.02,0,0.01
32,0.03,0,0.005
33,0.03,0,0.01
34,0.04,0,0.005
35,0.04,0,0.01
36,0.05,0,0.005
37,0.05,0,0.01
38,0.06,0,0.005
39,0.06,0,0.01
40,0.07,0,0.005
41,0.07,0,0.01
42,0.08,0,0.005
43,0.08,0,0.01
44,0.095,0,0.01
45,0.005,0,0.01
46,0.015,0,0.01
47,0.025,0,0.01
48,0.035,0,0.01
49,0.045,0,0.01
50,0.055,0,0.01
51,0.065,0,0.01
52,0.075,0,0.01
53,0.085,0,0.01
54,0.05,-0.005,0
55,0.05,-0.01,0
56,0.05,-0.005,0.01
57,0.05,-0.01,0.01
58,0.04,-0.005,0.01
59,0.04,-0.01,0.01
60,0.04,-0.005,0
61,0.04,-0.01,0
62,0.06,-0.005,0
63,0.06,-0.01,0
64,0.06,-0.005,0.01
65,0.06,-0.01,0.01
66,0.03,-0.005,0.01
67,0.03,-0.01,0.01
68,0.03,-0.005,0
69,0.03,-0.01,0
70,0.07,-0.005,0
71,0.07,-0.01,0
72,0.07,-0.005,0.01
73,0.07,-0.01,0.01
74,0.02,-0.005,0.01
75,0.02,-0.01,0.01
76,0.02,-0.005,0
77,0.02,-0.01,0
78,0.08,-0.005,0
79,0.08,-0.01,0
80,0.08,-0.005,0.01
81,0.08,-0.01,0.01
82,0.01,-0.005,0.01
83,0.01,-0.01,0.01
84,0.01,-0.005,0
85,0.01,-0.01,0
86,0.09,-0.005,0
87,0.09,-0.01,0
88,0.09,-0.005,0.01
89,0.09,-0.01,0.01
90,0,-0.005,0.01
91,0,-0.01,0.01
92,0,-0.005,0
93,0,-0.01,0
94,0.1,-0.005,0
95,0.1,-0.01,0
96,0.1,-0.005,0.01
97,0.1,-0.01,0.01
98,0.05,-0.01,0.005
99,0.045,-0.01,0.01
100,0.04,-0.01,0.005
101,0.045,-0.01,0
102,0.06,-0.01,0.005
103,0.055,-0.01,0.01
104,0.055,-0.01,0
105,0.035,-0.01,0.01
106,0.03,-0.01,0.005
107,0.035,-0.01,0
108,0.07,-0.01,0.005
109,0.065,-0.01,0.01
110,0.065,-0.01,0
111,0.025,-0.01,0.01
112,0.02,-0.01,0.005
113,0.025,-0.01,0
114,0.08,-0.01,0.005
115,0.075,-0.01,0.01
116,0.075,-0.01,0
117,0.015,-0.01,0.01
118,0.01,-0.01,0.005
119,0.015,-0.01,0
120,0.09,-0.01,0.005
121,0.085,-0.01,0.01
122,0.085,-0.01,0
123,0.005,-0.01,0.01
124,0,-0.01,0.005
125,0.005,-0.01,0
126,0.1,-0.01,0.005
127,0.095,-0.01,0.01
128,0.095,-0.01,0
129,0,0,-0.03
130,0.1,0,-0.03
131,0.01,0,-0.03
132,0.02,0,-0.03
133,0.03,0,-0.03
134,0.04,0,-0.03
135,0.05,0,-0.03
136,0.06,0,-0.03
137,0.07,0,-0.03
138,0.08,0,-0.03
139,0.09,0,-0.03
140,0.095,0,-0.03
141,0.005,0,-0.03
142,0.015,0,-0.03
143,0.025,0,-0.03
144,0.035,0,-0.03
145,0.045,0,-0.03
146,0.055,0,-0.03
147,0.065,0,-0.03
148,0.075,0,-0.03
149,0.085,0,-0.03
*ELEMENT,TYPE=DC3D20
1,8,37,35,11,55,57,59,61,36,49,34,17,98,99,100,
101,54,56,58,60
2,4,39,37,8,63,65,57,55,38,50,36,18,102,103,98,
104,62,64,56,54
3,11,35,33,9,61,59,67,69,34,48,32,16,100,105,106,
107,60,58,66,68
4,10,41,39,4,71,73,65,63,40,51,38,19,108,109,102,
110,70,72,64,62
5,9,33,31,7,69,67,75,77,32,47,30,15,106,111,112,
113,68,66,74,76
6,6,43,41,10,79,81,73,71,42,52,40,20,114,115,108,
116,78,80,72,70
7,7,31,29,5,77,75,83,85,30,46,28,14,112,117,118,
119,76,74,82,84
8,3,23,43,6,87,89,81,79,22,53,42,21,120,121,114,
122,86,88,80,78
9,5,29,27,1,85,83,91,93,28,45,26,13,118,123,124,
125,84,82,90,92
10,2,25,23,3,95,97,89,87,24,44,22,12,126,127,120,
128,94,96,88,86
*ELEMENT,TYPE=B32
11,139,140,130
12,129,141,131
13,131,142,132
14,132,143,133
15,133,144,134
16,134,145,135
17,135,146,136
18,136,147,137
19,137,148,138
20,138,149,139
*NSET,NSET=TEMPERATURE_FACES
1
26
27
90
91
92
93
124
129
*ELSET,ELSET=SOLIDM
1
2
3
4
5
6
7
8
9
10
*ELSET,ELSET=BEAMM
11
12
13
14
15
16
17
18
19
20
*PHYSICAL CONSTANTS,ABSOLUTEZERO=0,STEFANBOLTZMANN=5.670373E-08
*MATERIAL,NAME=MATERIAL
*ELASTIC,TYPE=ISOTROPIC
210000000000,0.3
*CONDUCTIVITY,TYPE=ISO
55.6,0
*SPECIFIC HEAT
460

*SOLID SECTION,ELSET=SolidM,MATERIAL=MATERIAL
*BEAM SECTION,ELSET=BeamM,MATERIAL=MATERIAL,SECTION=RECT
0.01,0.01
0,1,0

*STEP
*HEAT TRANSFER,STEADYSTATE
1,1,0,0
*BOUNDARY
TEMPERATURE_FACES,11,,1000
*RADIATE
10,R3,300,0.98
11,R4,300,0.98
*NODE FILE,GLOBAL=YES
NT
*NODE PRINT,NSET=TEMPERATURE_FACES,GLOBAL=YES
NT
*END STEP
2

Which may seem a small temperature difference and a detail without importance reveals as a much more noticeable problem when looking at T3: One-dimensional transient heat transfer benchmark.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test T3 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Target solution: Temperature of 36.60°C at x=0.08 m at 32 secs.

C3D20 = 36.6 ºC at x= 0.08 m at 32 secs

B32 = 25.0 ºC at x= 0.08 m at 32 secs

imagen
imagen1005×582 73.9 KB

*NODE
1,0,0,0
2,0.1,0,0
3,0.09,0,0
4,0.06,0,0
5,0.01,0,0
6,0.08,0,0
7,0.02,0,0
8,0.05,0,0
9,0.03,0,0
10,0.07,0,0
11,0.04,0,0
12,0.095,0,0
13,0.005,0,0
14,0.015,0,0
15,0.025,0,0
16,0.035,0,0
17,0.045,0,0
18,0.055,0,0
19,0.065,0,0
20,0.075,0,0
21,0.085,0,0
22,0.09,0,0.005
23,0.09,0,0.01
24,0.1,0,0.005
25,0.1,0,0.01
26,0,0,0.005
27,0,0,0.01
28,0.01,0,0.005
29,0.01,0,0.01
30,0.02,0,0.005
31,0.02,0,0.01
32,0.03,0,0.005
33,0.03,0,0.01
34,0.04,0,0.005
35,0.04,0,0.01
36,0.05,0,0.005
37,0.05,0,0.01
38,0.06,0,0.005
39,0.06,0,0.01
40,0.07,0,0.005
41,0.07,0,0.01
42,0.08,0,0.005
43,0.08,0,0.01
44,0.095,0,0.01
45,0.005,0,0.01
46,0.015,0,0.01
47,0.025,0,0.01
48,0.035,0,0.01
49,0.045,0,0.01
50,0.055,0,0.01
51,0.065,0,0.01
52,0.075,0,0.01
53,0.085,0,0.01
54,0.05,-0.005,0
55,0.05,-0.01,0
56,0.05,-0.005,0.01
57,0.05,-0.01,0.01
58,0.04,-0.005,0.01
59,0.04,-0.01,0.01
60,0.04,-0.005,0
61,0.04,-0.01,0
62,0.06,-0.005,0
63,0.06,-0.01,0
64,0.06,-0.005,0.01
65,0.06,-0.01,0.01
66,0.03,-0.005,0.01
67,0.03,-0.01,0.01
68,0.03,-0.005,0
69,0.03,-0.01,0
70,0.07,-0.005,0
71,0.07,-0.01,0
72,0.07,-0.005,0.01
73,0.07,-0.01,0.01
74,0.02,-0.005,0.01
75,0.02,-0.01,0.01
76,0.02,-0.005,0
77,0.02,-0.01,0
78,0.08,-0.005,0
79,0.08,-0.01,0
80,0.08,-0.005,0.01
81,0.08,-0.01,0.01
82,0.01,-0.005,0.01
83,0.01,-0.01,0.01
84,0.01,-0.005,0
85,0.01,-0.01,0
86,0.09,-0.005,0
87,0.09,-0.01,0
88,0.09,-0.005,0.01
89,0.09,-0.01,0.01
90,0,-0.005,0.01
91,0,-0.01,0.01
92,0,-0.005,0
93,0,-0.01,0
94,0.1,-0.005,0
95,0.1,-0.01,0
96,0.1,-0.005,0.01
97,0.1,-0.01,0.01
98,0.05,-0.01,0.005
99,0.045,-0.01,0.01
100,0.04,-0.01,0.005
101,0.045,-0.01,0
102,0.06,-0.01,0.005
103,0.055,-0.01,0.01
104,0.055,-0.01,0
105,0.035,-0.01,0.01
106,0.03,-0.01,0.005
107,0.035,-0.01,0
108,0.07,-0.01,0.005
109,0.065,-0.01,0.01
110,0.065,-0.01,0
111,0.025,-0.01,0.01
112,0.02,-0.01,0.005
113,0.025,-0.01,0
114,0.08,-0.01,0.005
115,0.075,-0.01,0.01
116,0.075,-0.01,0
117,0.015,-0.01,0.01
118,0.01,-0.01,0.005
119,0.015,-0.01,0
120,0.09,-0.01,0.005
121,0.085,-0.01,0.01
122,0.085,-0.01,0
123,0.005,-0.01,0.01
124,0,-0.01,0.005
125,0.005,-0.01,0
126,0.1,-0.01,0.005
127,0.095,-0.01,0.01
128,0.095,-0.01,0
129,0,0,-0.03
130,0.1,0,-0.03
131,0.01,0,-0.03
132,0.02,0,-0.03
133,0.03,0,-0.03
134,0.04,0,-0.03
135,0.05,0,-0.03
136,0.06,0,-0.03
137,0.07,0,-0.03
138,0.08,0,-0.03
139,0.09,0,-0.03
140,0.095,0,-0.03
141,0.005,0,-0.03
142,0.015,0,-0.03
143,0.025,0,-0.03
144,0.035,0,-0.03
145,0.045,0,-0.03
146,0.055,0,-0.03
147,0.065,0,-0.03
148,0.075,0,-0.03
149,0.085,0,-0.03
*ELEMENT,TYPE=DC3D20
1,8,37,35,11,55,57,59,61,36,49,34,17,98,99,100,
101,54,56,58,60
2,4,39,37,8,63,65,57,55,38,50,36,18,102,103,98,
104,62,64,56,54
3,11,35,33,9,61,59,67,69,34,48,32,16,100,105,106,
107,60,58,66,68
4,10,41,39,4,71,73,65,63,40,51,38,19,108,109,102,
110,70,72,64,62
5,9,33,31,7,69,67,75,77,32,47,30,15,106,111,112,
113,68,66,74,76
6,6,43,41,10,79,81,73,71,42,52,40,20,114,115,108,
116,78,80,72,70
7,7,31,29,5,77,75,83,85,30,46,28,14,112,117,118,
119,76,74,82,84
8,3,23,43,6,87,89,81,79,22,53,42,21,120,121,114,
122,86,88,80,78
9,5,29,27,1,85,83,91,93,28,45,26,13,118,123,124,
125,84,82,90,92
10,2,25,23,3,95,97,89,87,24,44,22,12,126,127,120,
128,94,96,88,86
*ELEMENT,TYPE=B32
11,139,140,130
12,129,141,131
13,131,142,132
14,132,143,133
15,133,144,134
16,134,145,135
17,135,146,136
18,136,147,137
19,137,148,138
20,138,149,139
*NSET,NSET=BC_TEMP_0
1
26
27
90
91
92
93
124
129
*NSET,NSET=ALLNODES
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
*NSET,NSET=BC_TEMP_SIN
2
24
25
94
95
96
97
126
130
*ELSET,ELSET=SOLIDM
1
2
3
4
5
6
7
8
9
10
*ELSET,ELSET=BEAMM
11
12
13
14
15
16
17
18
19
20
*AMPLITUDE,NAME=A_1
0,273.15
1.0592,281.4593455043
1.8336,287.501334917
2.5344,292.9239462691
3.1776,297.8485482687
3.8016,302.5660431403
4.3968,307.0001440421
4.9664,311.1744042045
5.5136,315.1129523937
5.792,317.0874835686
6.0672,319.0186776394
6.3392,320.906363945
6.6048,322.7286099583
6.8672,324.5077194146
7.1296,326.2650167558
7.3856,327.9577191216
7.6416,329.6282657203
7.8944,331.255528441
8.144,332.8397232455
8.3936,334.4009801011
8.64,335.9191361291
8.8864,337.4137853432
9.1296,338.8654261211
9.3696,340.2744645966
9.6096,341.6596540694
9.856,343.0564539826
10.1024,344.4270741823
10.3456,345.7537210038
10.5888,347.0538796173
10.8288,348.3105001619
11.0688,349.5404165387
11.3088,350.7431917642
11.5456,351.9029122441
11.7824,353.0353933412
12.016,354.1254988139
12.2496,355.1883479872
12.4832,356.223583107
12.7168,357.2308557136
12.9472,358.1966088733
13.1776,359.1345142989
13.4048,360.0318236225
13.6352,360.9135186481
13.8624,361.7548277485
14.0896,362.567924303
14.3168,363.3525494146
14.544,364.1084532519
14.768,364.82535867
14.992,365.5138903069
15.216,366.1738350601
15.44,366.8049886748
15.664,367.4071558073
15.888,367.9801500851
16.1088,368.5162352652
16.3328,369.030783722
16.5536,369.5089396975
16.7744,369.9581182987
16.9952,370.3781844473
17.2224,370.7799029092
17.4496,371.1505351629
17.6768,371.489963196
17.9008,371.7939571393
18.128,372.071105506
18.352,372.3135157202
18.5792,372.528036416
18.8032,372.7085585159
19.0304,372.8601821756
19.2544,372.9785894866
19.4816,373.0671257221
19.7056,373.1232695648
19.9296,373.1484713996
20.1536,373.1427234263
20.3776,373.1060274241
20.6048,373.0372045267
20.8288,372.9382146588
21.056,372.8062611339
21.28,372.6451016981
21.5072,372.4501832347
21.7312,372.2270565927
21.9584,371.9694179422
22.1824,371.6846042655
22.4096,371.364568935
22.6368,371.0132612335
22.864,370.6307930207
23.0912,370.2172860776
23.3184,369.7728720685
23.5456,369.2976924986
23.7728,368.7918986692
24,368.2556516295
24.2304,367.6809274295
24.4576,367.0838732098
24.688,366.447866507
24.9184,365.7813102713
25.1488,365.0844227605
25.3792,364.357432164
25.6128,363.5898555277
25.8432,362.8029731188
26.0768,361.975192578
26.3104,361.1175135362
26.544,360.2302246876
26.7808,359.3008664439
27.0176,358.3417099824
27.2544,357.3530870601
27.4912,356.335339626
27.7312,355.2744821583
27.9712,354.1844462532
28.2112,353.0656191951
28.4544,351.9029122441
28.6976,350.7114736593
28.9408,349.4917381164
29.1872,348.2275513669
29.4336,346.9352483467
29.6832,345.5979914112
29.9328,344.2328936978
30.1856,342.8224533056
30.4384,341.3845478418
30.6944,339.901032388
30.9504,338.390533138
31.2096,336.8342855321
31.472,335.2319453047
31.7344,333.6032382806
32,331.9285252292
*INITIAL CONDITIONS,TYPE=TEMPERATURE
ALLNODES,273.15
*PHYSICAL CONSTANTS,ABSOLUTEZERO=0,STEFANBOLTZMANN=5.670373E-08

*MATERIAL,NAME=MATERIAL1
*DENSITY
7200
*CONDUCTIVITY,TYPE=ISO
35,0
*SPECIFIC HEAT
440.5

*SOLID SECTION,ELSET=SolidM,MATERIAL=MATERIAL1
*BEAM SECTION,ELSET=BeamM,MATERIAL=MATERIAL1,SECTION=RECT
0.01,0.01
0,1,0

*AMPLITUDE,NAME=A_1
0,273.15
1.0592,281.4593455043
1.8336,287.501334917
2.5344,292.9239462691
3.1776,297.8485482687
3.8016,302.5660431403
4.3968,307.0001440421
4.9664,311.1744042045
5.5136,315.1129523937
5.792,317.0874835686
6.0672,319.0186776394
6.3392,320.906363945
6.6048,322.7286099583
6.8672,324.5077194146
7.1296,326.2650167558
7.3856,327.9577191216
7.6416,329.6282657203
7.8944,331.255528441
8.144,332.8397232455
8.3936,334.4009801011
8.64,335.9191361291
8.8864,337.4137853432
9.1296,338.8654261211
9.3696,340.2744645966
9.6096,341.6596540694
9.856,343.0564539826
10.1024,344.4270741823
10.3456,345.7537210038
10.5888,347.0538796173
10.8288,348.3105001619
11.0688,349.5404165387
11.3088,350.7431917642
11.5456,351.9029122441
11.7824,353.0353933412
12.016,354.1254988139
12.2496,355.1883479872
12.4832,356.223583107
12.7168,357.2308557136
12.9472,358.1966088733
13.1776,359.1345142989
13.4048,360.0318236225
13.6352,360.9135186481
13.8624,361.7548277485
14.0896,362.567924303
14.3168,363.3525494146
14.544,364.1084532519
14.768,364.82535867
14.992,365.5138903069
15.216,366.1738350601
15.44,366.8049886748
15.664,367.4071558073
15.888,367.9801500851
16.1088,368.5162352652
16.3328,369.030783722
16.5536,369.5089396975
16.7744,369.9581182987
16.9952,370.3781844473
17.2224,370.7799029092
17.4496,371.1505351629
17.6768,371.489963196
17.9008,371.7939571393
18.128,372.071105506
18.352,372.3135157202
18.5792,372.528036416
18.8032,372.7085585159
19.0304,372.8601821756
19.2544,372.9785894866
19.4816,373.0671257221
19.7056,373.1232695648
19.9296,373.1484713996
20.1536,373.1427234263
20.3776,373.1060274241
20.6048,373.0372045267
20.8288,372.9382146588
21.056,372.8062611339
21.28,372.6451016981
21.5072,372.4501832347
21.7312,372.2270565927
21.9584,371.9694179422
22.1824,371.6846042655
22.4096,371.364568935
22.6368,371.0132612335
22.864,370.6307930207
23.0912,370.2172860776
23.3184,369.7728720685
23.5456,369.2976924986
23.7728,368.7918986692
24,368.2556516295
24.2304,367.6809274295
24.4576,367.0838732098
24.688,366.447866507
24.9184,365.7813102713
25.1488,365.0844227605
25.3792,364.357432164
25.6128,363.5898555277
25.8432,362.8029731188
26.0768,361.975192578
26.3104,361.1175135362
26.544,360.2302246876
26.7808,359.3008664439
27.0176,358.3417099824
27.2544,357.3530870601
27.4912,356.335339626
27.7312,355.2744821583
27.9712,354.1844462532
28.2112,353.0656191951
28.4544,351.9029122441
28.6976,350.7114736593
28.9408,349.4917381164
29.1872,348.2275513669
29.4336,346.9352483467
29.6832,345.5979914112
29.9328,344.2328936978
30.1856,342.8224533056
30.4384,341.3845478418
30.6944,339.901032388
30.9504,338.390533138
31.2096,336.8342855321
31.472,335.2319453047
31.7344,333.6032382806
32,331.9285252292

*STEP,INC=3200,AMPLITUDE=STEP
*HEAT TRANSFER
0.01,32,0,0.1
*BOUNDARY,AMPLITUDE=A_1
BC_TEMP_SIN,11,,1
*BOUNDARY
BC_TEMP_0,11,,273.15
*NODE FILE,GLOBAL=YES
NT
*END STEP
3

This looks very similar to the problem of imposed displacement BCs on B32. Perhaps it’s just not applying the temperature to the midside nodes.

4

That’s the same thought I had. Was that ever fixed on 2.22?

5

maybe it’s a limitation not a bugs, similar with node to face contact problem of quadratic element.

2024-12-25 15_30_30-ccx_2.22.pdf - Adobe Reader
2024-12-25 15_30_30-ccx_2.22.pdf - Adobe Reader777×395 62 KB

6

Good point, it is documented. But it makes those BCs kind of useless on end nodes. They don’t really work properly on midside nodes either.