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Bisbos, C. D.; Makrodimopoulos, A.; Pardalos, P. M.

Second-order cone programming approaches to static shakedown analysis in steel plasticity. (English) Zbl 1068.90099

Optim. Methods Softw. 20, No. 1, 25-52 (2005).
Summary: The finite element method discretized static shakedown analysis of steel constructions leads to large, sparse convex optimization problems. Under the von Mises yield criterion, they lead to second-order cone programming problems, for which the most appropriate techniques are interior point methods. Various approaches exploiting the specific characteristics of the shakedown problems are presented and discussed.

Cited in 19 Documents

MSC:

90C30 Nonlinear programming

Keywords:

shakedown; plasticity; second-order cone programming; large sparse optimization; FEM

Software:

Benchmarks for Optimization Software; LSQR; SDPT3
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Full Text: DOI

References:

[1] Melan E, Sitzungsbericht der Österreichischer Akademie der Wissenschaften der Mathematisch-Naturwissenschaftlichen Klasse IIa 145 pp 195– (1936)
[2] DOI: 10.1007/BF02084409 · JFM 64.0840.01 · doi:10.1007/BF02084409
[3] Koiter WT, Progress in Solid Mechanics pp pp. 165–221– (1960)
[4] DOI: 10.1007/BF02133439 · Zbl 0219.73039 · doi:10.1007/BF02133439
[5] DOI: 10.1016/0020-7683(91)90211-W · Zbl 0735.73027 · doi:10.1016/0020-7683(91)90211-W
[6] DOI: 10.1016/0020-7683(95)00185-9 · Zbl 0909.73030 · doi:10.1016/0020-7683(95)00185-9
[7] DOI: 10.1016/0749-6419(93)90021-H · Zbl 0850.73084 · doi:10.1016/0749-6419(93)90021-H
[8] DOI: 10.1016/0749-6419(86)90009-4 · Zbl 0612.73034 · doi:10.1016/0749-6419(86)90009-4
[9] DOI: 10.1016/0029-5493(81)90183-7 · doi:10.1016/0029-5493(81)90183-7
[10] Maier G, European Journal of Mechanics A – Solids 19 pp S79– (2000)
[11] DOI: 10.1115/1.1379368 · Zbl 1110.74577 · doi:10.1115/1.1379368
[12] Kamenjarzh J, Limit Analysis of Solids and Structures (1996)
[13] König JA, Shakedown of Elastic-Plastic Structures (1987)
[14] Save MA, Plastic limit analysis of plates, shells and disks (1997) · Zbl 0903.73001
[15] Cohn MZ, Engineering Plasticity by Mathematical Programming (1977)
[16] Smith DL, Mathematical Programming Methods in Structural Plasticity (1990)
[17] DOI: 10.1007/978-94-011-0271-1 · doi:10.1007/978-94-011-0271-1
[18] Weichert D, Inelastic analysis of structures under variable loads: Theory and engineering applications (2000) · Zbl 1099.74008 · doi:10.1007/978-94-010-9421-4
[19] Christiansen E, Handbook of Numerical Analysis 4 pp pp. 193–312– (1996)
[20] Heitzer M, Numerical methods for limit and shakedown analysis 15 (2003)
[21] Duvaut G, Inequalities in Mechanics and Physics (1976) · doi:10.1007/978-3-642-66165-5
[22] Panagiotopoulos PD, Inequality Problems in Mechanics and Applications. Convex and nonconvex energy functions (1985) · doi:10.1007/978-1-4612-5152-1
[23] DOI: 10.1016/0377-0427(94)00031-U · Zbl 0831.73080 · doi:10.1016/0377-0427(94)00031-U
[24] DOI: 10.1137/S1064827594275303 · Zbl 0924.73074 · doi:10.1137/S1064827594275303
[25] DOI: 10.1002/(SICI)1097-0207(19970615)40:11<2063::AID-NME159>3.0.CO;2-# · Zbl 0886.73060 · doi:10.1002/(SICI)1097-0207(19970615)40:11<2063::AID-NME159>3.0.CO;2-#
[26] DOI: 10.1002/(SICI)1097-0207(19991120)46:8<1185::AID-NME743>3.0.CO;2-N · Zbl 0951.74060 · doi:10.1002/(SICI)1097-0207(19991120)46:8<1185::AID-NME743>3.0.CO;2-N
[27] DOI: 10.1016/S0029-5493(99)00190-9 · doi:10.1016/S0029-5493(99)00190-9
[28] DOI: 10.1016/S0045-7825(96)01105-X · Zbl 0891.73021 · doi:10.1016/S0045-7825(96)01105-X
[29] DOI: 10.1016/S0997-7538(00)00171-6 · Zbl 0979.74065 · doi:10.1016/S0997-7538(00)00171-6
[30] DOI: 10.1016/S0749-6419(95)00004-6 · Zbl 0853.73021 · doi:10.1016/S0749-6419(95)00004-6
[31] DOI: 10.1016/0749-6419(92)90036-C · Zbl 0766.73026 · doi:10.1016/0749-6419(92)90036-C
[32] Stein E, Progress in Computational Analysis of Inelastic Structures (1993) · doi:10.1007/978-3-7091-2626-4
[33] DOI: 10.1016/0045-7825(95)00121-6 · Zbl 0860.73014 · doi:10.1016/0045-7825(95)00121-6
[34] DOI: 10.1016/S0045-7825(01)00374-7 · Zbl 1054.74064 · doi:10.1016/S0045-7825(01)00374-7
[35] DOI: 10.1007/s10107-002-0339-5 · Zbl 1153.90522 · doi:10.1007/s10107-002-0339-5
[36] DOI: 10.1137/1.9780898718829 · Zbl 0986.90032 · doi:10.1137/1.9780898718829
[37] DOI: 10.1016/S0024-3795(98)10032-0 · Zbl 0946.90050 · doi:10.1016/S0024-3795(98)10032-0
[38] Nesterov Y, Interior-Point Polynomial Algorithms in Convex Programming (1994) · Zbl 0824.90112 · doi:10.1137/1.9781611970791
[39] Pardalos PM, Topics in Semidefinite and Interior-Point Methods 18 (1998) · Zbl 0890.00019 · doi:10.1090/fic/018
[40] Ramana M, Interior Point Methods of Mathematical Programming pp pp. 369–398– (1996)
[41] DOI: 10.1137/1038003 · Zbl 0845.65023 · doi:10.1137/1038003
[42] Wolkowicz H, Handbook of Semidefinite Programming (2000) · doi:10.1007/978-1-4615-4381-7
[43] DOI: 10.1007/PL00011378 · doi:10.1007/PL00011378
[44] DOI: 10.1287/moor.22.1.1 · Zbl 0871.90064 · doi:10.1287/moor.22.1.1
[45] DOI: 10.1137/S1052623495290209 · Zbl 0922.90110 · doi:10.1137/S1052623495290209
[46] Tuncel I, Foundations of Computational Mathematics 1 pp 229– (2001) · doi:10.1007/s002080010009
[47] DOI: 10.1080/10556789908805750 · Zbl 0957.90129 · doi:10.1080/10556789908805750
[48] DOI: 10.1007/s10107-002-0349-3 · Zbl 1030.90137 · doi:10.1007/s10107-002-0349-3
[49] DOI: 10.1080/1055678021000045123 · Zbl 1032.90021 · doi:10.1080/1055678021000045123
[50] DOI: 10.1007/s10107-002-0347-5 · Zbl 1030.90082 · doi:10.1007/s10107-002-0347-5
[51] DOI: 10.1007/s10107-002-0355-5 · Zbl 1030.90080 · doi:10.1007/s10107-002-0355-5
[52] DOI: 10.1002/nme.551 · Zbl 1116.74404 · doi:10.1002/nme.551
[53] Borges L, European Journal of Mechanics A – Solids 15 pp 487– (1996)
[54] Yan AM, Numerical Methods for Limit and Shakedown Analysis pp pp. 85–146– (2003)
[55] Makrodimopoulos A, Computational approaches to the shakedown phenomena of metal structures under plane and axisymmetric stress state (2001)
[56] Makrodimopoulos A, Numerical Methods for Limit and Shakedown Analysis pp pp. 184–216– (2003)
[57] DOI: 10.1002/nme.537 · Zbl 1027.74075 · doi:10.1002/nme.537
[58] DOI: 10.1137/S1064827500380350 · Zbl 1163.90796 · doi:10.1137/S1064827500380350
[59] DOI: 10.1145/355993.356000 · doi:10.1145/355993.356000
[60] DOI: 10.1007/BF01182585 · Zbl 0756.73033 · doi:10.1007/BF01182585
[61] DOI: 10.1007/BF00047073 · Zbl 0732.73026 · doi:10.1007/BF00047073
[62] Gao DY, The Quarterly of Applied Mathematics 47 pp 487– (1989) · Zbl 0691.73012 · doi:10.1090/qam/1012271
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