Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion
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University of Zielona Gora, Institute of Civil Engineering, Szafrana sjr 1, 65-516 Zielona Góra, tel.+48683282322, Poland
Vilnius Gediminas Technical University, Department of Structural Mechanics, Saulétekio ave 11, 10223 Vilnius, tel-37052745216, Lithuania
Online publication date: 2016-10-21
Publication date: 2016-09-01
Civil and Environmental Engineering Reports 2016;22(3):5-24
Paper focuses on the problems of application of extreme energy principles and nonlinear mathematical programing in the theory of structural shakedown. By means of energy principles, which describes the true stress-strain state conditions of the structure, the dual mathematical models of analysis problems are formed (static and kinematic formulations). It is shown how common mathematical model of the structures optimization at shakedown with safety and serviceability constraints (according to the ultimate limit state (ULS) and serviceability limit state (SLS) requirements) on the basis of previously mentioned mathematical models is formed. The possibilities of optimization problem solution in the context of physical interpretation of optimality criterion of Rosen’s algorithm are analyzed.
Alawdin P, Bulanov G.: Shakedown of Composite Frames Taking into Account Plastic and Brittle Fracture of Elements. Civ Environ Eng Reports. 2015;15(4). doi: 10.1515/ceer-2014-0031.
Alawdin P, Kasabutski S.: Limit and shakedown analysis of RC rod cross_sections. J Civ Eng Manag. 2009;15(1):59-66. doi: 10.3846/1392-3730.2009.15.59-66.
Alawdin P, Liepa L.: Optimal shakedown analysis of plane reinforced concrete frames according to Eurocodes. Int J Mech Mater Des. December 2015. doi: 10.1007/s10999-015-9331-0.
Alawdin P, Muzychkin Y.: Limit analysis of structures with destructible elements under impact loadings. Eng Trans. 2011;59(3):139-159.
Alawdin P.: Limit Analysis of Structures under Variable Loads. Minsk: Tekhnoprint; 2005. http://isbnplus.org/9789854647....
Atkočiūnas J, Karkauskas R.: Optmization of Elastic Plastic Beam Structures. Vilnius, Lithuania: Vilnius Gediminas Technical University; 2010. doi: 10.3846/1137-S.
Atkočiūnas J, Norkus A.: Method of fictitious system for evaluation of frame shakedown displacements. Comput Struct. 1994;50(4):563-567. doi: 10.1016/0045-7949(94)90027-2.
Atkočiūnas J, Ulitinas T, Kalanta S, Blaževičius G.: An extended shakedown theory on an elastic-plastic spherical shell. Eng Struct. 2015;101:352-363. doi: 10.1016/j.engstruct.2015.07.021.
Atkočiūnas J. Mathematical models of optimization problems at shakedown. Mech Res Commun. 1999;26(3):319-326. doi: 10.1016/S0093-6413(99)00030-0.
Atkočiūnas J.: Optimal Shakedown Design of Elastic-Plastic Structures. Vilnius, Lithuania: Vilnius Gediminas Technical University; 2012. doi: 10.3846/1240-S.
Bazaraa MS, Sherali HD, Shetty CM. Nonlinear Programming: Theory and Algorithms. Hoboken, NJ, USA: John Wiley & Sons, Inc.; 2006. doi: 10.1002/0471787779.
Belytschko T, Liu WK, Moran B, Elkhodary K.: Nonlinear Finite Elements for Continua and Structures. II edition.; 2013. http://eu.wiley.com/WileyCDA/W....
BS EN 1993-1-1. Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings. 2005.
Capurso M, Corradi L, Maier G.: Bounds on deformations and displacements in shakedown theory. In: Materiaux et Structures Sous Chargement Cyclique, Ass. Amicale Des Ingenieurs Anciencs Eleves de l’E.N.P.C. Paris; 1979:231-244.
Casciaro R, Garcea G.:An iterative method for shakedown analysis. Comput Methods Appl Mech Eng. 2002;191(49-50):5761-5792. doi: 10.1016/S0045-7825(02)00496-6.
Cohn MZ, Maier G.: Engineering Plasticity by Mathematical Programming. Pergamon Press; 1979.
Čyras A, Atkočiūnas J.: Mathematical model for the analysis of elasticplastic structures under repeated-variable loading. Mech Res Commun. 1984;11(5):353-360. doi: 10.1016/0093-6413(84)90082-X.
Čyras A.: Extremum principles and optimization problems for linearly strain hardening elastoplastic structures. Appl Mech. 1986;22(4):89-96.
Daniūnas A, Kvedaras AK, Šapalas A, Šaučiuvėnas G.: Design basis of Lithuanian steel and aluminium structure codes and their relations to Eurocode. J Constr Steel Res. 2006;62(12):1250-1256. doi: 10.1016/j.jcsr.2006.04.018.
Gallagher RH. Finite Element Analysis: Fundamentals. Englewood Cliffs: Prentice-Hall; 1975. http://doi.wiley.com/10.1002/n....
Giambanco F, Palizzolo L, Caffarelli A.: Computational procedures for plastic shakedown design of structures. Struct Multidiscip Optim. 2004;28(5):317-329. doi: 10.1007/s00158-004-0402-3.
Kala Z.: Sensitivity analysis of the stability problems of thin-walled structures. J Constr Steel Res. 2005;61(3):415-422. doi: 10.1016/j.jcsr.2004.08.005.
Kalanta S.: The equilibrium finite elements in computation of elastic structures. Statyba. 1995;1(1):25-47. doi: 10.1080/13921525.1995.10531500.
Kaliszky S, Lógó J.: Plastic behaviour and stability constraints in the shakedown analysis and optimal design of trusses. Struct Multidiscip Optim. 2002;24(2):118-124. doi: 10.1007/s00158-002-0222-2.
Kaliszky S.: Elastoplastic Analysis with Limited Plastic Deformations and Displacements. Mech Struct Mach. 1996;24(1):39-50. doi: 10.1080/08905459608905254.
Karkauskas R.: Optimisation of geometrically non-linear elastic-plastic structures in the state prior to plastic collapse. J Civ Eng Manag. 2007;13(3):37-41. doi: 10.1080/13923730.2007.9636436.
Koiter WT.: General Theorems for Elastic-plastic Solids. In: Sneddon IN, Hill R, eds. Progress in Solid Mechanics. Amsterdam: North-Holland; 1960:165-221. https://books.google.lt/books?....
König JA, Kleiber M.: On a new method of shakedwon analysis. Bull l’academie Pol des Sci Ser des Sci Tech. 1978;26(4):167-171.
König JA.: Shakedown of Elastic-Plastic Structures. Vol 7. Amsterdam: Elsevier; 1987. doi: 10.1016/B978-0-444-98979-6.50018-9.
Lange-Hansen P. Comparative Study of Upper Bound Methods for the Calculation of Residual Deformations After Shakedown. Department of Structural Engineering and Materials, Technical University of Denmark; 1998.
Liepa L, Karkauskas R.: Calculation of elastic-plastic geometrically nonlinear frames. Sci - Futur Lith. 2012;4(4):326-334. doi: 10.3846/mla.2012.51.
Mróz Z, Weichert D, Dorosz S, eds.: Inelastic Behaviour of Structures under Variable Loads. Vol 36. Dordrecht: Springer Netherlands; 1995. doi: 10.1007/978-94-011-0271-1.
Rosen JB.: The Gradient Projection Method for Nonlinear Programming. Part I. Linear Constraints. J Soc Ind Appl Math. 1960;8(1):181-217. doi: 10.1137/0108011.
Rosen JB. The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints. J Soc Ind Appl Math. 1961;9(4):514-532. doi: 10.1137/0109044.
Saka MP, Kameshki ES.: Optimum design of unbraced rigid frames. Comput Struct. 1998;69(4):433-442. doi: 10.1016/S0045-7949(98)00117-5.
Stein E, Zhang G, Mahnken R.: Shakedown analysis for perfectly plastic and kinematic hardening materials. In: CISM. Progress in Computernal Analysis or Inelastic Structures. Vienna: Springer Vienna; 1993:175-244. doi: 10.1007/978-3-7091-2626-4_4.
STR 2.05.08:2005. Design of Steel Structures. 2005.
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