Compliance optimization of the truss structures

• Autorzy: Czarnecki S.
• Konferencja: Optimal design of materials and strutures OPTY-2001 (August 27-29, 2001 ; Poznań ; Polska)
• Języki publikacji: EN

Abstrakty

EN

The paper discusses the problem of designing the stiffest truss with a given and fixed number of joints and element connections. The design variables are the cross sectional areas of the bars or/and the nodal points locations. In each case a maximal volume of a truss, constituting an isoperimetric unilateral condition is prescribed. The nodal force vector is assumed to be independent of the design variables, hence fixed during the optimization process. The equilibrium problems of the trusses are modeled by the conventional linear as well as nonlinear finite element analyses taking into account large nodal displacements and small deformations of members. New optimal layouts of plane and space trusses are presented. These new layouts are found by using the moving asymptotes algorithm, the simplex method and the optimality criteria method.

Słowa kluczowe

EN

truss structures; optimization

PL

kratownica; optymalizacja

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 2
• Strony: 117--137
• Opis fizyczny: Bibliogr. 19 poz., rys., wykr

Twórcy

autor

Czarnecki S.

• Warsaw University of Technology [Politechnika Warszawska] Al. Armii Ludowej 16, 00-637 Warsaw, Poland

Bibliografia

• [1] W. Achtziger. Topology Optimization of Discrete Structures: An Introductory Course Using Convex and Nonsmooth Analysis. Advanced School, International Centre for Mechanical Sciences (CISM), Udine, June 24-28, 1996.
• [2] M. Bendsøe. Optimization of Structural Topology, Shape, and Material. Springer, Berlin, 1995.
• [3] M. Crisfield. Non-linear Finite Element Analysis of Solids and Structures. John Wiley and Sons, New York, 1991.
• [4] S. Czarnecki. Non-linear stability analysis of the truss structures (in Polish). Computer Methods in Civil Engineering, 2: 17-30, 1996.
• [5] S. Czarnecki. Topology and shape optimization in the minimum compliance problems for shell bar structures. Lightweight Structures in Civil Engineering. Local Seminar of IASS Polish Chapter, 24-29, Warsaw-Cracow, December 1, 2000.
• [6] S. Czarnecki. Topology and shape optimization of shell bar structures. 2nd European Conference on Computational Mechanics. Solids, Structures and Coupled Problems in Engineering. 430-431, Cracow, Poland, June 26-29, 2001.
• [7] S. Czarnecki. Numerical comparative analysis of the selected algorithms in topology and shape optimization of the truss structures (in Polish). Research work No. 503/1111, Institute of Structural Mechanics, Warsaw University of Technology, June 2001.
• [8] S. Czarnecki. Compliance optimization in shape and topology designing of the truss structures. In: Book of Abstracts of the OPTY-2001, Mathematical and Engineering Aspects of Optimal Design of Materials and Structures, 27-29 August 2001, Poznan, Poland.
• [9] W. Hemp. Optimum Structures. Clarendon Press, Oxford, 1973.
• [10] T. Lewinski, M. Zhou, G. Rozvany. Extended exact solutions for least weight truss layouts - Part I: Cantilever with a horizontal axis of symmetry. Int. J. Mech. Sci., 36(5): 375-398, 1994.
• [11] T. Lewinski, M. Zhou, G. Rozvany. Extended exact solutions for least weight truss layouts - Part II: Unsymetric Cantilevers. Int. J. Mech. Sci., 36(5): 399-419, 1994.
• [12] A. Michell. The limits of economy of material in frame structures. Phil. Mag., 8: 589-597, 1904.
• [13] W. Press, S. Teukolsky, W. Vetterling, B. Flannery. Numerical Recipes in C. Cambridge University Press, 1992.
• [14] E. Riks. An incremental approach o the solution of snapping and buckling problems. Int. J. Solids Structures, 15: 529-551, 1979.
• [15] K. Svanberg. The method of moving asymptotes - a new method for structural optimization. Int. J. Num. Meth. Eng., 24: 359-373, 1987.
• [16] K. Svanberg. The method of moving asymptotes (MMA) with some extensions. In: G.I.N. Rozvany, ed., Optimization of Large Structural Systems, Vol. I, 555-566. Kluwer Academic Publishers, 1993.
• [17] W. Zabłocki. Optimization of structures and new architectural forms of tall buildings (in Polish). Architektura, 74: 96-98, 2000.
• [18] W. Zalewski, W. Zabłocki. Engineering inspiration in shaping of tall buildings (in Polish). Magazyn Budowlany, 8: 50-54, 1999.
• [19] W. Zalewski. The strength and the lightness - the muses of a structural engineer (in Polish). Architektura, 74: 94-95, 2000.