Keywords: discrete optimisation, genetic algorithms, geometrically non-linear analysis.

There are several optimisation techniques that are used to obtain optimum designs of structural systems. Khot and Kamat [1] and Saka [2] independently developed optimisation methods based on optimality criteria technique for the optimum design of geometrically non-linear truss structures with continuous design variables subject to constraints on displacements and system non-linear stability. Saka and Ulker [3] used the same optimisation method for the optimum design of geometrically non-linear space trusses with continuous design variables subject to stress and displacement constraints. It was observed by Saka and Ulker [3] that there could be a significant variation in the solution based on linear and non-linear analyses to the extent that sometimes the direction of the member force is reversed when geometric non-linearity is taken into account indicating its importance of obtaining realistic solutions.

In recent years, genetic algorithms (GAs), which are applications of biological principle into computational algorithms, has become most successful and powerful for solving structural design problems, because of their simplicity, global perspective and inherent parallel processing. Detailed and formal proof for this optimisation technique can be found in Goldberg [4] (1989). Many research studies have recently reported the solution of truss structure optimisation problems via GAs. Golberg and Samtani [5] (1986) appear to be the first to suggest the use of GAs for the optimal design of truss structure. Rajeev and Krishnamoorthy [6] (1992), Shyue and Pei-Tse [7] (1995) and Erbatur at al. [8] (2000) used GAs to find the minimum weight design trusses with discrete design variables.

All these studies have shown that GA is an effective tool for the optimal design of truss structures and is simple to implement when compared to other optimisation techniques. Furthermore, consideration of design variables as discrete quantities is essential in the optimisation of most structural system.

Much of the reported optimisation techniques for the optimum design of trusses are based on linear behaviour. However, in structural optimisation there are cases, such as long-span and slender structures (for example suspension bridges), where non-linear analysis is necessary to better represent the behaviour of the structures under the different loading conditions. In addition, much of the optimisation techniques used for the optimum design of structures are based on continuous variables, thus yielding member dimensions that are practically unachievable. None of the previous studies is based on non-linear analysis with discrete variables using GA as the optimisation tool.

In the present study an optimum design algorithm is developed for geometrically non-linear plane and space trusses composed of elements that are chosen from a given set of cross-sections. In the optimisation process the non-linear analyses of trusses are solved by an incremental strategy, non-linear equation are linearsed and iteratively solved by the Newton-Raphson method.

In order to bench mark the solutions obtained using non-linear analysis, an optimisation technique based on linear analysis is also developed. Results from the optimisation technique based on non-linear analysis are compared with the linear analysis. In addition, when possible these results are compared with the results of published examples. These comparisons proved that the developed technique is a viable technique that leads to optimum structures efficiently.

1

N.S. Khot, M.P Kamat, "Minimum weight design of structures with geometric non-linear behaviour", AIAA/ASME/ASCE/AHS, 24th Structures, Structural Dynamics and Materials Conference, Lake Tahoe, Nevada, 1983.

2

M.P. Saka, "Optimum design of non-linear space trusses", Journal of Computers & Structures 30(3), 545-551, 1988. doi:10.1016/0045-7949(88)90288-X

3

M.P. Saka, M. Ulker, "Optimum design of geometrically non-linear space trusses", Journal of Computers & Structures, 42(3), 289-299, 1992. doi:10.1016/0045-7949(92)90025-U

4

D.E. Goldberg, "Genetic algorithms in search, optimization and machine learning", Reading, MA: Addison-Wesley, 1989.

5

D.E. Goldberg, M.P. Samtani, "Engineering optimization via genetic algorithm", Ninth conference on Electronic computation, ASCE, New York, 471-482, 1986.

6

S. Rajeev, C.S. Krishnamoorthy, "Discrete optimization of structures using genetic algorithms", Journal Struct. Engrg., ASCE, 118(5), 1233-1250, 1992. doi:10.1061/(ASCE)0733-9445(1992)118:5(1233)

7

J.W. Shyue, C. Pei-Tse, "Integrated discrete and configuration optimization of trusses using genetic algorithms". J. of Computers & Structures, 55(4), 695-702, 1995. doi:10.1016/0045-7949(94)00426-4

8

F. Erbatur, H. Oguzhan, T. Ilker, K. Hakan, "Optimal design of planer and space structures with genetic algorithms", Journal of Computers & Structures, 75, 206-224, 2000. doi:10.1016/S0045-7949(99)00084-X

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