Keywords: genetic algorithm, discrete optimization, plastic collapse, space trusses.

In the practical considerations the optimal design of steel structures is formulated as discrete optimization problem, searching for global or local optimal solution. However, most optimization methods are suited and developed for continuous design variables. In this paper, a genetic algorithm (GA) method is provided for discrete minimal weight design of space structures with plastic collapse constraints using a path-following method for stability investigation.

The GA methods are search algorithms that are based on the concepts of natural selection and natural genetics. Recently GA methods are very popular and have been used for sizing, shape, and topology optimization of structures. Most GA methods are variation of the simple GA proposed by Goldberg and Samtani [4], which consists of three basic genetic operators: reproduction, crossover, and mutation. By varying these parameters, the convergence of the problem may be altered. Much attention has been focused on finding the theoretical relationship among these parameters. Rajeev and Krishnamoorty [8] applied the GA for optimal truss design and transmission tower. They presented all the computations for three successive generations.

The optimal design of statically indeterminate structures with constraints on the collapse loading gives a lighter structure than methods concerning linear elastic material low [6]. A good review of different available methods for structural optimization problems is given by Kirsch and Rozvany [7]. However, the number of the recently published papers concerning plastic constraints is limited. Limit analysis (LA) is an alternative analytical procedure for obtaining the ultimate loading of a structure for collapse. Limit analysis [6] can formulate minimum weight design of trusses with elastic-plastic material low as a linear programming problem. However, the main difficulty of the problem formulation and its solution is the fact that the collapse loading is a non-smooth function of the design variables. Kaneko and Maier [5] proposed a simultaneous analysis and design (SAND) with a path-independent elastic-plastic material. For linear strain hardening material, the analysis represents a transformation from elastic to plastic region by using complementarity constraints. This formulation, under displacement constraints can be described as a nonlinear programming problem. It includes the nonlinear equilibrium equations as equality constraints and a branch-and-bound method is used to solve the nonlinear problem.

The applied plastic collapse oriented path-following method is a modification of the elastic path-following method described in [2]. In the optimal design searching process a design is characterised by its maximal collapse free load intensity factor. The design variables are the cross-sectional areas selected from a given set of cross-sections. The materially and geometrically non-linear truss structure is formulated as a large displacement model, using a total Lagrange representation. In this paper, an inversed Ramberg-Osgood model [1] is applied in comparison with previous result [3] using only linear elastic material low.

The results obtained using the proposed genetic algorithm for discrete optimization problem have illustrated the effectiveness for medium size structural design problems. Two of the permanently used test examples are considered.

1

Chan, S.L., Chui, P.P.T. "Non-linear static and Cyclic Analysis of steel frames with semi-rigid connections", Elsevier, 2000

2

Csébfalvi A. "A non-linear path-following method for computing the equilibrium curve of structures", Annals of Operation Research, 81, 15-23, 1998 doi:10.1023/A:1018944804979

3

Csébfalvi A., G. Csébfalvi, "A new-discrete optimization procedure for geometrically non-linear space trusses", Third World Congress of Structural and Multidisciplinary Optimization, Buffalo, New York, (WCSMO-3) 1999, On-line publication.

4

Goldberg, D.E., Samtani, M.P. "Engineering Optimization via Genetic Algorithms", 9th Conference on Electronic Computation, ASCE, New York, 471-482, 1986.

5

Kaneko, I., Maier, G. "Optimum design of plastic structures under displacement constraints", Computer Methods Appl. Mechanics Engrg. 27, 369-391, 1981. doi:10.1016/0045-7825(81)90139-0

6

Kirsh, U. "Optimum Structural Design", McGraw-Hill, 1981

7

Kirsh, U., Rozvany, G.I.N. "Alternative formulations of structural optimization", Structural Optimization, 7 32-41, 1994. doi:10.1007/BF01742501

8

Rajeev, S., Krishnamoorty, C.S. "Discrete optimization of structures using genetic algorithms", J. Structural Engineering ASCE, 118(5), 1233-1250, 1992. doi:10.1061/(ASCE)0733-9445(1992)118:5(1233)

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