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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 206
The Effect of Nonlinearity on the Design Optimization of Truss Structures T. Talaslioglu
Technical Vocational School of Osmaniye, Cukurova University, Turkey T. Talaslioglu, "The Effect of Nonlinearity on the Design Optimization of Truss Structures", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 206, 2006. doi:10.4203/ccp.83.206
Keywords: genetic algorithm, multiobjective optimization, truss, nonlinear, line search, arclength.
Summary
Optimization and structural analysis models are two main elements in the design
optimisation of truss structures. Therefore, the degree of optimality in the design of
pinconnected trusses by linear response is varied with the use of a realistic nonlinear
response. In this paper, the variation in the design optimisation by linear and
nonlinear response is considered with multiobjective genetic algorithm optimization
method with the multipopulations. While, in optimization model, pareto ranking
based on the multiobjective genetic algorithm method is employed, linesearch with
arclength method (cylindrical arclength technique) is used for the nonlinear response
in the structural analysis model. Considering that one of the preferable approaches used
by both linear and nonlinear analysis is that the total potential energy has a
stationary value at the equilibrium position, the objective functions minimize the
weight of the pinconnected truss together with its strain energy that exists in
structural mechanic.
In the following part, the proposed design model is presented by introducing: firstly the optimisation, then the structural analysis model with a comparison of the other strategies. In the design of pinconnected trusses, genetic algorithms have received considerable attention regarding their potential as a novel approach to multiobjective optimization approach. Therefore, various approaches based on the fitness assignment are adapted for the implementation with the genetic algorithm. These approaches can roughly be classified as: a) vector evaluation, b) weightedsum, c) pareto based, d) compromise and e) goal programming [1]. The method of paretoranking which is managed by fitness assignment was first suggested by Goldberg [2], as a means of achieving equal reproductive potential for all pareto individuals. In this method, the population is ranked on the basis of nondominated individuals. However, the fitness sharing must be implemented for maintaining the diversity as a result of genetic drift. After the sharing process, an appropriate selection method is used to reproduce a new generation. As to the structural analysis model, the geometric nonlinearity due to either the strain or the displacement, or both, response causes the equilibrium equations to be nonlinear. Most of the early work on the solution of the nonlinear equations are primarily based on incremental procedures. In later works, an alternative approach to the incremental procedure, the iterative procedure (Newton or Newton Raphson) is also used. However, due to uncertainty about the obtained maximization in loaddeformation response, iterative failure does not corresponded to the actual structural failure. This issue leads the development new solution methods based on load or displacement control. One class of these methods is continuation methods. The working principle of the continuation methods is based on tracing the equilibrium path by accounting for the limit points. Some of the continuum methods are quasinewton, linesearch and arclengths [3]. Quasinewton methods are developed in order to speed up the convergence of modifiedNewton method, due to existing singular points. The linesearch procedure is more successful in obtaining the iterative direction in an inexpensive way and thus, may be viewed as a useful tool to increase the robustness of the Newton methods. As to arclength methods, they are developed as a remedy in cases when the solutions exhibit limit load states, and work by following a prescribed path around the previous converged equilibrium state. The compatibility in the working of the principle of the arclength method leads to it being hybridized with the linesearch method. In order to demonstrate the variation in the optimal design with regard to the linear and nonlinear response, two of wellknown optimization examples are designed. As a result, it is shown that the effect of nonlinearity causes the increase in the weight of the truss structure. References
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