Grouping Concept in Optimum Sizing of Truss Structures: Optimization of Truss Structures

Grouping Concept in Optimum Sizing of Truss Structures: Optimization of Truss Structures

Gebrail Bekdaş (Istanbul University, Turkey), Sinan Melih Nigdeli (Istanbul University, Turkey) and Osman Hürol Türkakın (Istanbul University, Turkey)
DOI: 10.4018/978-1-5225-4766-2.ch005

Abstract

In the optimum design of truss structures, the cross-sectional areas of structural members are optimized in order to minimize the total weight of the structures. This process is done by considering two design constraints, which are the limitation of stress of structural members and displacement of nodes of the structure. The members of truss structures are generally grouped for two reasons related to reduction of computation time and practical production of members. In this chapter, the optimum sizing of truss structures is found by using a non-linear programing tool considering the interior-point algorithm handling a Hessians for the nonlinear constrained multivariable problem. The aim of the chapter is to find the best grouping option for trusses by proposing a strategy. As a conclusion, the best grouping options for the numerical examples are found different from the existing groups in the documented methods.
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Introduction

The optimization of truss structures is an important application which is also useful in the practical design of systems. The main idea of the optimization is the minimize the total weight of truss structures by using non-linear constraints related to the maximum stress capacity of structural members and the maximum displacement of the nodal points of truss structures. In that case, the constraints are found according to analysis results of truss structures and the problems have non-linear constraints. For that reason, the sizing optimization of truss structure is a nonlinear optimization problem.

In recent years, the truss optimization problem is very active research area. Most of the proposed methods employ heuristic algorithms. In order to find a feasible solution, the members of truss structures are grouped. By grouping the structural members and reducing the number of design variables, the exact optimum results cannot be found, but a practical solution can be found by reducing the number of different structural members.

In the last decade, the optimization efforts on truss structures are mentioned in this section. Camp (2007) developed a Big Bang-Big Crunch (BB-BC) algorithm based methodology for optimum design of truss structures. Li et al. (2007) developed a methodology based on Particle Swarm Optimizer (PSO) and Harmony Search (HS) algorithm in order to optimize planar and spatial truss structures. Togan and Daloglu (2008) developed an improved Genetic Algorithm (GA) and grouped several variables after a preliminary design of the system with a constant cross-section for all structural members. Lamberti (2008) proposed a Simulated Annealing (SA) based method for both sizing and layout optimization of truss structures. BB-BC algorithm and PSO were combined in order to form a hybrid approach for optimum sizing of 3 dimensional trusses by Kaveh and Talatahari (2009a). For discrete (Kaveh & Talatahari, 2009b) and continuous (Kaveh & Talatahari, 2009c) design variables, Kaveh and Talatahari developed a hybrid method using PSO, HS and Ant Colony Optimization (ACO) for truss structures. Artificial Bee Colony and Adaptive Penalty Function (ABC-AP) was proposed by Sonmez (2011) for optimization of trusses. Degertekin (2012) studied on two different variants of HS (effective HS and self-adaptive HS) in the optimization truss structure. The education inspired Teaching Learning Based Optimization (TLBO) technique applied to the sizing optimization of trusses by Degertekin and Hayalioglu (2013). Also, the modified version of TLBO was employed by Camp and Farschin (2014) for truss structures. The hybrid particle swallow swarm optimization was developed by Kaveh et al. (2014a) and the algorithm was tested with optimization of truss structures. Kaveh et al. (2014b) developed a swarm intelligent and chaos theory based method called Chaotic Swarming of particles and the results of the algorithm were tested on sizing optimization problems of truss structures in documented methods. Dede and Ayvaz (2015) worked on the sizing and layout optimization of trusses by employing TLBO. Kaveh et al. (2015) improved magnetic charged system search algorithm in order to solve the sizing optimization problem of trusses. Colliding bodies optimization is another metaheuristic algorithm employed for the truss optimization problem by Kaveh and Mahdavi (2014) and Kaveh and Ilchi Ghazaan (2014) for the enhanced algorithm. Ray optimization (Kaveh & Khayatazad, 2013) and flower pollination (Bekdaş, G., Nigdeli, S.M., Yang, X.-S., 2015, Nigdeli, S.M., Bekdaş, G., Yang, X.-S., 2016) are the examples of the other metaheuristic algorithms used in the optimum design of truss structures.

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