International Journal of Recent Development in Engineering and Technology Website: www.ijrdet.com (ISSN 2347-6435(Online) Volume 3, Issue 1, July 2014) 105 Discrete Optimization of Truss Structure Using Genetic Algorithm Mallika Alapati 1 Associate Professor, Dept. of Civil Engineering, VNR Vignana Jyothi Institute of Engineering & Technology/Hyderabad/ Andhra Pradesh, India Abstract-- During the last few years, several methods have been developed for the optimal design of structures. However, most of them, because of their calculus-based nature, treat the search space of the problem as continuous, when it is really discrete. Sometimes this leads to unrealistic solutions and therefore, they are not used in practice, which still prefers to rely on the more traditional iterative methods. This paper describes and uses genetic algorithm approach which explains that in a certain community, only the best organisms survive from all the adverse effects, i.e.,“ survival of the fittest ”. This paper describes the use of genetic algorithm (GA) in performing optimization of 2D truss structures to achieve minimum weight. The GA uses fixed length vector of the design variables which are the cross-sectional areas of the members. The objective considered here is minimizing the weight of the structure. The constraints in this problem are the stress and deflection in no member of the structure should exceed the allowable stress and deflection of the material. As a case study this method is applied to a bench mark example of 10 bar truss and the results provided show that the minimum weight obtained is further reduced by the methodology adopted. Keywords-- Optimal design, optimization, Genetic algorithm I. INTRODUCTION Typical structural optimization problem evolves the search for the minimum of a stated objective function subject to various constraints on such performance measures as stresses and deflections, and also restricted by practical minimum sizes, or dimensions of structural members or components. If the design variables may be continuously varied between practical extremes, the problem is termed continuous, while if the design variables represent a selection from a set of parts, the problem is considered discrete. Many of the mathematical and numerical methods for optimization rely on the assumption of continuity of both the design variables and objective function. Under these assumptions, if the structural problem is actually discrete in nature, than the resulting optimum values of the continuous design variables must be converted to appropriate discrete values. A conservative approach is to round to the next larger available values and to check that the constraints are still satisfied. Park and Lee (1992) have proposed an alternative method of conversion as a post-processor of structural optimization problems. But this approach seems to be limited to moderate size problems. A. Structural Optimization Structural optimization involves the challenge of providing the most efficient design: i.e. the least expensive design which will satisfy all the design criteria for the entire life span of the structure. The cost of the structure is reduced by optimizing the use of materials (which is related to the weight of the structure) and labor (which involves fabrication and construction time and is related to the weight and complexity – topology and configuration of the structure). Since, configuration and topological optimization are nearly impossible to conduct using existing design and optimization methods, only sizing optimization is usually attempted in structural design. Topological and configuration optimization are, thus actively researched fields in structural optimization. The introduction of GAs into the field of structural optimization has opened new avenues for research because they have been successful where traditional methods have failed. B. Trusses and Design of trusses A truss is a system of straight bars joined together at their ends to form a rigid framework to transfer the loads applied to the supports in the form of purely axial (compressive or tensile) forces. All trusses are actually three-dimensional structures, but most can be reduced to planar or two dimensional trusses with the loads and reactions acting in their plane. The trusses that are analyzed here are based on a mathematical model, called the ideal planar truss, which is subject to the following assumptions: (1) all external forces are applied at the nodes or joints. (2) Bars are connected by frictional less hinges. (3) Each bar is subjected to axial stress only and this stress is constant along the length.