1 International Symposium “Steel Structures:Culture & Sustainability 2010” 21-23 September 2010, Istanbul, Turkey Paper No: TOTAL POTENTIAL OPTIMIZATION METHOD APPLIED TO ANALYSIS OF STRUCTURES Y. Cengiz TOKLU 1 , S. Caglar TOKLU 2 and Ozden ATES 3 1 Professor, Yeditepe University, Department of Civil Engineering 2 Post Graduate, TTG International, Besiktas, Istanbul 3 Assistant, Yeditepe University, Department of Civil Engineering ABSTRACT Analysis of structures is classically carried on by solving systems of equations. Although there can be found in structural monographs some applications where it is shown that analysis can be performed by energy methods, this is generally not the common way of solving statics problems. Recently, combining minimum energy principle and meta-heuristic techniques, a method called “Total Potential Optimization Method” has been introduced and it has been shown that this method is a powerful alternative to classical methods including the well known and widely applied Finite Element Method and its derivatives. In this study a brief discussion of the method is presented and formulations of the method on applications to trusses which are basic steel structures are given. Another subject dealt with is the differences in engineering approaches to solving problems of structural design and analysis. Keywords: Analysis, Finite Element Method, Meta-heuristic Techniques, Nonlinear, Total Potential Optimization Method, Truss INTRODUCTION Design and analysis are two types of problems often encountered in engineering. Usually design is considered to be an optimization process, and analysis is considered to be associated with solving systems of equations. Design in engineering is always associated with some optimization process which is usually very difficult since it cannot be carried on by simple rules like defining a function and equating its derivative with respect to a variable or to a set of variables to zero. The reason for this impossibility firstly comes from the difficulty in formulating such functions. Even for the cases where such a function can be written, it is generally nonlinear and/or undifferentiable. There are important works in the literature dealing with these difficulties (See for instance Bugeda and Oliver, 1992; Frangopol and Cheng, 1997; Haftka and Gürdal, 1992; Kamat, 1985; Prager, 1974). Seeing these difficulties, except for very simple demonstrative cases, iterative methods are to be tackled in this process of optimization (Hatay and Toklu, 2002). Analysis, on the other hand, is usually handled by solving a system of equations which are derived from equilibrium and compatibility conditions. These equations can be linear and nonlinear depending on the assumptions and the magnitude of deformations and also on the type of the materials making the structure. So, the usual trend is solving directly or iteratively these equation, i.e., finding the roots of a matrix equation.