MINLP Optimization Of Steel Frames
Free (open access)
S. Kravanja & U. Klanšek
In this paper we deal with the topology and standard optimization of unbraced steel frames with rigid beam-to-column connections. The optimization has been performed by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP performs a discrete topology and standard dimension optimization, while continuous parameters are simultaneously calculated inside the continuous space. As the discrete/continuous optimization problem of steel frames is non-convex and highly non-linear, the Modified Outer-Approximation/Equality- Relaxation (OA/ER) algorithm has been used for the optimization. Two practical examples with the results of the optimization are shown at the end of the paper. 1 Introduction The paper presents the topology and standard dimension optimization of unbraced steel frames with rigid beam-to-column connections. The optimization of frames is performed by the Mixed-Integer Nonlinear Programming, MINLP. The MINLP is a combined discrete-continuous optimization technique. In this way, the MINLP performs the discrete topology (i.e. the number of columns and beams) and standard dimension optimization (i.e. standard cross-section sizes) simultaneously with the continuous optimization of parameters (e.g. internal forces, deflections, mass, costs, etc.). The MINLP discrete/continuous optimization problems of frames are in most cases comprehensive, non-convex and highly non-linear. This optimization approach is proposed to be performed through three steps. The first one includes the generation of a mechanical superstructure of different topology and standard dimension alternatives, the second one involves the development of an MINLP model formulation and the last one consists of a solution for the defined MINLP optimization problem.