Abstract
The paper presents the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of trusses. The solution of continuous/discrete non-convex and non-linear optimization problems is discussed with respect to the simultaneous topology, shape and discrete sizing optimization of trusses. A truss MINLP superstructure of different topology and design alternatives has been generated, and a special MINLP model formulation for trusses has been developed. In the optimization model, a mass objective function of the structure has been defined and subjected to design, load and dimensioning constraints. The MINLP problems are solved using the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm. Multi-level MINLP strategies are introduced to accelerate the convergence of the algorithm. The Modified Two-Phase and the Sequential Two-Phase MINLP strategies are proposed in order to solve highly combinatorial topology, shape and discrete sizing optimization problems. The importance of local buckling constraints on topology optimization is also discussed. Some simple numerical examples are shown at the end of the paper to demonstrate the suitability and efficiency of the proposed method.
Highlights
Optimization of different processes and systems has become an important factor in every aspect of human life, especially in the fields of science, industry and business.Numerous attempts have been made in the past in order to improve the efficiency and economic viability of structures in structural engineering
The present paper introduces the structural synthesis of trusses performed by the Mixed-Integer Non-linear Programming (MINLP) optimization approach
The Proposed MINLP Strategies for Truss Synthesis. Both the TP and Linked Two-Phase (LTP) multi-level MINLP strategies were applied to truss synthesis problems
Summary
Optimization of different processes and systems has become an important factor in every aspect of human life, especially in the fields of science, industry and business. At the end of the previous millennium, many efficient optimization techniques were developed for solving the discrete/continuous topology, shape and discrete dimension optimization. These techniques were developed for the solution of real engineering structures with discrete/standard dimensions. The present paper discusses the simultaneous topology, shape and discrete/standard dimension optimization of trusses using the Mixed-Integer Non-linear Programming (MINLP) approach. The general MINLP model formulation for truss structures is presented. This discrete/continuous non-convex and non-linear optimization problem is proposed to be solved by the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm by Kravanja and Grossmann [4]. The suitability and efficiency of the proposed method are shown through some numerical examples
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