Structural Synthesis Using The MINLP Optimization Approach
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This paper presents a structural synthesis using the Mixed-Integer Non-Linear Programming (MINLP) approach. The MINLP is a combined discrete/continuous optimization technique, where discrete binary 0-1 variables are defined for optimization of discrete alternatives and continuous variables for optimization of parameters. The MINLP optimization to a structural synthesis is performed through three steps: i.e. the generation of a mechanical superstructure, the modelling of an MINLP model formulation and the solution of the defined MINLP problem. As the discrete/continuous optimization problems are usually non-convex and highly non-linear, the Modified Outer-Approximation/Equality- Relaxation (OA/ER) algorithm is selected to be used for the optimization. The accompanied Linked Multilevel Hierarchical Strategy (LMHS) is developed to accelerate the convergence of the above-mentioned algorithm. Some examples are presented at the end of the paper. 1 Introduction The paper presents structural synthesis using Mixed-Integer Non-Linear Programming (MINLP) approach. The MINLP handles with continuous and discrete binary 0-1 variables simultaneously. While continuous variables are defined for the continuous optimization of parameters (dimensions, stresses, strains, weights, costs, etc.), discrete variables are used to express discrete decisions, i.e. usually the existence or non-existence of structural elements inside the defined structure. Different materials, standard dimensions and rounded continuous dimensions may also be defined as discrete alternatives. Since continuous and discrete optimizations are carried out simultaneously, the MINLP approach also finds optimal continuous parameters, structural topology, material, standard and rounded dimensions simultaneously.