Using optimization to solve truss topology design problems

Fernando Bastos *

  Adelaide Cerveira †

  Joaquim Gromicho ‡

fbastos@fc.ul.pt

† Departamento de Matemática, UTAD, Vila Real, Portugal

cerveira@utad.pt

‡ Vrije Universiteit, Amsterdam & ORTEC International, Gouda, The Netherlands

jgromicho@ortec.nl

 

Abstract:

The design of truss structures is an important engineering activity which has traditionally been done without optimization support. Nowadays we witness an increasing concern for efficiency and therefore engineers seek aid on Mathematical Programming to optimize a design. In this article, we consider a mathematical model where we maximize the stiffness with a volume constraint and bounds in the cross sectional area of the bars, [2]. The basic model is a large-scale non-convex constrained optimization problem but two equivalent problems are considered. One of them is a minimization of a convex non-smooth function in several variables (much less than in the basic model), being only one non-negative. The other is a semidefinite programming problem. We solve some instances using both alternatives and we present and compare the results.

Keywords: truss topology design, stiffness, non-smooth convex programming, descent method, semidefinite programming, duality, interior point methods

 

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