Konferensartikel

In this talk we present an optimization model and a solution method for optimal design of two-dimensional mechanical mechanisms. The mechanism design problem is modeled as a nonconvex mixed integer program which allows the optimal topology and geometry of the mechanism to be determined simultaneously. The underlying mechanical analysis model is based on a truss (pin jointed assembly of straight bars) representation allowing for large displacements. For mechanisms undergoing large displacement elastic stability is of major concern. We derive conditions; modeled by nonlinear matrix inequalities; that guarantee that a stable mechanism is found. The feasible set of the design problem is described by nonlinear constraints as well as nonlinear matrix inequalities.

To solve the mechanism design problem a branch and bound method based on convex relaxations is developed. The relaxations are strengthened by adding valid inequalities to the feasible set. Encouraging computational results; which will be presented; indicate that the branch and bound method can reliably solve mechanism design problems of realistic size to global optimality.

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