Iterative Design for Optimal Geometry

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Abstract
Iterative design is considered for the case in which the node locations are not fixed and an optimality condition is developed that involves the geometric stiffness matrix. It extends somewhat existing work on optimal design for trusses when node locations are allowed to vary. It uses an extremely simple truss model that does not consider questions of buckling, multiple loading, deflection constraints, etc., sacrificing realism in favor of simplicity. The member forces and node locations are determined subject to joint equilibrium. The Kuhn-Tucker conditions are derived in the usual manner and are solved to obtain an optimal solution using Newton's method for nonlinear systems. It would appear that the assumption of constant allowable stresses would correspond to a linearization of a more realistic truss model, but that remains to be shown.

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