The nominal force method for truss geometry and topology optimization incorporating stability considerations

摘要

This paper presents a computationally efficient method for truss layout optimization with stability constraints. Previously proposed approaches that ensure stability of optimal frameworks are first reviewed, showing that existing studies are generally restricted to topology optimization. The present contribution aims to generalize the approach to simultaneous geometry and topology optimization. A lower-bound plastic design formulation under multiple loading will serve as basis for this purpose. The numerical difficulties associated with geometrical variations are identified and the parametrization is adapted accordingly. To avoid nodal instability, the nominal force method is adopted, which introduces artificial loading cases to simulate the effect of geometric imperfections. Hence, the truss systems with unstable nodes are eliminated from the set of optimal solutions. At the same time, the local stability of structural members is ensured via a consistent local buckling criterion. This novel formulation leads to optimal configurations that can be practically used for the preliminary design of structural frameworks. Four applications illustrate the impact of stability constraints on the solution. The importance of geometry optimization is also pointed out by comparing with results that would be unattainable by topology optimization only.