Multimodal optimization of space frames for maximum frequency

The paper presents optimization methodology for the design of maximum natural frequency space frames subjected to constant volume constraint. Optimization of frames with an element's cross-sectional properties described by more than one parameter is inherently multi-modal, i.e. the fundament;ll frequency of the optimal structure is multiple. In contrast to the widely used Kuhn-Tucker conditions, the presented optimality conditions as well as the optimization algorithm based on them are valid for a multi-modal case. Rectangular cross-sections of the frame members are considered, and the limits on the maximum and minimum sizes, as well as on the ratio of two dimensions of each cross-section, are imposed. The optimization method has been implemented in a computer code which automatically detects the modality of the problem. Solutions of several space frame problems indicate that formulation of the optimality conditions based on separation of bending energy in two orthogonal planes accelerates the convergence. (C) 1997 Published by Elsevier Science Ltd.