Shape optimal design of elastic space frames with non-linear response

This paper describes an approach to shape optimal design of elastic space frames with kinematically non-linear response. A space frame structure is treated as to be assembled from several frame design elements each of them being deÞned as a skeleton lying on a rational Be«zier patch. The design variables may inßuence the control points of each patch and the cross-sectional quantities of beam elements. Highly accurate beam Þnite elements are employed based on a modiÞed formulation of the beam element proposed by Jelenic« and Saje. The modiÞed element is able to account for arbitrary initial curvature and it Þts nicely into the context of both the proposed design element technique and the optimization process. The formulation of the shape optimal design problem in form of non-linear mathematical programming problem and its solution by employing gradient-based methods of mathematical programming are discussed brießy. The theory is illustrated in detail with three numerical examples