SHAPE OPTIMAL-DESIGN OF ELASTIC PLANAR FRAMES WITH NONLINEAR RESPONSE

This paper describes an approach to shape optimal design of elastic pl anar frames with non-linear response. The foundation of the proposed a pproach forms an appropriate strategy of shape representation of the s tructure, based on the design element technique. A frame structure is treated as to be assembled from several frame design elements, which i n turn may consist of several appropriately joined beam finite element s. The shape of each frame design element is defined-by convenient fun ctions involving Bezier blending polynomials. The original formulation of the beam finite element, proposed by Saje, is modified in order to fit nicely into the context of the frame design element technique. Th e formulation, of the shape optimal design problem in a form of a prob lem of non-linear mathematical programming and its solution by employi ng gradient-based methods of mathematical programming are discussed br iefly. The theory is illustrated with two numerical examples.