| Abstract: | This paper describes an approach to shape optimal design of elastic planar frames with non-linear response. The foundation of the proposed approach forms an appropriate strategy of shape representation of the structure, based on the design element technique. A frame structure is treated as to be assembled from several frame design elements, which in turn may consist of several appropriately joined beam finite elements. The shape of each frame design element is defined by convenient functions 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. The formulation of the shape optimal design problem in a form of a problem of non-linear mathematical programming and its solution by employing gradient-based methods of mathematical programming are discussed briefly. The theory is illustrated with two numerical examples. |
