Topology optimization of beam crosssection （拓扑优化梁的横截面）.pdf

Struct Multidisc Optim DOI 10.1007/s00158-007-0138-y RESEARCH PAPER Topology optimization of beam cross-section considering warping deformation Shutian Liu Xiaomin An Haipeng Jia Received: 14 August 2006 /Revised: 24 February 2007 /Accepted: 25 March 2007 # Springer-Verlag 2007 Abstract The beam cross-section optimization problems 1 Introduction have been very important as beams are widely used as efficient load-carrying structural components. Most of the Beams are very important load-carrying components in earlier investigations focus on the dimension and shape engineering structures. For example, the rotor blades of optimization or on the topology optimization along the modern helicopters and large wind generators (Giavotto et axial direction. An important problem in beam section al. 1983) are typical beam structures. In the design of design is to find the location and direction of stiffeners, for modern structures, such as aeronautic and astronautic the introduction of a stiffener in a closed beam section may structures, weight reduction is an important requirement result in a topologically different configuration from the besides catering to certain structural performance. There- original; the existing section shape optimization theory fore, it is extremely concerned to design structural cannot be used. The purpose of this paper is to formulate a formations of beams by investigating the optimization section topology optimization technique based on an techniques. At present, for the structural design of beams, anisotropic beam theory considering warping of sections the focus is mainly on the dimensions, shape optimization and coupling among defor