Topology Optimization Of Beam Cross Section Considering Warping Deformation

At present, the designers wish to utilize more rational methods to design the industrial, aeronautic and astronautic structures, so the designers' experience is not enough. As a kind of rational conceptual designing method, the topology optimization technique is important more and more. Especially in the aeronautic and astronautic field, there is a sort of structure such as the airplane's wing and the helicopter's rotor blade, in the design of these structures, one of the important problems is to find the location and direction of stiffeners, because the external profile (the shape and dimension) of the cross section usually can not be modified due to the aeroelastic design requirement, only stiffening inside the beam's cross section is allowed to modify. But now, topology optimization of beam cross sections is rarely found in literatures. Therefore, this paper focuses on this research work, including:1. Introduce the development about the topology optimization technique in short, and expatiate the method utilized in this paper: topology optimization based on Homogenization Method and SIMP (Solid Isotropic Material Penalization).2. Because of the shortcoming of the classical Euler-Bernouilli beam theory and Timoshenko beam theory which assume the cross section keeping plane during deforming and doesn't consider the warping deformation, this paper introduce a beam theory which considers the cross-section's warping deformation.3. The model of the topology optimization is presented: to minimize the average compliance is taken as the objective function, and the constraint is the material volume constraint. And the program is developed to realize the topology optimization technique.4. Several typical examples validate the program, and the warping displacement indicates that the II cross section has less warping deformation than the I cross section. And then, the software ANSYS is utilized to validate this paper's results.5. Topology optimization design of beam cross section under multiple loading conditions is realized, and the validity of the results is confirmed in details.6. An example in past article (Yoon Young Kim, Tae Soo Kim. Topology optimization of beam cross sections. Int. J. Solids and Structures. 37 (2000):477-493) is repeatedusing the technique of this paper, and better results are obtained. This paper concludes that our optimization technique is more applicable than the past article. 7. Topology optimization technique of this paper can find the location and direction of stiffeners in the cross section, and an airfoil designing is realized.This research was supported by the Major Research Plan (90205029) and the Major Program (10332010) of the National Nature Science Foundation of China, the Excellent Young Teacher's Program of MOE of China (2004). The financial supports are gratefully acknowledged.