دانلود رایگان مقاله روش طراحی توپولوژی ساختاری بر اساس خط تنش اصلی

Abstrac Topology optimization is an important topic in structural mechanics. One common application is to obtain the optimal distribution of material that maximizes the stiffness of the solution (minimize the compliance). However, as an iterative process, topology optimization of large and complex structures is computationally intensive. The problem becomes even more complicated if the manufacturing constraints are taken into account in the optimization process. In this paper, a novel growth method based on principal stress lines (PSLs) is presented for topology optimization. The PSLs are traced in the design domain along the direction of principal stresses, in which the materials would be located to define the geometry and topology of the structure. Consequently, the optimization problem is converted into a geometric design problem. Compared to previous methods, the computation based on PSLs is fast, and the designer can have explicit control over the number of structural members. In addition, the manufacturing constraints can easily be incorporated. Multiple test cases are given to illustrate the presented method. The PSL-based method is promising for building practical designing tools for various structural applications.

6. Conclusions and discussion

Based on the principle of minimum shear stress in the Michelltype structure and the proposition of uniform strain energy density in discrete truss structures, we presented a new structural topology design framework that is computationally fast and easy to control. Three design principles are derived from the Michell’s theorem. The principal stress lines are used to identify the topology and shape of the designed structure. The PSL-based topology growth process is to reduce the difference between the generated structure and the PSLs computed in the design domain. The fabrication constraints given by additive manufacturing processes have been incorporated in the structure design process. With a given minimum fabrication size, the refinement of the structure needs to be controlled; the finest refinement may not lead to the optimal structure. An algorithm with the topology growth as the outer loop and the size optimization as the inner loop has been developed to control the optimal refinement level. A number of examples have been used to test the PSL-based design method. The results have demonstrated its effectiveness and efficiency. In addition, the PSL-based method is general. The same design process and user interface can be used for symmetric and asymmetric cases, convex and concave domains, as well as single and multiple external forces.