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| Topology optimization of thin-and-long structures |
| Revised:May 05, 2003 |
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| DOI：10.7511/jslx20046117 |
| KeyWord:topology optimization,compliance,cantilever beam,SIMP |
| Liu Shutian~ |
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| Abstract: |
| Generally, an optimal topology is obtained by optimizing the material distribution in a given design domain. A distinctive topology configuration can be obtained when the design domain has similar size along the width and length for a plane problem. However, it is often difficult to solve the topology optimization problem for a long-and-thin structure using conventional algorithm. To ensure that the ground structure includes topology configurations as more as possible, enough divisions along the width should be made, which leads to the addition of the elements and/or design variables and makes the problem difficult to solve. In this paper, a method of topology optimization of long-and-thin structures through repeating the base structure is proposed. The base structure can be obtained by a minimum averaged compliance density (ACD) based algorithm, in which the ACD is taken as the objective function, and the topology or the material distribution and the domain dimensions of the structure are optimized simultaneously. As an illustrated example, a cantilever beam with large aspect ratio is optimized, and the effects of the relative value of the moment to shear force on the dangerous section and the weight limit on the optimal topology configurations are discussed in detail. Results show that different relative value of the moment may correspond to different optimal topology, and the optimal topology varies from truss-like structure to vertical stiffened box-like structure with increasing the moment relative to shear force. |
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