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| Structural topology optimization method using high accuracy approximation of the step function |
| Received:October 13, 2009 Revised:January 17, 2010 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20106002 |
| KeyWord:step function exponential type function ICM method structural topology optimization |
| Author | Institution |
| 隋允康 |
北京工业大学,北京 |
| 宣东海 |
北京工业大学,北京 |
| 叶红玲 |
北京工业大学,北京 |
| 铁军 |
北京工业大学,北京 |
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| Abstract: |
| To increase efficiency of solving problems of structural topology optimization by using the ICM (Independent Continuous and Mapping) method, some functions are improved to approximate the step function and its inverse function in this paper. Firstly, the polish function and filter function in ICM method are classified by their properties of approximation, and the concepts of left polish function, upper polish function, fast filter function and slow filter function are presented respectively. Then two discriminant theorems, which distinguish two types of polish functions and two types of filter functions respectively, are derived. Two corresponding theorems, which represent the corresponding relationships between upper polish function and fast filter function, left polish function and slow filter function, are also proposed. Furthermore, a use criterion and construction method of the polish function and filter function are given in the paper. A new structural topology optimization model, which approximates the original model with higher precision, is formulated by using exponential type function as left polish function to approximate the step function. Above mentioned strategies bring the nonlinear degree of optimization model higher, so it can solve the optimization model with increased difficulties. In order to overcome the difficulties, a sequential quadratic approximate algorithm is proposed based on exact dual mapping. Finally, an algorithm is formulated by taking weight minimization with displacement constraints as an example. Compared with the past results when a power function is used as the polish function, it indicates that our optimization model is more rational and the corresponding algorithm is more efficient. Moreover, since the accuracy of approximating the step function is increased by taking a fast filter function as the filter function, number of iterations of optimization solution is greatly reduced. |
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