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| Bi-mapping Solving Approach for the ICM Method of Structural Topology Optimization |
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Abstract Based on the ICM (independent, continuous, mapping) method of structural topology optimization, a new approach for solving approach with bi-mapping is developed. Because the prefix “bi-” is abbreviated as B in English, it is called B-ICM approach. This approach consists of two steps: the first step is to apply L (linear) mapping to the structural topology optimization problem, making it a discrete model, and then construct the constraint function; the second step is to apply NL (nonlinear) mapping to the discrete model, making it a continuous model, and realizing the conversion of elemental topology variables from discrete to continuous. In the previous ICM method, the first step above only plays a theoretical derivation role, and the construction of constraint function, modeling and solving algorithms are included in the second step, so it belongs to the "one-step" approach. Although B-ICM belongs to the "two-steps" approach, the sequential dual quadratic programming algorithm commonly used in the ICM method is still adopted to solve the optimization model.The volume minimization problem with displacement constraints is taken as an example to illustrate the above modeling and solving process. The examples with single load case and multi-load cases confirm that the research achieves the expected results. Compared with the three methods aiming at obtaining clear topology (1, SIMP method with Heaviside projection; 2, Floating Projection Topology Optimization (FPTO) method; 3, Non-Penalized Smooth Boundary Material Distribution Topology Optimization (SEMDOT) method ) and the previous solving approach of the ICM method, the iteration times, clarity, optimization ability and other aspects are compared. The results show that the B-ICM solving approach performs best. This study not only enriches the modeling strategy of ICM method, promotes the improvement of solving approach of ICM method, but also provides a superior approach for solving blurry boundary problems. In the past topology optimization solving of continuum structure, the filtering operation adopted to eliminate the checkerboard and mesh dependence problems leads to blurry boundary of the optimal topology. And the larger the filtering radius, the more blurry the boundary.This paper overcomes the problem, and can successfully obtain the clear boundary of the optimal topology. It is worth mentioning that the key techniques of this study can be transplanted to all continuous variable optimization methods, including the variable density method.
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Received: 31 July 2024
Published: 23 April 2025
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2025, Vol. 46 
