Keywords: topology optimization, solid isotropic microstructure with penalization method, multicriterion optimization, global optimum.

Bendsøe [1] proposed the solid isotropic microstructure with penalization (SIMP) method, similar to the homogenization method, but with fewer design variables and a simpler procedure. It utilizes the concept of material distribution and sets mesh elements as the design variables, compliance as the objective function, and fixed volume as the constraint function. The stiffness of each mesh element may be calculated using the penalty parameter. The SIMP method is currently the most comprehensive and widely used topology optimization method. It can achieve optimal material distribution and maximum structural stiffness under the constraint of a fixed volume. Bendsøe and Sigmund [2] and Rozvany [3] provided extended reviews and detailed explanation.

The SIMP method can obtain the detailed optimal structural topology with a large number of design variables. However, local optima are often formed in the rather complicated design domain. Besides, the searching domain for the optimal value is limited by the constraint, making it difficult to obtain a consistent global optimum using the SIMP method. Therefore, this paper proposes a consistent and efficient unconstrained multicriterion approach for topology optimization. The objective function of this new method includes both compliance and volume, trying to implement a multicriterion function to improve the multimodality of the model. At the same time, this method also cancels all constraint function, reducing the computation time and increasing the efficiency significantly. To prove this new method both consistent and efficient, one design example was thoroughly studied and compared with the SIMP method.

The design example, a concentrated vertical force applied at the middle of the free end of the cantilever, is conducted to compare the results of the unconstrained multicriterion approach for topology optimization and the SIMP method. It demonstrated that by introducing the multicriterion function and removing the constraint function, the unconstrained multicriterion approach for topology optimization is more consistent, more efficient, and produces better topology optimization results than the SIMP method. In addition, the elimination of the constraint function not only increases the searching domain of the optimization process and the chance of finding the global optimum, but also reduces the number of function calls and increases the efficiency.

1

M.P. Bendsøe, "Optimal Shape Design as a Material Distribution Problem", Structural Optimization, 1, 193-202, 1989. doi:10.1007/BF01650949

2

M.P. Bendsøe, O. Sigmund, "Topology Optimization: Theory, Methods, and Applications", Springer Verlag, Berlin, Germany, 2003.

3

K. Saitou, K. Izui, S. Nishiwaki, "A Survey of Structural Optimization in Mechanical Product Development", Journal of Computing and Information Science in Engineering, 5, 214-226, 2005. doi:10.1115/1.2013290

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