Explicit multi-material topology optimization embedded with variable-size movable holes using moving morphable bars

Abstract

In this article, an explicit topology optimization method is proposed for maximizing the overall stiffness of a multi-material continuum structure embedded with multiple variable-size movable holes based on the Moving Morphable Bars (MMB) method. To this end, multiple sets of morphable bars are used to describe the structural topology of multiphase materials, and level-set functions are used to describe the geometrical shapes of variable-size movable holes. The morphable bars and embedded holes are then projected onto multiple density fields to avoid remeshing the grids. A Solid Isotropic Material with Penalization (SIMP)-like multi-material interpolation scheme that considers embedding holes is introduced for material parameterization. Several numerical examples are performed to illustrate the effectiveness of the proposed formulation. It is seen that far fewer design variables are involved in the present formulation for multi-material topology optimization when compared to the existing optimization framework with embedded movable holes.

Keywords:

• Topology optimization
• variable-size holes
• multi-materials
• moving morphable bars

Acknowledgments

The authors are grateful to Professor Krister Svanberg for providing the MATLAB${}^{\circledR }$ code of the MMA algorithm.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [no. 11972143]; the Fundamental Research Funds for the Central Universities [nos. JZ2020HGTA0080, JZ2019HGBZ0127, PA2019GDPK0039, PA2019GDQT0016, JZ2020HGPA0112]; the Natural Science Foundation of Anhui Province [no. 2008085QA21]. The support is gratefully acknowledged.