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

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.

Automated summary

An explicit topology optimization method based on the MMB method is proposed for a multi-material continuum structure with multiple variable-size movable holes. The method utilizes multiple sets of morphable bars and level-set functions to describe the structural topology and geometrical shapes of the holes, projecting them onto density fields to avoid remeshing. The effectiveness of the proposed formulation is demonstrated through numerical examples, showing a reduction in design variables compared to existing optimization frameworks with embedded movable holes.