In this paper we present a variational method — phase transition — to address the topology optimization problem (Bendsoe & Sigmund 2003). Similar to the setting of material distribution approach, the design is restricted within a fixed reference domain. A continuous variable ρ(x) is used within the design domain x ∈ Ω such that the characteristic function of the structure being designed is defined by χ(x) : Ω → [0,1]. However, in contrast to the use of homogenized or penalized material properties, the model of material properties is isotropic and linear with respect to the design variable ρ(x), such as ρ(x) resembles the material density in the case of a single material structure.

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