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This paper proposes a novel density-based method for structural designconsidering restrictions of multi-axis machining processes. A new mathematicalformulation based on Heaviside function is presented to transform the designfield into a geometry which can be manufactured by multi-axis machiningprocess. The formulation is developed for 5-axis machining, which can be alsoapplied to 2.5D milling restriction. The filter techniques are incorporated toeffectively control the minimum size of void region. The proposed method isdemonstrated by solving the compliance minimization problem for differentmachinable freeform designs. Several two and three-dimensional numericalexamples are presented and discussed in detail.

A Novel Mathematical Formulation for Density-based Topology Optimization Method Considering Multi-Axis Machining Constraint