Graded infill design within free-form surfaces by conformal mapping

Abstract

The infill design for free-form surfaces is challenging due to the mismatch of both the geometric feature and physical response between the curved surface on the macroscale and the regular-shaped infill unit cells on the meso/micro scale. Thus, this study proposes a novel optimization method to provide insight into the optimal design for the free-form surfaces consisting of micro-structured infills, where both the microstructural geometry and macroscopic distribution of the spatial-varying infills are optimized concurrently. In this method, a local level sets approach is proposed to generate a series of graded and connectable infill microstructures that are related to the volume fraction of each unit cell. The cubic polynomials interpolation is utilized to predict the effective properties for those graded infills rapidly. A computational conformal mapping technology is used to map the geometries between a 3D free-form surface and a regular 2D parameter space, such that the graded infills can be properly filled into the parameter domain, and then conformally mapped back onto the free-form surface to allow the infill unit cells to fit the curved surface without losing any geometric feature. Conformal shell finite element analysis defined in an orthogonal curvilinear coordinate system is derived in the lower-dimensional parameter domain to calculate the physical responses for the infill optimization during the conformal mapping. The infill optimization formulation for the free-form surface is established, which is recast as a 2D optimization problem defined in the parameter domain, aiming at minimizing the structural compliance subject to a global volume constraint. Thus, the dimension of the 3D free-form surface design problem is reduced. Several examples of the free-form surface demonstrate the features of the proposed method.