  Inspired by natural cellular materials such as trabecular bone, lattice
structures have been developed as a new type of lightweight material. In this
paper we present a novel method to design lattice structures that conform with
both the principal stress directions and the boundary of the optimized shape.
Our method consists of two major steps: the first optimizes concurrently the
shape (including its topology) and the distribution of orthotropic lattice
materials inside the shape to maximize stiffness under application-specific
external loads; the second takes the optimized configuration (i.e.
locally-defined orientation, porosity, and anisotropy) of lattice materials
from the previous step, and extracts a globally consistent lattice structure by
field-aligned parameterization. Our approach is robust and works for both 2D
planar and 3D volumetric domains. Numerical results and physical verifications
demonstrate remarkable structural properties of conforming lattice structures
generated by our method.
