Anisotropy

Engineering

Materials science

Planar

Computer graphics (images)

Computer science

Acoustics

Orthotropic material

Lattice (music)

Physics

Finite element method

Mathematics

Optics

Geometry

Composite material

Combinatorics

Structural engineering

Topology (electrical circuits)

Stiffness

IEEE Transactions on Visualization and Computer Graphics

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.

Design and Optimization of Conforming Lattice Structures