# Design and Optimization of Conforming Lattice Structures

## TL;DR

This paper introduces a new method for designing conforming lattice structures that optimize shape and internal material distribution to maximize stiffness, applicable to both 2D and 3D domains, with demonstrated structural benefits.

## Contribution

It presents a novel two-step approach for shape and lattice material optimization, including conforming lattice extraction, which is robust and applicable to complex geometries.

## Key findings

- Enhanced structural stiffness in optimized lattice designs
- Effective conforming lattice structures for 2D and 3D domains
- Physical verification confirms numerical results

## Abstract

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.