# Structural Design Using Laplacian Shells

## TL;DR

This paper presents a novel method for designing lightweight, structurally robust shell objects by iteratively adjusting local thickness based on stress analysis, ensuring smooth, intersection-free boundaries through Laplace's equation solutions.

## Contribution

It introduces a shape parametrization using Laplace's equation and a gradient-free optimization approach for efficient, intersection-free shell design under complex forces.

## Key findings

- Successfully designed lightweight shells for various 3D models
- Validated structural robustness through physical experiments
- Ensured smooth, intersection-free boundaries in shell shapes

## Abstract

We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally-sound minimum weight shell object. Our approach works by altering the local shell thickness repeatedly based on the stresses that develop inside the object. A key issue in shell design is that large thickness values might result in self-intersections on the inner boundary creating a significant computational challenge during optimization. To address this, we propose a shape parametrization based on the solution to the Laplace's equation that guarantees smooth and intersection-free shell boundaries. Combined with our gradient-free optimization algorithm, our method provides a practical solution to the structural design of hollow objects with a single inner cavity. We demonstrate our method on a variety of problems with arbitrary 3D models under complex force configurations and validate its performance with physical experiments.