Computational Design of Flexible Structures

Abstract

Computational fabrication technologies have revolutionized manufacturing by offering unprecedented control over the shape and material of the fabricated objects at accessible costs. These technologies allow users to design and create objects with arbitrary properties of motion, appearance or deformation. This rich environment spurs the creativity of designers and produces an increasing demand for computer-aided design tools that alleviate design complexity even for non-expert users. Motivated by this fact, in this thesis, we address the computational design and automatic fabrication of flexible structures, assemblies of interrelated elements that exhibit elastic behavior. We build upon mechanical simulation and numerical optimization to create innovative computational tools that model the attributes of the fabricated objects, predict their static deformation behavior, and automatically infer design attributes from user-specified goals. With this purpose, we propose a novel mechanical model for the efficient simulation of flexible rod meshes that avoid using numerical constraints. Then, we devise compact and expressive parameterizations of flexible structures, that naturally produce coherent designs. Our tools implement inverse design functionalities based on a sensitivity-based optimization algorithm, which we further extend to deal with local minimum solutions and highly constrained problems. Additionally, we propose interaction approaches that guide the user through the design process. Finally, we validate all these contributions by developing computer-aided design solutions that facilitate the creation of flexible rod meshes and Kirchhoff-Plateau surfaces. In the first part of this work, we overview the relevant foundations of mechanical simulation, analyze the optimization problem that arises from the inverse elastic design and discuss alternative solutions. Then, in the second part, we propose a computational method for the design of flexible rod meshes that automatically computes a fabricable design from user-de ned deformation examples. Finally, in the last part, we study the design and fabrication of Kirchhoff-Plateau surfaces and present a tool for interactively exploring the space of fabricable solutions.