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Structural Design Using Laplacian Shells
Author(s) -
Ulu E.,
McCann J.,
Kara L. B.
Publication year - 2019
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13791
Subject(s) - shell (structure) , computer science , intersection (aeronautics) , laplace operator , key (lock) , boundary (topology) , parametrization (atmospheric modeling) , planar , object (grammar) , mathematical optimization , algorithm , mathematics , artificial intelligence , mathematical analysis , mechanical engineering , computer graphics (images) , physics , engineering , computer security , quantum mechanics , radiative transfer , aerospace engineering
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.