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Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints
Author(s) -
Maharaj Yeshern,
James Kai A.
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6273
Subject(s) - topology optimization , buckling , asymptote , finite element method , topology (electrical circuits) , structural engineering , isotropy , metamaterial , stiffness , stress (linguistics) , linear elasticity , mathematical optimization , mathematics , mathematical analysis , materials science , engineering , physics , optoelectronics , combinatorics , quantum mechanics , linguistics , philosophy
Summary This article presents the design of a metamaterial for the shear layer of a nonpneumatic tire using topology optimization, under stress and buckling constraints. These constraints are implemented for a smooth maximum function using global aggregation. A linear elastic finite element model is used, implementing solid isotropic material with penalization. Design sensitivities are determined by the adjoint method. The method of moving asymptotes is used to solve the numerical optimization problem. Two different optimization statements are used. Each requires a compliance limit and some aspect of continuation. The buckling analysis is linear, considering the generalized eigenvalue problem of the conventional and stress stiffness matrices. Various symmetries, base materials, and starting geometries are considered. This leads to novel topologies that all achieve the target effective shear modulus of 10 MPa, while staying within the stress constraint. The stress‐only designs generally were susceptible to buckling failure. A family of designs (columnar, noninterconnected representative unit cells) that emerge in this study appears to exhibit favorable properties for this application.