Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints

Abstract

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.

Structural stability and artificial buckling modes in topology optimization

“…The operating load level λ op and the safety factor s ≥ 1 are problem specific parameters. We follow Ferrari and Sigmund (2019) and Maharaj and James (2020) and employ an alternative representation of (26), whereby the N λ -constraints ( 26) are replaced by the single constraint…”

Stress‐constrained multiscale topology optimization with connectable graded microstructures using the worst‐case analysis

“…31 Maharaj and James handled the stress and bulking constraints by the global aggregation approach. 32 Alacoque et al studied the robust topology optimization of the multi-material microstructure under stress constraints and thermal load. Microstructures with high stiffness, robust strength, and unique thermal expansion properties were obtained in their works.…”

“…Coelho et al used parallel computing to reduce the computational burden of the stress‐constrained microstructural topology optimization 31 . Maharaj and James handled the stress and bulking constraints by the global aggregation approach 32 . Alacoque et al studied the robust topology optimization of the multi‐material microstructure under stress constraints and thermal load.…”

A parameter space approach for isogeometrical level set topology optimization

“…Beside improving the basics of the method, many engineering optimization problems have also been addressed in recent years. [10][11][12][13][14][15][16][17][18][19] Due to variety of topology optimization applications in real-life engineering problems, the optimization methods frequently face complicated physical domains. This leads to employ irregular discretizing mesh for the computational model of the problem.…”

“…Also, Dunning et al 8,9 used the sequential quadratic programming to enhance the level set method for considering multiple optimization constraints. Beside improving the basics of the method, many engineering optimization problems have also been addressed in recent years 10–19 …”