Systematic Design Optimization of the Metamaterial Shear Beam of a Nonpneumatic Wheel for Low Rolling Resistance

Czech, Christopher; Guarneri, Paolo; Thyagaraja, Niranjan; Fadel, Georges

doi:10.1115/1.4029518

Cited by 11 publications

(15 citation statements)

References 18 publications

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“…Hence, the shear strain is at its maximum at the edge of the contact region— the most onerous deformation seen by the prospective metamaterial. By considering a vertical force balance, we arrive at the following relation for (average) contact pressure,

{\overset{true‾}{p}}_{contact}

, in terms of the effective shear modulus,

\overset{true‾}{G}

, tire radius, R , and shear layer thickness, h :

{\overset{true‾}{p}}_{contact} \approx \frac{\overset{true‾}{G} h}{R} .

…”

Section: Problem Descriptionmentioning

confidence: 99%

“…The elements cover a rectangular domain (Figure ) of the prospective shear layer RVE (Figure , Table ) in preparation for a (material design) layout optimization . Notwithstanding the complexities of even the idealized NPT deformation and loading described above, we apply a fixed horizontal load on the top boundary of the domain . We will optimize with a domain 2 h wide (further explanation is given in Section 4.5).…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Recall from Equation that the average contact pressure is proportional to

\overset{true‾}{G}

. A lower

\overset{true‾}{G}

(ie, lower than can be provided by monolithic low‐loss materials) stems from limitations on allowable tire contact pressure, which in turn stem from higher level requirements such as passenger comfort and high‐speed dynamic loading . The compliance, C , is defined as

C = F^{p} \cdot u^{p} .

…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Depiction of a nonpneumatic tire (adapted from Czech et al) [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Introductionmentioning

confidence: 99%

“…This model realized a reentrant auxetic honeycomb topology. Czech et al used the globally optimized results from Thyagaraja et al as input to the metamaterial topology optimization of the shear layer. This was performed mainly using polycarbonate as a candidate material for a range of optimal shear layer thicknesses and metamaterial shear modulus combinations.…”

Section: Introductionmentioning

confidence: 99%

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Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints

Maharaj

James

2019

Numerical Meth Engineering

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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.

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{\overset{true‾}{p}}_{contact}

, in terms of the effective shear modulus,

\overset{true‾}{G}

, tire radius, R , and shear layer thickness, h :

{\overset{true‾}{p}}_{contact} \approx \frac{\overset{true‾}{G} h}{R} .

…”

Section: Problem Descriptionmentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

“…Recall from Equation that the average contact pressure is proportional to

\overset{true‾}{G}

. A lower

\overset{true‾}{G}

C = F^{p} \cdot u^{p} .

…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Depiction of a nonpneumatic tire (adapted from Czech et al) [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints

Maharaj

James

2019

Numerical Meth Engineering

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show abstract

A comprehensive review on non-pneumatic tyre research

Deng¹,

Wang²,

Shen³

et al. 2023

Materials & Design

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Investigation on static grounding analysis model of non-pneumatic tire with nonlinear spokes

et al. 2021

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A static grounding analysis model of non-pneumatic tire (NPT) was built and presented in this paper. The proposed NPT analysis model considers the non-linearity of the spoke stiffness and is suitable for the performance exploration of various structures of the NPT. First, the shear band, rigid rim, and spoke structure of the NPT were simplified, the main structural parameters and mechanical parameters were extracted, and an analysis model was established. The model can describe the deformation of the NPT when it is subjected to external forces. On this basis, the different stiffness of the spokes during tension and compression was considered, an iterative method was used to compensate for the difference in the deformation caused by the difference in radial stiffness of the spokes, and an analysis model of NPT with nonlinear spokes was established. Then, the contact between the tire and the road surface was introduced to iteratively compensate for the reaction force of the road surface, and the deformation of the NPT with nonlinear spokes on the road surface was obtained. Finally, the finite element software ABAQUS was used to verify the accuracy of the model. This model contains more comprehensive structural parameters and material parameters, which can more realistically simulate the structural characteristics and static grounding behavior of the NPT.

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Systematic Design Optimization of the Metamaterial Shear Beam of a Nonpneumatic Wheel for Low Rolling Resistance

Cited by 11 publications

References 18 publications

Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints

Metamaterial topology optimization of nonpneumatic tires with stress and buckling constraints

A comprehensive review on non-pneumatic tyre research

Investigation on static grounding analysis model of non-pneumatic tire with nonlinear spokes

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