Inverse design methodology of a tire

摘要

Most rubber components usually suffer large deformation, thus one should consider finite deformation theories when designing rubber products such as tires. Although finite element analysis (FEA) is useful for computing nonlinear structural response in standard problems, it is more difficult to predict the undeformed original to-be-manufactured shape of a part corresponding to a design constraint involving a prescribed deformed shape under a given load. For example, one can use an optimization technique to predict the original shape in the sense of an inverse problem via successive iteration. As another procedure to solve such inverse problems, Govindjee and Mihalic [4, 5] have proposed a new computational procedure to predict undeformed (to-be-manufactured) shapes for prescribed exterior deformed configurations, Cauchy tractions and displacement boundary conditions. In this paper, we demonstrate applications of the inverse shape determination problem for a tire design. The proposed methodology enables us to predict an undeformed (to-be-manufactured) tire shape corresponding to the design constraint of a prescribed exterior deformed configuration. After reviewing the formulation of the inverse shape determination, some numerical examples illustrating the methodology in a tire design ate presented.