Nonlinear Elastic Deformation of Mindlin Torus

Bohua Sun

doi:10.20944/preprints202107.0371.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 14 July 2021 / Approved: 16 July 2021 / Online: 16 July 2021 (12:47:16 CEST)

The nonlinear deformation and stress analysis of a circular torus is a difficult undertaking due to its complicated topology and the variation of the Gauss curvature. A nonlinear deformation (only one term in strain is omitted) of Mindlin torus was formulated in terms of the generalized displacement, and a general Maple code was written for numerical simulations. Numerical investigations show that the results obtained by nonlinear Mindlin, linear Mindlin, nonlinear Kirchhoff-Love, and linear Kirchhoff-Love models are close to each other. The study further reveals that the linear Kirchhoff-Love modeling of the circular torus gives good accuracy and provides assurance that the nonlinear deformation and stress analysis (not dynamics) of a Mindlin torus can be replaced by a simpler formulation, such as a linear Kirchhoff-Love theory of the torus, which has not been reported in the literature.

circular torus; nonlinear deformation; shear deformation; Mindlin; Gauss curvature; Maple

PHYSICAL SCIENCES, Acoustics

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Nonlinear Elastic Deformation of Mindlin Torus

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