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Lookup NU author(s): Dr Weicheng Huang
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© 2024 The AuthorsIn this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical model leverages differential geometry principles to accurately capture the complex nonlinear deformation patterns exhibited by axisymmetric shells. By discretizing the axisymmetric shell into interconnected 1D elements along the meridional direction, the in-plane stretching and out-of-bending potentials are formulated based on the geometric principles of 1D nodes and edges under the Kirchhoff–Love hypothesis, and elastic force vector and associated Hessian matrix required by equations of motion are later derived based on symbolic calculation. Through extensive validation with available theoretical solutions and finite element method (FEM) simulations in literature, our model demonstrates high accuracy in predicting the nonlinear behavior of axisymmetric shells. Importantly, compared to the classical theoretical model and three-dimensional (3D) FEM simulation, our model is highly computationally efficient, making it suitable for large-scale real-time simulations of nonlinear problems of shell structures such as instability and snap-through phenomena. Moreover, our framework can easily incorporate complex loading conditions, e.g., boundary nonlinear contact and multi-physics actuation, which play an essential role in the use of engineering applications, such as soft robots and flexible devices. This study demonstrates that the simplicity and effectiveness of the 1D discrete differential geometry-based approach render it a powerful tool for engineers and researchers interested in nonlinear mechanics analysis of axisymmetric shells, with potential applications in various engineering fields.
Author(s): Huang W, Liu T, Liu Z, Xu P, Liu M, Chen Y, Hsia KJ
Publication type: Article
Publication status: Published
Journal: International Journal of Mechanical Sciences
Year: 2024
Volume: 283
Print publication date: 01/12/2024
Online publication date: 21/09/2024
Acceptance date: 17/09/2024
Date deposited: 08/10/2024
ISSN (print): 0020-7403
ISSN (electronic): 1879-2162
Publisher: Elsevier Ltd
URL: https://doi.org/10.1016/j.ijmecsci.2024.109742
DOI: 10.1016/j.ijmecsci.2024.109742
Data Access Statement: The code generated during the current study is available from the corresponding author on reasonable request. Data will be made available on request.
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