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2024 | OriginalPaper | Chapter

Finite Dimensional Modeling of an Elastic Rib

Authors : Ivan Alpatov, Marat Dosaev, Vitaly Samsonov, Ekaterina Vorobyeva, Vadim Dubrov

Published in: Perspectives in Dynamical Systems I — Applications

Publisher: Springer International Publishing

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Abstract

Finite dimensional modeling is the most important method of modeling biological objects. Our goal was to apply this method to build thorax models for patients with pectus carinatum. We presented a workflow for building finite element models from CT scans with the focus on using free open-source software, including 3D Slicer and Ansys Student.

We also developed a mechanical model of a flat rib under load and proposed a method for its parameters’ identification. The rib is modeled by five rigid rods connected by torsion springs. We took into account the compliance in costovertebral joint by including to the model two cylindrical springs that connect the head of the rib with fixed perpendicular planes (which models that corresponding vertebra is fixed). There is also a torsion spring in the head of the rib that hinders the rotation of the rib in costovertebral joint. The load is applied to the free end of the last rod in the system.

We obtained the equations of equilibrium for the described system. Stiffnesses’ identification was made from the assumption that small displacements of the first rod’s free end and displacements of non-fixed end of homogeneous isotropic linear elastic curved beam are equal.

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Title: Finite Dimensional Modeling of an Elastic Rib
Authors: Ivan Alpatov
Marat Dosaev
Vitaly Samsonov
Ekaterina Vorobyeva
Vadim Dubrov
Publisher: Springer International Publishing
Book: Perspectives in Dynamical Systems I — Applications
Print ISBN: 978-3-031-56491-8

Electronic ISBN: 978-3-031-56492-5

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-56492-5_4

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