Modal analysis of hyperelastic structures in non-trivial equilibrium states via higher-order plate finite elements

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Modal analysis of hyperelastic structures in non-trivial equilibrium states via higher-order plate finite elements

Piero Chiaia

Abstract. The present work proposes a higher-order plate finite element model for the three-dimensional modal analysis of hyperelastic structures. Refined higher-order 2D models are defined in the well-established Carrera Unified Formulation (CUF) framework, coupled with the classical hyperelastic constitutive law modeling based on the strain energy function approach. Matrix forms of governing equations for static nonlinear analysis and modal analysis around nontrivial equilibrium conditions are carried out using the Principle of Virtual Displacements (PVD). The primary investigation of the following study is about the natural frequencies and modal shapes exhibited by hyperelastic soft structures subjected to pre-stress conditions.

Keywords
Higher-Order Finite Elements, Plate Models, Hyperelasticity, Compressible Soft Materials, Modal Analysis, Undamped Vibrations

Published online 6/1/2024, 5 pages
Copyright © 2024 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Piero Chiaia, Modal analysis of hyperelastic structures in non-trivial equilibrium states via higher-order plate finite elements, Materials Research Proceedings, Vol. 42, pp 26-30, 2024

DOI: https://doi.org/10.21741/9781644903193-7

The article was published as article 7 of the book Aerospace Science and Engineering

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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