Abstract
This article is based on the planar beam theories presented in Eugster and Harsch (2020) and deals with the finite element analysis of their presented beam models. A Bubnov-Galerkin method, where B-splines are chosen for both ansatz and test functions, is applied for discretizing the variational formulation of the beam theories. Five different planar beam finite element formulations are presented: The Timoshenko beam, the Euler–Bernoulli beam obtained by enforcing the cross-section’s orthogonality constraint as well as the inextensible Euler–Bernoulli beam by additionally blocking the beam’s extension. Furthermore, the Euler–Bernoulli beam is formulated with a minimal set of kinematical descriptors together with a constrained version that satisfies inextensibility. Whenever possible, the numerical results of the different formulations are compared with analytical and semi-analytical solutions. Additionally, numerical results reported in classical beam finite element literature are collected and reproduced.
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Acknowledgements
This research has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Grant No. 405032572 as part of the priority program 2100 Soft Material Robotic Systems.
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Harsch, J., Eugster, S.R. (2020). Finite Element Analysis of Planar Nonlinear Classical Beam Theories. In: Abali, B., Giorgio, I. (eds) Developments and Novel Approaches in Nonlinear Solid Body Mechanics. Advanced Structured Materials, vol 130. Springer, Cham. https://doi.org/10.1007/978-3-030-50460-1_10
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