%0 Book Section %1 Harsch2020 %A Harsch, Jonas %A Eugster, Simon R. %B Developments and Novel Approaches in Nonlinear Solid Body Mechanics %C Cham %D 2020 %E Abali, Bilen Emek %E Giorgio, Ivan %I Springer International Publishing %K %P 123--157 %R 10.1007/978-3-030-50460-1_10 %T Finite Element Analysis of Planar Nonlinear Classical Beam Theories %U https://doi.org/10.1007/978-3-030-50460-1_10 %X 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. %@ 978-3-030-50460-1

@inbook{Harsch2020, 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.}, added-at = {2023-04-19T09:19:49.000+0200}, address = {Cham}, author = {Harsch, Jonas and Eugster, Simon R.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2c87aee921c19c9d7dab883ad8049ade0/jharsch}, booktitle = {Developments and Novel Approaches in Nonlinear Solid Body Mechanics}, doi = {10.1007/978-3-030-50460-1_10}, editor = {Abali, Bilen Emek and Giorgio, Ivan}, file = {:Harsch2020a.pdf:PDF}, interhash = {422d9982d9dc5f3aef6efc9a1632787e}, intrahash = {c87aee921c19c9d7dab883ad8049ade0}, isbn = {978-3-030-50460-1}, keywords = {}, pages = {123--157}, publisher = {Springer International Publishing}, timestamp = {2023-04-19T09:19:56.000+0200}, title = {Finite Element Analysis of Planar Nonlinear Classical Beam Theories}, url = {https://doi.org/10.1007/978-3-030-50460-1_10}, year = 2020 }