A simple finite element for the geometrically exact analysis of Bernoulli–Euler rods

被引：0
作者：
Cátia da Costa e Silva
Sascha F. Maassen
Paulo M. Pimenta
Jörg Schröder
机构：
[1] University of São Paulo,Polytechnic School
[2] Universität Duisburg-Essen,undefined
来源：
Computational Mechanics | 2020年 / 65卷
关键词：
Non-linear analysis; Geometrically exact beam theory; Bernoulli–Euler; Large rotations; Finite elements;
D O I：
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中图分类号：
学科分类号：
摘要：
This work develops a simple finite element for the geometrically exact analysis of Bernoulli–Euler rods. Transversal shear deformation is not accounted for. Energetically conjugated cross-sectional stresses and strains are defined. A straight reference configuration is assumed for the rod. The cross-section undergoes a rigid body motion. A rotation tensor with the Rodrigues formula is used to describe the rotation, which makes the updating of the rotational variables very simple. A formula for the Rodrigues parameters in function of the displacements derivative and the torsion angle is for the first time settled down. The consistent connection between elements is thoroughly discussed, and an appropriate approach is developed. Cubic Hermitian interpolation for the displacements together with linear Lagrange interpolation for the torsion incremental angle were employed within the usual Finite Element Method, leading to adequate C1 continuity. A set of numerical benchmark examples illustrates the usefulness of the formulation and numerical implementation.
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页码：905 / 923
页数：18
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