TY - JOUR
T1 - Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam
AU - Borković, A.
AU - Marussig, B.
AU - Radenković, G.
N1 - Funding Information:
We acknowledge the support of the Austrian Science Fund (FWF) : M 2806-N .
Publisher Copyright:
© 2021 The Author(s)
PY - 2022/2/15
Y1 - 2022/2/15
N2 - The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli–Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness on the nonlinear distribution of axial strain over the cross section. The exact constitutive relation between energetically conjugated pairs is employed, along with four reduced relations. The isogeometric approach, which allows smooth connections between finite elements, is used for the spatial discretization of the weak form. Two methods for updating the local vector basis are applied and discussed in the context of finite rotations. All the requirements of geometrically exact beam theory are satisfied, such as objectivity and path-independence. The accuracy of the formulation is verified by a thorough numerical analysis. The influence of the curviness on the structural response is scrutinized for two classic examples. If the exact response of the structure is sought, the curviness must be considered when choosing the appropriate beam model.
AB - The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli–Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness on the nonlinear distribution of axial strain over the cross section. The exact constitutive relation between energetically conjugated pairs is employed, along with four reduced relations. The isogeometric approach, which allows smooth connections between finite elements, is used for the spatial discretization of the weak form. Two methods for updating the local vector basis are applied and discussed in the context of finite rotations. All the requirements of geometrically exact beam theory are satisfied, such as objectivity and path-independence. The accuracy of the formulation is verified by a thorough numerical analysis. The influence of the curviness on the structural response is scrutinized for two classic examples. If the exact response of the structure is sought, the curviness must be considered when choosing the appropriate beam model.
KW - Analytical constitutive relation
KW - Geometrically exact analysis
KW - Spatial Bernoulli–Euler beam
KW - Strongly curved beams
UR - http://www.scopus.com/inward/record.url?scp=85122281382&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2021.114447
DO - 10.1016/j.cma.2021.114447
M3 - Article
AN - SCOPUS:85122281382
SN - 0045-7825
VL - 390
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 114447
ER -