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A new Kirchhoff-Love beam element and its application to polymer mechanics

Record Type:	Electronic resources : Monograph/item
Title/Author:	A new Kirchhoff-Love beam element and its application to polymer mechanicsby Matthias C. Schulz.
Author:	Schulz, Matthias C.
Published:	Cham :Springer International Publishing :2023.
Description:	xxi, 134 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	PolymersMechanical properties.
Online resource:	https://doi.org/10.1007/978-3-031-06340-4
ISBN:	9783031063404$q(electronic bk.)

A new Kirchhoff-Love beam element and its application to polymer mechanics
Schulz, Matthias C.

A new Kirchhoff-Love beam element and its application to polymer mechanics[electronic resource] /by Matthias C. Schulz. - Cham :Springer International Publishing :2023. - xxi, 134 p. :ill., digital ;24 cm. - Mechanics and adaptronics,2731-622X. - Mechanics and adaptronics..

Introduction -- Modeling of slender bodies -- Finite-element formulation of slender bodies modeled by geometrically exact beams -- Modeling the mechanics of single polymer chains in the fi nite-element framework -- Conclusion.

The novel finite element formulations fall into the category of geometrically exact Kirchhoff-Love beams. A prominent characteristic of this category is that the absence of shear deformation is strongly enforced by removing two degrees of freedom. Further, the corresponding beam theories exhibit not only translational but also rotational degrees of freedom and their configurations thus form a non-additive and non-commutative space. Sophisticated interpolation schemes are required that need to be tested not only for locking, spatial convergence behavior, and energy conservation, but also for observer invariance and path-independence. For the three novel beam element formulations all these properties are analytically and numerically studied and confirmed, if applicable. Two different rotation parameterization strategies are employed based on the well-known geodesic interpolation used in many Simo-Reissner beams and the lesser known split into the so-called smallest rotation and a torsional part. Application of the former parameterization results in a mixed finite element formulation intrinsically free of locking phenomena. Additionally, the first geometrically exact Kirchhoff-Love beam element is presented, which strongly enforces inextensibility by removing another degree of freedom. Furthermore, the numerical efficiency of the new beam formulations is compared to other beam elements that allow for or suppress shear deformation. When modeling very slender beams, the new elements offer distinct numerical advantages.

ISBN: 9783031063404$q(electronic bk.)

Standard No.: 10.1007/978-3-031-06340-4doiSubjects--Topical Terms:

190300
Polymers
--Mechanical properties.

LC Class. No.: TA455.P58

Dewey Class. No.: 620.192

A new Kirchhoff-Love beam element and its application to polymer mechanics
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505 0 $a Introduction -- Modeling of slender bodies -- Finite-element formulation of slender bodies modeled by geometrically exact beams -- Modeling the mechanics of single polymer chains in the fi nite-element framework -- Conclusion.
520 $a The novel finite element formulations fall into the category of geometrically exact Kirchhoff-Love beams. A prominent characteristic of this category is that the absence of shear deformation is strongly enforced by removing two degrees of freedom. Further, the corresponding beam theories exhibit not only translational but also rotational degrees of freedom and their configurations thus form a non-additive and non-commutative space. Sophisticated interpolation schemes are required that need to be tested not only for locking, spatial convergence behavior, and energy conservation, but also for observer invariance and path-independence. For the three novel beam element formulations all these properties are analytically and numerically studied and confirmed, if applicable. Two different rotation parameterization strategies are employed based on the well-known geodesic interpolation used in many Simo-Reissner beams and the lesser known split into the so-called smallest rotation and a torsional part. Application of the former parameterization results in a mixed finite element formulation intrinsically free of locking phenomena. Additionally, the first geometrically exact Kirchhoff-Love beam element is presented, which strongly enforces inextensibility by removing another degree of freedom. Furthermore, the numerical efficiency of the new beam formulations is compared to other beam elements that allow for or suppress shear deformation. When modeling very slender beams, the new elements offer distinct numerical advantages.
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