Finite element formulations for constrained spatial nonlinear beam theories. (December 2021)

• Record Type: Journal Article
• Authors: Harsch, Jonas; Capobianco, Giuseppe; Eugster, Simon R
• Is Part Of: Mathematics and mechanics of solids. Volume 26:Number 12(2021)
• Page Start: 1838
• Page End: 1863
• Publication Date: 2021-12
• Subjects: Constrained theories -- B-splines -- geometrically exact beams -- initial curvature -- isogeometric analysis -- nonlinear beam elements -- objectivity; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865211000790
• Languages: English
• ISSNs: 1081-2865

Abstract

A new director-based finite element formulation for geometrically exact beams is proposed by weak enforcement of the orthonormality constraints of the directors. In addition to an improved numerical performance, this formulation enables the development of two more beam theories by adding further constraints. Thus, the paper presents a complete intrinsic spatial nonlinear theory of three kinematically different beams which can undergo large displacements and which can have precurved reference configurations. Moreover, the hyperelastic constitutive laws allow for elastic finite strain material behavior of the beams. Furthermore, the numerical discretization using concepts of isogeometric analysis is highlighted in all clarity. Finally, all presented models are numerically validated using exclusive analytical solutions, existing finite element formulations, and a complex dynamical real-world example.