An objective isogeometric mixed finite element formulation for nonlinear elastodynamic beams with incompatible warping strains

Abstract

We present a stable mixed isogeometric finite element formulation for geometrically and materially nonlinear beams in transient elastodynamics, where a Cosserat beam formulation with extensible directors is used. The extensible directors yield a linear configuration space incorporating constant in-plane cross-sectional strains. Higher-order (incompatible) strains are introduced to correct stiffness, whose additional degrees-of-freedom are eliminated by an element-wise condensation. Further, the present discretization of the initial director field leads to the objectivity of approximated strain measures, regardless of the degree of basis functions. For physical stress resultants and strains, we employ a global patch-wise approximation using B-spline basis functions, whose higher-order continuity enables to use much less degrees-of-freedom, compared to element-wise approximation. For time-stepping, we employ an implicit energy-momentum consistent scheme, which exhibits superior numerical stability in comparison to standard trapezoidal and mid-point rules. Several numerical examples are presented to verify the present method.

65 pages, 30 figures

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• Geometrically Exact Finite Element Formulations for Curved Slender Beams: Kirchhoff-Love Theory vs. Simo-Reissner Theory
• An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
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Cited by in corpus (1)

• A dual lumping procedure for static condensation in mixed NURBS-based isogeometric elements with optimal convergence rates for arbitrary open knot vectors