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

Multibody System Dynamics, vol. 63, pp. 615–668

Abstract

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 using much fewer degrees of freedom than an element-wise approximation. For time-stepping, we employ 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.

Authors 3

1. Sven Klinkel Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Mies-van-der-Rohe Str. 1, Aachen, 52074, Germany

2. Simon Klarmann Aachen Chair of Structural Analysis and Dynamics

   RWTH Aachen University

   Affiliation as printed

   Chair of Structural Analysis and Dynamics, RWTH Aachen University, Mies-van-der-Rohe Str. 1, Aachen, 52074, Germany

3. Roger A. Sauer

   Ruhr University Bochum · Indian Institute of Technology Guwahati · Gdańsk University of Technology

   Affiliation as printed

   Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Assam, 781039, India

   Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, ul. Narutowicza 11/12, Gdańsk, 80-233, Poland

   Institute for Structural Mechanics, Ruhr University Bochum, Universitätsstraße 150, Bochum, 44801, Germany