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Explicit free‐floating beam element
Author(s) -
Nielsen Martin B.,
Krenk Steen
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4623
Subject(s) - beam (structure) , mathematics , finite element method , quadratic equation , mathematical analysis , classical mechanics , geometry , physics , optics , thermodynamics
SUMMARY A two‐node free‐floating beam element capable of undergoing arbitrary large displacements and finite rotations is presented in explicit form. The configuration of the beam in three‐dimensional space is represented by the global components of the position of the beam nodes and an associated set of convected base vectors (directors). The local constitutive stiffness is derived from the complementary energy of a set of six independent deformation modes, each corresponding to an equilibrium state of constant internal force or moment. The deformation modes are characterized by generalized strains, formed via scalar products of the element related vectors. This leads to a homogeneous quadratic strain definition in terms of the generalized displacements, whereby the elastic energy becomes at most bi‐quadratic. Additionally, the use of independent equilibrium modes to set up the element stiffness avoids interpolation of kinematic variables, resulting in a locking‐free formulation in terms of three explicit matrices. A set of classic benchmark examples illustrates excellent performance of the explicit beam element. Copyright © 2014 John Wiley & Sons, Ltd.