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An equilibrium‐based formulation with nonlinear configuration dependent interpolation for geometrically exact 3D beams
Author(s) -
Santana Murillo V. B.,
Sansour Carlo,
Hjiaj Mohammed,
Somja Hugues
Publication year - 2021
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.6862
Subject(s) - tangent stiffness matrix , nonlinear system , kinematics , computation , finite element method , quartic function , tangent , numerical integration , mathematical analysis , interpolation (computer graphics) , mathematics , classical mechanics , stiffness matrix , geometry , physics , algorithm , motion (physics) , quantum mechanics , thermodynamics , pure mathematics
Abstract This article describes a novel equilibrium‐based geometrically exact beam finite element formulation. First, the spatial position and rotation fields are interpolated by nonlinear configuration‐dependent functions that enforce constant strains along the element axis, completely eliminating locking phenomena. Then, the resulting kinematic fields are used to interpolate the spatial sections force and moment fields in order to fulfill equilibrium exactly in the deformed configuration. The internal variables are explicitly solved at the element level and closed‐form expressions for the internal force vector and tangent stiffness matrix are obtained, allowing for explicit computation, without numerical integration. The objectivity and absence of locking are verified and some important numerical and theoretical aspects leading to a computationally efficient strategy are highlighted and discussed. The proposed formulation is successfully tested in several numerical application examples.