Finite Element Analysis of Beam-to-Beam Contact
Springer Science & Business Media, Apr 24, 2010 - Technology & Engineering - 175 pages
Phenomena occurring during a contact of two bodies are encountered in everyday life. In reality almost every type of motion is related to frictional contact between a moving body and a ground. Moreover, modeling of simple and more complex processes as nailing, cutting, vacuum pressing, movement of machines and their elements, rolling or, finally, a numerical simulation of car crash tests, requires taking contact into account. Therefore, its analysis has been a subject of many research efforts for a long time now. However, it is author’s opinion that there are relatively few efforts related to contact between structural elements, like beams, plates or shells. The purpose of this work is to fill this gap. It concerns the beam-to-beam contact as a specific case of the 3D solids contact. A numerical formulation of frictional contact for beams with two shapes of cross-section is derived. Further, a couple of effective methods for modeling of smooth curves representing beam axes are presented. A part of the book is also devoted to analyze some aspects of thermo-electro-mechanical coupling in contact of thermal and electric conductors. Analyses in every chapter are illustrated with numerical examples showing the performance of derived contact finite elements.
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3D view beam elements beam finite elements beam-to-beam contact beams axes beams with rectangular Bezier calculated co-ordinates components conductors configuration of beams constraint contact between beams contact element contact finite element contact formulation contact points contact search contacting beams cross-section dimensions deformation process deformed configurations derivatives diff a2 diff b3 discretisation elastic electric conductivity electro-mechanical contact end of beam Finite Element Analysis finite element method fortran friction coefficient friction force increments initial configuration iterations kinematic variables Lagrange multipliers method linearisation Litewka matrix G mn,m Newton-Raphson method nodal displacements node-preserving nodes normal force numerical pair penalty method penalty parameter penetration function Plane XY position vectors presented in Fig rectangular cross-sections residual vector shown in Fig six+ sliding smooth tangent stiffness matrix tangential displacements temperature thermal tion values voltage Wriggers X Y Z X Y Zavarise δ δ δ ε ε ξ ξ