By Przemyslaw Litewka
Phenomena taking place in the course of a touch of 2 our bodies are encountered in lifestyle. actually virtually all types of movement is said to frictional touch among a relocating physique and a flooring. additionally, modeling of straightforward and extra complicated tactics as nailing, slicing, vacuum urgent, stream of machines and their parts, rolling or, ultimately, a numerical simulation of auto crash assessments, calls for taking touch under consideration. consequently, its research has been a topic of many examine efforts for a very long time now. in spite of the fact that, it really is author’s opinion that there are quite few efforts regarding touch among structural components, like beams, plates or shells. the aim of this paintings is to fill this hole. It matters the beam-to-beam touch as a particular case of the 3D solids touch. A numerical formula of frictional touch for beams with shapes of cross-section is derived. extra, a number of potent equipment for modeling of tender curves representing beam axes are awarded. part of the e-book can be dedicated to study a few points of thermo-electro-mechanical coupling in touch of thermal and electrical conductors. Analyses in each bankruptcy are illustrated with numerical examples exhibiting the functionality of derived touch finite parts.
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Additional resources for Finite Element Analysis of Beam-to-Beam Contact (Lecture Notes in Applied and Computational Mechanics, 53)
However, if a quite reasonable assumption is made, that the length of the beam elements is not smaller than their cross-section dimensions, then the actual contact point candidate lies within the found element or at the most extreme case within one of neighbouring elements. I–2 I–1 I beam m xmI IC I+1 xmIC xmI+1 I+2 dmin J+2 xsJ+1 xsJ xsJC I+3 J+1 JC J beam s J–1 J–2 Fig. 4 Search for the pair of closest beam elements The further stages of the contact search must differ for different shapes of the beams cross-sections.
These formulae contain a unit normal vector defined as n= (x mn − x sn ) = dN x mn,m × x sn,s x mn,m × x sn,s . 26) must be determined at the current positions of the contact points Cmn and Csn, what is emphasized with an additional subscript n. 25)3 involves two rather unusual variables: Δδumn and Δδusn, which in the typical finite element formulations are zero. It is so because usually a displacement approximation is linearly dependent on nodal displacements, so its second partial derivatives vanish.
10) is positive, then the friction is in the slip state. A too large value of the friction force must be reduced to the maximum value corresponding to the sliding limit. 14) et − FTsn sign g Tsn . The orientation of the displacements is controlled by the sign of the value of its trial elastic part. 20) applied to the elastic part of the tangential displacement is fulfilled exactly. Hence, the entire value of the tangential displacement is equal to its plastic part – it is non-zero only in the slip state.
Finite Element Analysis of Beam-to-Beam Contact (Lecture Notes in Applied and Computational Mechanics, 53) by Przemyslaw Litewka