By Przemyslaw Litewka
Phenomena taking place in the course of a touch of 2 our bodies are encountered in lifestyle. actually virtually every kind of movement is expounded to frictional touch among a relocating physique and a flooring. furthermore, modeling of easy and extra complicated techniques as nailing, slicing, vacuum urgent, circulate of machines and their components, rolling or, eventually, a numerical simulation of vehicle crash exams, calls for taking touch into consideration. accordingly, its research has been a topic of many examine efforts for a very long time now. even if, it's author’s opinion that there are quite few efforts relating to touch among structural parts, like beams, plates or shells. the aim of this paintings is to fill this hole. It matters the beam-to-beam touch as a selected case of the 3D solids touch. A numerical formula of frictional touch for beams with shapes of cross-section is derived. additional, a number of powerful equipment for modeling of tender curves representing beam axes are offered. part of the ebook is usually dedicated to learn a few features of thermo-electro-mechanical coupling in touch of thermal and electrical conductors. Analyses in each bankruptcy are illustrated with numerical examples displaying the functionality of derived touch finite components.
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Additional info for Finite Element Analysis of Beam-to-Beam Contact (Lecture Notes in Applied and Computational Mechanics)
Example text
3, cross-section dimensions bs = bt = 5, length 100, penalty parameter εN = 40000. Deformed configurations of the beams in the assembly for four selected moments of the deformation process are presented in Fig. 13. Due to the symmetry all four contact zones have the same characteristics. In the first stage only one pair of edges is active there and following the increase of displacement, penetration and rotations next pairs are switched on and at the end of the process all four edge pairs are active.
53) ( ) − e p s ε Tm g Tmn (F ) t 2 T − x mn − x mpf e p s ε Ts gTsn (F ) t 2 T x sn − x spf p s ε Tm FT t (1 − t m ⊗ t m ) S m − (F ) t 2 (F T t ) o t m t mT S m T ⎫ Δu ⎪⎡ M ⎤ FT (1 − t s ⊗ t s ) S s ⎬⎢ ⎥. 54) ⎡Δu M ⎤ Δp s = Ps ⎢ ⎥. ⎢⎣ Δu S ⎥⎦ Now all the required variables are discretised. 31) are used. 3. In this way the residual vector and the tangent stiffness matrix related to friction for the beam-to-beam contact finite element can be derived. 6 the total vectors and matrices for frictional contact can be found.
There are also the maximal penetration values presented. 01% of the cross-section dimension – just over the assumed limit. 1 Friction Model In the present analysis the Coulomb model of the dry friction with a constant friction coefficient μ between the friction force FT and the normal force FN in the contact point between beams is used FT = μFN . 1) The advantage is taken of the analogy to the rigid-ideally plastic material suggested in the paper by Michałowski and Mróz (1978). This allows to distinguish between two friction states: the stick state, which is characterized by no relative displacement between the bodies, and the slip state, where the relative displacement in the form of sliding is present.