By T.A. Laursen (auth.), Peter Wriggers Professor Dr., Udo Nackenhorst Professor Dr. (eds.)
Contact mechanics used to be and is a crucial department in mechanics which covers a extensive box of theoretical, numerical and experimental investigations. during this conscientiously edited booklet the reader will receive a state of the art evaluation on formula, mathematical research and numerical resolution techniques of touch difficulties. The contributions accrued during this quantity summarize the lectures provided through the 4th touch Mechanics overseas Symposium (CMIS) held in Hannover, Germany, 2005, through prime scientists within the region of touch mechanics.
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Additional resources for Analysis and Simulation of Contact Problems
3. Left: problem deﬁnition in 3D and 2D; middle: initial grid and distorted grid on level 0; right: eﬀective von Mises stress on level 2. 05 2 0 0 0 5 10 z−coordinate 15 0 5 10 z−coordinate 15 Fig. 4. Left: normal part λh · n and tangential part (λh )τ of the Lagrange multiplier λh ; right: tangential part (ush )τ of the displacement on the slave side and tangential part (um h )τ of the displacement on the master side. 1 1 ψp (s)φq (s)r(s) ds = δpq 0 φp (s)r(s) ds, p, q ∈ S, (3) 0 where r(s) = ra + s(re − ra ).
The total contact detection time comprises of the sort time and search time and is given by T ∝N (8) The mapping of discrete elements onto the cells is represented by a list. In order for the list to represent the spatial distribution of the bounding boxes, it is necessary to sort the list according to a criterion that has spatial meaning as shown in Fig. 8. This is achieved by using the MR-linear sort. The MR-Linear sort algorithm is based on the assumptions that no discrete body can move more than the size of a single cell in a given time interval.
Reversible loading process We consider the sliding of an elastic block on the rigid base loaded with horizontally prescribed reversible displacements, see Fig. 4(a). 3 . 1 · 106 . The main point is to show the update procedure for sliding displacements. The loading is applied as prescribed displacements at the top side of the deformable block. For contact the ”node-to-segment” approach is taken. The hysteresis curve representing the computed horizontal displacement at point D vs. the applied displacement at point C is given in Fig.