Analysis and Simulation of Contact Problems (Lecture Notes - download pdf or read online

By Peter Wriggers, Udo Nackenhorst

This conscientiously edited e-book bargains a cutting-edge evaluate on formula, mathematical research and numerical answer approaches of touch difficulties. The contributions accumulated during this quantity summarize the lectures offered by way of top scientists within the quarter of touch mechanics, through the 4th touch Mechanics overseas Symposium (CMIS) held in Hannover, Germany, 2005.

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3. e: t ∝ ln (N ) (5) However, Eq. (5) is valid only when the tree is balanced - a nearly balanced tree is easily built using a balanced tree storage and retrieval algorithm [9]. As the CPU time for building a balanced tree is proportional to N lnN , the total contact detection CPU time is proportional to N lnN where N is the total number of discrete elements. For moderate size systems this can be fine. However, with very large systems CPU constraints can become very important. Thus, in recent years the first linear contact detection algorithms (with total detection time T proportional to N) such as C-GRID and NBS [10,11], MR and MMR have been developed [12].

The discrete form of the weak non-penetration up ≤ dp . For the discrete form (1) condition reads as (ˆ un )p,s := np D[p, p]ˆ of the upper bound for the Lagrange multiplier (2), we get (λτ )p,s ≤ gp , where (λτ )p,s := D[p, p](λτ )p , where ( τ )p := p − ( p · np )np . For details of the formulation and the discretization, we refer to [8, 7]. The application of mortar methods for contact problems was also considered in [2, 6, 9, 11, 4]. Our implementation is based on the finite element toolbox UG, see [1].

Physics of contact is aimed at producing realistic contact forces between interacting boundaries. A good example of a model dealing with physics of interaction is a rock joint model. Contact kinematics is concerned with geometry of the interacting boundary, velocity fields, displacements fields and stress fields and integration of contact forces in such a way that for instance energy balance is preserved. Contact detection (also called neighbour search) is a necessary part of contact processing especially when large systems are handled.

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