By Valentin L. Popov, Markus Heß
This booklet describes for the 1st time a simulation procedure for the quick calculation of touch homes and friction among tough surfaces in an entire shape. not like latest simulation equipment, the tactic of dimensionality aid (MDR) is predicated at the specified mapping of assorted varieties of third-dimensional touch difficulties onto contacts of one-dimensional foundations. in the confines of MDR, not just are 3 dimensional platforms diminished to one-dimensional, but in addition the ensuing levels of freedom are self sufficient from one other. as a result, MDR ends up in an incredible aid of the advance time for the numerical implementation of touch difficulties in addition to the direct computation time and will finally imagine an identical function in tribology as FEM has in constitution mechanics or CFD equipment, in hydrodynamics. additionally, it considerably simplifies analytical calculation and provides a type of “pocket booklet edition” of everything touch mechanics. Measurements of the rheology of our bodies involved in addition to their floor topography and adhesive houses are the inputs of the calculations. specifically, it truly is attainable to seize the complete dynamics of a procedure – starting with the macroscopic, dynamic touch calculation down to the impact of roughness – in one numerical simulation version. consequently, MDR permits the unification of the equipment of fixing touch difficulties on diversified scales. The ambitions of this booklet are at the one hand, to turn out the applicability and reliability of the tactic and nonetheless, to provide an explanation for its very simple software to these .
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Extra resources for Method of Dimensionality Reduction in Contact Mechanics and Friction
4. Different illustrative numerical examples are presented in Chaps. 5– 15, where we consider uncoupled problems, multiple cracks and dynamic crack interaction phenomena, unbounded and bounded domains, inhomogeneous domains, domains with hole or crack and hole. For every particular case the BVP will be stated together with the corresponding boundary integral equation formulation. References 1. Aliabadi AM, Rooke D (1991) Numerical fracture mechanics. Computational Mechanics, Southampton 2. Alshits VIA, Chadwick P (1997) Concavities on the zonal slowness section of a transversely isotropic elastic material.
Solution of Eq. 44) is a vector-valued function with components u J ∈ C 2 (R 2 \Scr ) that satisfies the equation and boundary condition. In Chap. 44) into an integro–differential equation on Scr , the unknown is the crack opening displacement Δu J = u J | Scr+ − u J | Scr− . 45) In addition the unknown u J must satisfies the Somerfield type condition at infinity. Solution of Eq. 45) is a vector-valued function with components u J ∈ C 2 (R 2 \Scr ) that satisfies the equation and boundary condition.
23– 25]. Dynamic fundamental solutions in the time and frequency domain were also derived by Wang et al.  and Wang and Zhang  by using Radon transforms technique. Denda et al.  applied the obtained fundamental solutions to study 2D eigenvalue problems. Fundamental solutions for homogeneous isotropic/anisotropic elastic solids were obtained in Rangelov et al.  and for piezoelectric solids in Gross et al. [23–25] and in the next sections we will follow these works. 2 Preliminaries Fundamental solutions are generalized functions and the method to derive them is based on integral transformation technique.
Method of Dimensionality Reduction in Contact Mechanics and Friction by Valentin L. Popov, Markus Heß