By Alexander Konyukhov
This ebook encompasses a systematical research of geometrical occasions resulting in touch pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each touch pair is inherited with a different coordinate method in accordance with its geometrical homes corresponding to a Gaussian floor coordinate process or a Serret-Frenet curve coordinate system. The formula in a covariant shape permits in an easy style to contemplate a variety of constitutive kin for a definite pair equivalent to anisotropy for either frictional and structural elements. Then regular tools popular in computational touch mechanics akin to penalty, Lagrange multiplier tools, mixture of either and others are formulated in those coordinate structures. Such formulations require then the robust equipment of differential geometry of surfaces and curves in addition to of convex research. the ultimate pursuits of such modifications are then ready-for-implementation numerical algorithms in the finite point approach together with any arbitrary discretization innovations comparable to excessive order and isogeometric finite parts, that are so much handy for the thought of geometrical situation.
The ebook proposes a constant examine of geometry and kinematics, variational formulations, constitutive kinfolk for surfaces and discretization ideas for all thought of geometrical pairs and comprises the linked numerical research in addition to a few new analytical ends up in touch mechanics.
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