Download Computational Contact Mechanics: Geometrically Exact Theory by Alexander Konyukhov PDF

By Alexander Konyukhov

This ebook incorporates 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 one touch pair is inherited with a unique coordinate procedure in response to its geometrical homes comparable to a Gaussian floor coordinate process or a Serret-Frenet curve coordinate procedure. The formula in a covariant shape permits in an easy model to contemplate a number of constitutive relatives for a definite pair corresponding to anisotropy for either frictional and structural components. Then commonplace tools popular in computational touch mechanics akin to penalty, Lagrange multiplier equipment, blend of either and others are formulated in those coordinate platforms. Such formulations require then the robust equipment of differential geometry of surfaces and curves in addition to of convex research. the ultimate ambitions of such adjustments are then ready-for-implementation numerical algorithms in the finite aspect strategy together with any arbitrary discretization innovations equivalent to excessive order and isogeometric finite components, that are so much handy for the thought of geometrical situation.

The ebook proposes a constant examine of geometry and kinematics, variational formulations, constitutive family members for surfaces and discretization options for all thought of geometrical pairs and comprises the linked numerical research in addition to a few new analytical ends up in touch mechanics.

Show description

Read or Download Computational Contact Mechanics: Geometrically Exact Theory for Arbitrary Shaped Bodies PDF

Best mechanical engineering books

LabVIEW for Everyone: Graphical Programming Made Easy and Fun

The number 1 step by step consultant to LabVIEW--Now thoroughly up to date for LabVIEW eight! grasp LabVIEW eight with the industry's friendliest, such a lot intuitive educational: LabVIEW for everybody, 3rd variation. best LabVIEW specialists Jeffrey Travis and Jim Kring educate LabVIEW the straightforward method: via rigorously defined, step by step examples that offer you reusable code to your personal tasks!

Advances in the Flow and Rheology of Non-Newtonian Fluids

Those volumes include chapters written by means of specialists in such parts as bio and foodstuff rheology, polymer rheology, stream of suspensions, stream in porous media, electrorheological fluids, and so on. Computational in addition to analytical mathematical descriptions, related to applicable constitutive equations take care of complicated stream events of commercial significance.

Dynamics for Engineers

"Mechanics is one ofthe branches ofphysics within which the quantity ofprinciples is right away only a few and intensely wealthy in helpful results. nonetheless, there are few sciences that have required lots thought-the conquest of some axioms has taken greater than 2000 years. "-Rene Dugas, A historical past zero/ Mechanics Introductory classes in engineering mechanics (statics and dynamics) are as a rule came across very early in engineering curricula.

Systems engineering and architecting : creating formal requirements

''Preface This publication was once written to take a step to satisfy a target that George Friedman said in his president's keynote tackle in 1994 at simply the second one assembly of the foreign Council on platforms Engineering. George requested his viewers to supply a mathematical foundation for doing platforms engineering.

Additional info for Computational Contact Mechanics: Geometrically Exact Theory for Arbitrary Shaped Bodies

Example text

30 2 Differential Geometry of Surfaces and Curves Fig. 4 Structure of a surface in the vicinity of the parabolic point. are fulfilled for each surface point of the surface, then a flat surface is obtained. g. a cylinder, or a cone) can be unwrapped on a plane. 4) Both k1 = 0 and k2 = 0 — a planar point . The local structure can not be identified without the analysis of the higher order derivatives. Nevertheless, the case with k1 = 0, k2 = 0 for each point leads to a plane in 3D. Eqn. 21) and the mean curvature H is defined as H= 1 a22 h11 − 2a12 h12 + a11 h22 1 (k1 + k2 ) = .

1, as follows: r(ξ 1 , ξ 2 , ξ 3 ) = ρ(ξ 1 , ξ 2 ) + nξ 3 . 8) All necessary parameters are defined in the covariant basis of the surface ρ1 × ρ2 tangent vectors ρ1 , ρ2 and a unit normal vector n = . 2) will be considered in this coordinate system. The introduction of such a coordinate system is the basis of the covariant description for contact problems, developed in Konyukhov and Schweizerhof [87], [88] for isotropic frictional problems, and then in [89], [90] for anisotropic frictional problems.

4 Structure of a surface in the vicinity of the parabolic point. are fulfilled for each surface point of the surface, then a flat surface is obtained. g. a cylinder, or a cone) can be unwrapped on a plane. 4) Both k1 = 0 and k2 = 0 — a planar point . The local structure can not be identified without the analysis of the higher order derivatives. Nevertheless, the case with k1 = 0, k2 = 0 for each point leads to a plane in 3D. Eqn. 21) and the mean curvature H is defined as H= 1 a22 h11 − 2a12 h12 + a11 h22 1 (k1 + k2 ) = .

Download PDF sample

Rated 4.58 of 5 – based on 40 votes