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Fuses differential geometry into computational contact mechanics
Research monograph on computational contact mechanics formulated in a covariant form
Gives the necessary introductory treatment of differential geometry for curves and surfaces
Contains new analytical results for the verification of contact algorithms
Gives the reader a closed form algorithms for finite element implementations independently of the type of approximation involved in the discretization process as well as for any isogeometric analysis
This book contains a systematical analysis of geometrical situations leading to contact pairs -- point-to-surface, surface-to-surface, point-to-curve, curve-to-curve and curve-to-surface. Each contact pair is inherited with a special coordinate system based on its geometrical properties such as a Gaussian surface coordinate system or a Serret-Frenet curve coordinate system. The formulation in a covariant form allows in a straightforward fashion to consider various constitutive relations for a certain pair such as anisotropy for both frictional and structural parts. Then standard methods well known in computational contact mechanics such as penalty, Lagrange multiplier methods, combination of both and others are formulated in these coordinate systems. Such formulations require then the powerful apparatus of differential geometry of surfaces and curves as well as of convex analysis. The final goals of such transformations are then ready-for-implementation numerical algorithms within the finite element method including any arbitrary discretization techniques such as high order and isogeometric finite elements, which are most convenient for the considered geometrical situation.
The book proposes a consistent study of geometry and kinematics, variational formulations, constitutive relations for surfaces and discretization techniques for all considered geometrical pairs and contains the associated numerical analysis as well as some new analytical results in contact mechanics.
Content Level »Research
Keywords »Closest Point Projection Procedure - Computational Contact Mechanics - Contact Mechanics - Covariant - Existence - Finite Elements - Geometry of Surfaces and Curves - Linearization - Numerical Methods - Solid-Beam - Surface-To-Surface - Uniqueness
Differential Geometry of Surfaces and Curves.- Closest Point Projection Procedure and Corresponding Curvilinear Coordinate System.- Geometry and Kinematics of Contact.- Weak Formulation of Contact Conditions.- Contact Constraints and Constitutive Equations for Contact Tractions.- Linearization of the Weak Forms – Tangent Matrices in a Covariant Form.- Surface-To-Surface Contact – Various Aspects for Implementations.- Special Case of Implementation – Reduction into 2D Case.- Implementation of Contact Algorithms with High Order FE.- Anisotropic Adhesion-Friction Models – Implementation.- Experimental Validations of the Coupled Anistropi.- Various Aspects of Implementation of the Curve-To-Curve Contact Model.- 3D-Generalization of the Euler-Eytelwein Formula Considering Pitch.