Introduction to computational contact mechanics : a geometrical approach / / Alexander Konyukhov, Ridvan Izi

• Record Nr.: UNINA9910460446003321
• Autore: Konyukhov Alexander
• Pubbl/distr/stampa: Chichester, England : , : Wiley, , 2015; ©2015
• ISBN: 1-118-77064-1; 1-118-77063-3
• Descrizione fisica: 1 online resource (305 p.)
• Collana: Wiley Series in Computational Mechanics
• Disciplina: 620.1/05
• Soggetti: Contact mechanics; Mechanics, Applied; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Title Page; Copyright; Contents; Series Preface; Preface; Acknowledgments; Part I Theory; Chapter 1 Introduction with a Spring-Mass Frictionless Contact System; 1.1 Structural Part-Deflection of Spring-Mass System; 1.2 Contact Part-Non-Penetration into Rigid Plane; 1.3 Contact Formulations; 1.3.1 Lagrange Multiplier Method; 1.3.2 Penalty Method; 1.3.3 Augmented Lagrangian Method; Chapter 2 General Formulation of a Contact Problem; 2.1 Structural Part-Formulation of a Problem in Linear Elasticity; 2.1.1 Strong Formulation of Equilibrium; 2.1.2 Weak Formulation of Equilibrium; 2.2 Formulation of the Contact Part (Signorini's problem)Chapter 3 Differential Geometry; 3.1 Curve and its Properties; 3.1.1 Example: Circle and its Properties; 3.2 Frenet Formulas in 2D; 3.3 Description of Surfaces by Gauss Coordinates; 3.3.1 Tangent and Normal Vectors: Surface Coordinate System; 3.3.2 Basis Vectors: Metric Tensor and its Applications; 3.3.3 Relationships between Co- and Contravariant Basis Vectors; 3.3.4 Co- and Contravariant Representation of a Vector on a Surface; 3.3.5 Curvature Tensor and Structure of the Surface; 3.4 Differential Properties of Surfaces; 3.4.1 The Weingarten Formula3.4.2 The Gauss-Codazzi Formula; 3.4.3 ; Covariant Derivatives on the Surface; 3.4.4 Example: Geometrical Analysis of a Cylindrical Surface; Chapter 4 Geometry and Kinematics for an Arbitrary Two Body Contact Problem; 4.1 Local Coordinate System; 4.2 Closest Point Projection (CPP) Procedure-Analysis; 4.2.1 Existence and Uniqueness of CPP Procedure; 4.2.2 Numerical Solution of CPP Procedure in 2D; 4.2.3 Numerical Solution of CPP Procedure in 3D; 4.3 Contact Kinematics; 4.3.1 2D Contact Kinematics using Natural Coordinates s and ζ; 4.3.2 Contact Kinematics in 3D Coordinate SystemChapter 5 Abstract Form of Formulations in Computational Mechanics; 5.1 Operator Necessary for the Abstract Formulation; 5.1.1 Examples of Operators in Mechanics; 5.1.2 Examples of Various Problems; 5.2 Abstract Form of the Iterative Method; 5.3 Fixed Point Theorem (Banach); 5.4 Newton Iterative Solution Method; 5.4.1 Geometrical Interpretation of the Newton Iterative Method; 5.5 Abstract Form for Contact Formulations; 5.5.1 Lagrange Multiplier Method in Operator Form; 5.5.2 Penalty Method in Operator Form; Chapter 6 Weak Formulation and Consistent Linearization6.1 Weak Formulation in the Local Coordinate System; 6.2 Regularization with Penalty Method; 6.3 Consistent Linearization; 6.3.1 Linearization of Normal Part; 6.4 Application to Lagrange Multipliers and to Following Forces; 6.4.1 Linearization for the Lagrange Multipliers Method; 6.4.2 Linearization for Following Forces: Normal Force or Pressure; 6.5 Linearization of the Convective Variation δξ; 6.6 Nitsche Method; 6.6.1 Example: Independence of the Stabilization Parameter; Chapter 7 Finite Element Discretization; 7.1 Computation of the Contact Integral for Various Contact Approaches
• Sommario/riassunto: Introduction to Computational Contact Mechanics: A Geometrical Approach covers the fundamentals of computational contact mechanics and focuses on its practical implementation. Part one of this textbook focuses on the underlying theory and covers essential information about differential geometry and mathematical methods which are necessary to build the computational algorithm independently from other courses in mechanics. The geometrically exact theory for the computational contact mechanics is described in step-by-step manner, using examples of strict derivation from a mathematical point of vi