Contact in Structural Mechanics : A Weighted Residual Approach

• Record Nr.: UNINA9911019407203321
• Autore: Le van Anh
• Pubbl/distr/stampa: Newark : , : John Wiley & Sons, Incorporated, , 2024; ©2024
• ISBN: 9781394297535; 139429753X; 9781394297511; 1394297513
• Edizione: [1st ed.]
• Descrizione fisica: 1 online resource (283 pages)
• Disciplina: 620.105
• Soggetti: Contact mechanics; Structural analysis (Engineering)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1 Introduction to Contact Problems in Structural Mechanics -- 1.1 Solving a contact problem numerically via the penalty method -- 1.2 Numerical solution of a contact problem using the multiplier method -- 1.2.1 Preliminaries: problems with equality constraints -- 1.2.2 Problems with inequality constraints -- 1.3 Numerical solution of a contact problem by the augmented Lagrangian method -- 1.4 Book synopsis -- Chapter 2 Contact Kinematics -- 2.1 Motions and strains -- 2.2 Potential contact surfaces -- 2.3 Normal contact kinematics -- 2.4 Variation of kinematic quantities with respect to time -- 2.5 Tangential contact kinematics - Relative velocity -- Chapter 3 Sthenics of Contact -- 3.1 Stresses in bodies -- 3.2 Contact stress vector -- Chapter 4 The Constitutive Law -- 4.1 Hyperelastic materials -- 4.2 Elastoplastic materials with isotropic hardening -- Chapter 5 Contact Laws -- 5.1 Normal contact law -- 5.2 Tangential contact law -- Chapter 6 Strong Formulation of the Contact Problem -- 6.1 Field equations -- 6.2 Boundary conditions -- 6.3 Initial conditions -- 6.4 Remarks -- Chapter 7 Weak Formulation of the Contact Problem -- 7.1 Transforming the contact laws into equalities -- 7.2 Preliminary ideas ; for the weak form -- 7.3 Weak form of the contact problem -- 7.4 Equivalence between the strong and the weak forms -- 7.5 Final remarks -- Chapter 8 Matrix Equations of the Contact Problem -- 8.1 Introduction -- 8.2 Meshes -- 8.3 Matrix notation in finite elements -- 8.4 The element nodal vectors -- 8.5 Interpolation of positions, displacements and virtual velocities -- 8.5.1 Interpolation on the contactor surface -- 8.5.2 Interpolation on the target surface -- 8.6 Interpolation of multipliers -- 8.6.1 Definition of the vector λ -- 8.6.2 Interpolation of λ.; 8.6.3 Interpolation of λ∗ -- 8.7 Discretization of the element virtual contact power (P*contact)e(1) -- 8.7.1 Explicit expressions for {Φe(1)contact}, {Φe(2)contact} and {Re(1)^} in the three cases: algorithmic gap, algorithmic slip and algorithmic stick -- 8.8 System of matrix equations for the contact problem -- 8.8.1 Global nodal vectors -- 8.8.2 Discretization of the classical terms -- 8.8.3 Assembly of element virtual contact powers -- 8.8.4 System of matrix equations -- 8.9 Abnormal contact stresses -- 8.9.1 First cause of abnormal contact stresses -- 8.9.2 Second cause of abnormal contact stresses -- 8.9.3 Third cause of abnormal contact stresses -- 8.10 Projection calculation: contact detection -- 8.11 Discrete expression of the slip VTΔt -- 8.12 Physical units -- 8.13 Chapter summary -- Chapter 9 Solution of the Quasi-static Contact Problem -- 9.1 System of equations for the static contact problem -- 9.2 Incremental loop initialization: the vectors U0, Λ0 -- 9.3 Calculation of step n ≥ 1: calculating Un, Λn -- 9.3.1 Principle of the iterative Newton-Raphson scheme -- 9.3.2 Tangent matrix -- 9.3.3 Block matrix inversion -- 9.3.4 Iterative loop initialization: the vectors U0n and Λ0n -- 9.4 Solution algorithm -- 9.5 Calculation method for the tangent matrix -- 9.5.1 Direct method -- 9.5.2 Indirect method -- 9.5.3 Restriction to the contact tangent matrix -- 9.6 Calculation of the contact tangent matrix -- 9.6.1 Variations of the arguments of the functional P*contact -- 9.6.2 Calculation of the variation δP*contact -- 9.6.3 Calculation of the variation (δP*contact)e(1) -- 9.6.4 Discretization of the variation (δP*contact)e(1) - Element contact tangent matrix [Kecontact] -- 9.6.5 Discretization of the variation δP*contact - Contact tangent matrix [Kcontact] -- 9.6.6 Explicit expression for the element contact tangent matrix [Kecontact].; 9.6.7 [Kecontact] in the case of the algorithmic gap at the considered integration point -- 9.6.8 [Ke contact] in the case of algorithmic contact with slip at the considered integration point -- 9.6.9 [Ke contact] in the case of algorithmic contact with stick at the considered integration point -- 9.6.10 Symmetry of the contact tangent matrix [Kcontact] -- 9.7 Particular case of two non-contacting bodies -- 9.8 Particular case of the frictionless problem -- 9.8.1 Algorithmic gap case at the considered integration point -- 9.8.2 Algorithmic contact with slip case at the considered integration point -- 9.9 Solution via the arc-length method -- 9.10 Physical units -- 9.11 Summary of the chapter -- Chapter 10 Numerical Examples of Quasi-static Contact -- 10.1 Contact patch test -- 10.2 Hertzian contact problem -- 10.2.1 Frictionless contact case -- 10.2.2 Case of frictional contact with μ = 0.3 -- 10.3 Rolling disk -- 10.4 Contact between two beams -- 10.4.1 Dead load -- 10.4.2 Follower load -- 10.5 Contact of two pressurized membranes -- 10.5.1 Centered membranes -- 10.5.2 Membranes staggered along x -- 10.6 Extrusion of an elastoplastic cylinder -- 10.7 Interference fit problem -- 10.7.1 Abnormal contact stresses -- 10.7.2 Influence of the mesh -- 10.8 Conclusion -- Chapter 11 Solution of the Dynamic Contact Problem -- 11.1 A brief review of the computational methods in dynamic contact -- 11.2 Solution of the dynamic contact ; problem via Newmark's algorithm -- 11.2.1 Initializing the incremental loop: the vectors U0, V0, A0 and Λ0 -- 11.2.2 Calculation for a step n ≥ 1: calculating Un, Vn, An, Λn -- 11.2.3 Initializing the iterative loop: the vectors U0n, V0n, A0n, Λ0n -- 11.3 Solution algorithm -- 11.4 Summary -- Chapter 12 Numerical Examples of Dynamic Contact -- 12.1 Impact of two elastic rods -- 12.1.1 Analytical solution.; 12.1.2 Numerical applications -- 12.1.3 Numerical solution -- 12.2 Disk impacting a rigid plane -- 12.2.1 Frictionless case -- 12.2.2 Case with friction μ = 0.3 -- 12.3 Disk falling into a funnel -- 12.3.1 Frictionless case -- 12.3.2 Case with friction μ = 0.4 -- 12.4 Final remarks -- Appendix A: Variations of Kinematic Quantities -- References -- Index -- Other titles from ISTE in Mechanical Engineering and Solid Mechanics -- EULA.
• Sommario/riassunto: This book explores the complexities of contact problems in structural mechanics, offering a detailed examination of the mathematical and computational methods used to solve these issues. It covers numerical approaches such as the penalty method, multiplier method, and augmented Lagrangian method for addressing contact problems with both equality and inequality constraints. The book delves into the kinematics of contact, stress analysis, constitutive laws for different materials, and the formulation of contact laws. It provides a comprehensive framework for understanding contact mechanics through both strong and weak formulations, matrix equations, and solutions to quasi-static and dynamic contact problems. The content is tailored for engineers, researchers, and students in structural mechanics, with an emphasis on numerical methods and practical applications.