Details

Autor(en) / Beteiligte

• Le van, Anh

Titel

Contact in Structural Mechanics : A Weighted Residual Approach

Auflage

1st ed

Ort / Verlag

Newark : John Wiley & Sons, Incorporated,

Erscheinungsjahr

2024

Link zum Volltext

• Wiley Online Library - AutoHoldings Books

Beschreibungen/Notizen

• 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.
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