{"product_id":"introduction-to-computational-contact-mechanics-9781118770658","title":"Introduction to Computational Contact Mechanics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eIntroduction to Computational Contact Mechanics: A Geometrical Approach\u003c\/i\u003e 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 view. The final goal of the theory is to construct in the independent approximation form \/so-called covariant form, including application to high-order and isogeometric finite elements. \u003cbr\u003e \u003cbr\u003e The second part of a book is a practical guide for programming of contact elements and is written in such a way that makes it easy for a programmer to implement using any programming language. Al\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface viii\u003cbr\u003e\u003cbr\u003eAcknowledgements xi\u003cbr\u003e\u003cbr\u003ePart One Theory 1\u003cbr\u003e\u003cbr\u003e\u003cb\u003e1 Introduction with a spring-mass frictionless contact system  2\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e1.1 Structural part - deflection of spring-mass system 3\u003cbr\u003e\u003cbr\u003e1.2 Contact part – non-penetration into rigid plane 3\u003cbr\u003e\u003cbr\u003e1.3 Contact formulations 4\u003cbr\u003e\u003cbr\u003e\u003cb\u003e2 General formulation of a contact problem 11\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e2.1 Structural part – formulation of a problem in linear elasticity 11\u003cbr\u003e\u003cbr\u003e2.2 Formulation of the contact part (Signorini’s problem) 14\u003cbr\u003e\u003cbr\u003e\u003cb\u003e3 Differential geometry 19\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e3.1 Curve and its properties 19\u003cbr\u003e\u003cbr\u003e3.2 Frenet formulas in 2D 23\u003cbr\u003e\u003cbr\u003e3.3 Description of surfaces by Gauss coordinates 24\u003cbr\u003e\u003cbr\u003e3.4 Differential properties of surfaces 32\u003cbr\u003e\u003cbr\u003e\u003cb\u003e4 Geometry and kinematics for arbitrary two body contact problem 40\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e4.1 Local coordinate system 41\u003cbr\u003e\u003cbr\u003e4.2 Closest Point Projection (CPP) procedure – Analysis 43\u003cbr\u003e\u003cbr\u003e4.3 Contact kinematics. 50\u003cbr\u003e\u003cbr\u003e\u003cb\u003e5 Abstract form of formulations in computational mechanics 54\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e5.1 Operator necessary for the abstract formulation 54\u003cbr\u003e\u003cbr\u003e5.2 Abstract form of iterative method 55\u003cbr\u003e\u003cbr\u003e5.3 Fixed point theorem (Banach) 56\u003cbr\u003e\u003cbr\u003e5.4 Newton iterative solution method 58\u003cbr\u003e\u003cbr\u003e5.5 Abstract form for contact formulations 61\u003cbr\u003e\u003cbr\u003e\u003cb\u003e6 Weak formulation and consistent linearization 65\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e6.1 Weak formulation in the local coordinate system 66\u003cbr\u003e\u003cbr\u003e6.2 Regularization with penalty method 67\u003cbr\u003e\u003cbr\u003e6.3 Consistent linearization 67\u003cbr\u003e\u003cbr\u003e6.4 Application to the Lagrange multipliers and to the following forces 71\u003cbr\u003e\u003cbr\u003e6.5 Linearization of the convective variation δξ 73\u003cbr\u003e\u003cbr\u003e6.6 Nitsche method 73\u003cbr\u003e\u003cbr\u003e\u003cb\u003e7 Finite element discretization 76\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e7.1 Computation of the contact integral for various contact approaches 76\u003cbr\u003e\u003cbr\u003e7.2 Node-To-Node (NTN) contact element 78\u003cbr\u003e\u003cbr\u003e7.3 Nitsche Node-To-Node (NTN) contact element 80\u003cbr\u003e\u003cbr\u003e7.4 Node-To-Segment (NTS) contact element 81\u003cbr\u003e\u003cbr\u003e7.5 Segment-To-Analytical-Surface (STAS) approach 88\u003cbr\u003e\u003cbr\u003e7.6 Segment-To-Segment (STS) Mortar approach 94\u003cbr\u003e\u003cbr\u003e\u003cb\u003e8 Verification with analytical solution 99\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e8.1 Hertz problem 99\u003cbr\u003e\u003cbr\u003e8.2 Rigid flat punch problem 104\u003cbr\u003e\u003cbr\u003e8.3 Impact on moving pendulum – center of percussion 106\u003cbr\u003e\u003cbr\u003e8.4 Generalized Euler-Eytelwein problem 108\u003cbr\u003e\u003cbr\u003e\u003cb\u003e9 Frictional contact problems 111\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e9.1 Measures of contact interactions – sticking and sliding case. Friction law. 111\u003cbr\u003e\u003cbr\u003e9.2 Regularization of tangential force and return mapping algorithm 112\u003cbr\u003e\u003cbr\u003e9.3 Weak form and its consistent linearization 118\u003cbr\u003e\u003cbr\u003e9.4 Frictional Node-To-Node (NTN) contact element 119\u003cbr\u003e\u003cbr\u003e9.5 Frictional Node-To-Segment (NTS) contact element 123\u003cbr\u003e\u003cbr\u003e9.6 NTS frictional contact element 125\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePart Two Programming and Verification Tasks 127\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003e10 Introduction into programming and verification tasks 128\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003e11 Lesson 1 Nonlinear structural truss – \u003c\/b\u003e\u003cb\u003eelmt1.f \u003c\/b\u003e\u003cb\u003e132\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e11.1 Implementation 134\u003cbr\u003e\u003cbr\u003e11.2 Examples 138\u003cbr\u003e\u003cbr\u003e\u003cb\u003e12 Lesson 2 Nonlinear structural plane – \u003c\/b\u003e\u003cb\u003eelmt2.f \u003c\/b\u003e\u003cb\u003e144\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e12.1 Implementation 145\u003cbr\u003e\u003cbr\u003e12.2 Examples 150\u003cbr\u003e\u003cbr\u003e\u003cb\u003e13 Lesson 3 Penalty Node-To-Node (NTN) – \u003c\/b\u003e\u003cb\u003eelmt100.f \u003c\/b\u003e\u003cb\u003e154\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e13.1 Implementation 156\u003cbr\u003e\u003cbr\u003e13.2 Examples 158\u003cbr\u003e\u003cbr\u003e\u003cb\u003e14 Lesson 4 Lagrange multiplier Node-To-Node (NTN) – \u003c\/b\u003e\u003cb\u003eelmt101.f \u003c\/b\u003e\u003cb\u003e161\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e14.1 Implementation 163\u003cbr\u003e\u003cbr\u003e14.2 Examples 165\u003cbr\u003e\u003cbr\u003e\u003cb\u003e15 Lesson 5 Nitsche Node-To-Node (NTN) – \u003c\/b\u003e\u003cb\u003eelmt102.f \u003c\/b\u003e\u003cb\u003e167\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e15.1 Implementation 169\u003cbr\u003e\u003cbr\u003e15.2 Examples 171\u003cbr\u003e\u003cbr\u003e\u003cb\u003e16 Lesson 6 Node-To-Segment (NTS) – \u003c\/b\u003e\u003cb\u003eelmt103.f \u003c\/b\u003e\u003cb\u003e173\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e16.1 Implementation 175\u003cbr\u003e\u003cbr\u003e16.2 Examples 178\u003cbr\u003e\u003cbr\u003e16.3 Inverted contact algorithm – following force 182\u003cbr\u003e\u003cbr\u003e\u003cb\u003e17 Lesson 7 Segment-To-Analytical-Segment (STAS) – \u003c\/b\u003e\u003cb\u003eelmt104.f \u003c\/b\u003e\u003cb\u003e186\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e17.1 Implementation 188\u003cbr\u003e\u003cbr\u003e17.2 Examples 191\u003cbr\u003e\u003cbr\u003e17.3 Inverted contact algorithm – general case of following forces 194\u003cbr\u003e\u003cbr\u003e\u003cb\u003e18 Lesson 8 Mortar \/ Segment-To-Segment (STS) – \u003c\/b\u003e\u003cb\u003eelmt105.f \u003c\/b\u003e\u003cb\u003e202\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e18.1 Implementation 204\u003cbr\u003e\u003cbr\u003e18.2 Examples 207\u003cbr\u003e\u003cbr\u003e18.3 Inverted contact algorithm – following force 209\u003cbr\u003e\u003cbr\u003e\u003cb\u003e19 Lesson 9 Higher order Mortar \/ STS – \u003c\/b\u003e\u003cb\u003eelmt106.f \u003c\/b\u003e\u003cb\u003e213\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e19.1 Implementation 215\u003cbr\u003e\u003cbr\u003e19.2 Examples 219\u003cbr\u003e\u003cbr\u003e\u003cb\u003e20 Lesson 10 3D Node-To-Segment (NTS) \u003c\/b\u003e\u003cb\u003eelmt107.f \u003c\/b\u003e\u003cb\u003e223\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e20.1 Implementation 225\u003cbr\u003e\u003cbr\u003e20.2 Examples 229\u003cbr\u003e\u003cbr\u003e\u003cb\u003e21 Lesson 11 Frictional Node-To-Node (NTN) – \u003c\/b\u003e\u003cb\u003eelmt108.f \u003c\/b\u003e\u003cb\u003e233\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e21.1 Implementation 235\u003cbr\u003e\u003cbr\u003e21.2 Examples 237\u003cbr\u003e\u003cbr\u003e\u003cb\u003e22 Lesson 12 Frictional Node-To-Segment (NTS) – \u003c\/b\u003e\u003cb\u003eelmt109.f \u003c\/b\u003e\u003cb\u003e239\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e22.1 Implementation 241\u003cbr\u003e\u003cbr\u003e22.2 Examples 245\u003cbr\u003e\u003cbr\u003e\u003cb\u003e23 Lesson 13 Frictional higher order NTS – \u003c\/b\u003e\u003cb\u003eelmt110.f \u003c\/b\u003e\u003cb\u003e250\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e23.1 Implementation 251\u003cbr\u003e\u003cbr\u003e23.2 Examples 256\u003cbr\u003e\u003cbr\u003e\u003cb\u003e24 Lesson 14 Transient contact problems 259\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e24.1 Implementation 260\u003cbr\u003e\u003cbr\u003e24.2 Examples 262\u003cbr\u003e\u003cbr\u003e\u003cb\u003eA Numerical integration 264\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003eA.1 Gauss quadrature 266\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003eB Higher order shape functions of different classes 268\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003eB.1 General 268\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003eB.2 Lobatto class 268\u003cbr\u003e\u003cbr\u003e\u003c\/b\u003e\u003cb\u003eB.3 Bezier class 271\u003c\/b\u003e\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406919835991,"sku":"9781118770658","price":77.85,"currency_code":"GBP","in_stock":true}],"url":"https:\/\/bookcurl.com\/products\/introduction-to-computational-contact-mechanics-9781118770658","provider":"Book Curl","version":"1.0","type":"link"}