LEADER 05081nam 2200649 a 450 001 9910876846503321 005 20200520144314.0 010 $a1-118-61690-1 010 $a1-299-31421-X 010 $a1-118-61668-5 035 $a(CKB)2560000000100566 035 $a(EBL)1143609 035 $a(SSID)ssj0000833723 035 $a(PQKBManifestationID)11529306 035 $a(PQKBTitleCode)TC0000833723 035 $a(PQKBWorkID)10936598 035 $a(PQKB)11702148 035 $a(MiAaPQ)EBC1143609 035 $a(OCoLC)830161691 035 $a(EXLCZ)992560000000100566 100 $a20101214d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aNatural element method for the simulation of structures and processes /$fFrancisco Chinesta ... [et al.] 210 $aLondon $cISTE ;$aHoboken, N.J. $cWiley$d2011 215 $a1 online resource (255 p.) 225 1 $aISTE 300 $aDescription based upon print version of record. 311 $a1-84821-220-8 320 $aIncludes bibliographical references (p. [227]-238) and index. 327 $aCover; Natural Element Method for the Simulation of Structures and Processes; Title Page; Copyright Page; Table of Contents; Foreword; Acknowledgements; Chapter 1. Introduction; 1.1. SPH method; 1.2. RKPM method; 1.2.1. Conditions of reproduction; 1.2.2. Correction of the kernel; 1.2.3. Discrete form of the approximation; 1.3. MLS based approximations; 1.4. Final note; Chapter 2. Basics of the Natural Element Method; 2.1. Introduction; 2.2. Natural neighbor Galerkin methods; 2.2.1. Interpolation of natural neighbors; 2.2.2. Discretization 327 $a2.2.3. Properties of the interpolant based on natural neighbors2.3. Exact imposition of the essential boundary conditions; 2.3.1. Introduction to alpha shapes; 2.3.2. CNEM approaches; 2.4. Mixed approximations of natural neighbor type; 2.4.1. Considering the restriction of incompressibility; 2.4.2. Mixed approximations in the Galerkin method; 2.4.3. Natural neighbor partition of unity; 2.4.3.1. Partition of unity method; 2.4.3.2. Enrichment of the natural neighbor interpolants; 2.5. High order natural neighbor interpolants; 2.5.1. Hiyoshi-Sugihara interpolant 327 $a2.5.2. The De Boor algorithm for B-splines2.5.3. B-spline surfaces and natural neighboring; 2.5.3.1. Some definitions; 2.5.3.2. Surface properties; 2.5.3.3. The case of repeated nodes; Chapter 3. Numerical Aspects; 3.1. Searching for natural neighbors; 3.2. Calculation of NEM shape functions of the Sibson type; 3.2.1. Stage-1: insertion of point x in the existing constrained Voronoi diagram(CVD); 3.2.1.1. Look for a tetrahedron which contains point x; 3.2.1.2. Note concerning the problem of flat tetrahedrons; 3.2.2. Stage-2: calculation of the volume measurement common to c?x and cv 327 $a3.2.2.1. By the recursive Lasserre algorithm3.2.2.2. By means of a complementary volume; 3.2.2.3. By topological approach based on the CVD; 3.2.2.4. By topological approach based on the Constrained Delaunay tetrahedization(CDT); 3.2.2.5. Using the Watson algorithm; 3.2.3. Comparative test of the various algorithms; 3.3. Numerical integration; 3.3.1. Decomposition of shape function supports; 3.3.2. Stabilized nodal integration; 3.3.3. Discussion in connection with various quadratures; 3.3.3.1. 2D patch test with a technique of decomposition of shape function supports 327 $a3.3.3.2. 2D patch test with stabilized nodal integration3.3.3.3. 3D patch tests; 3.4. NEM on an octree structure; 3.4.1. Structure of the data; 3.4.1.1. Description of the geometry; 3.4.1.2. Interpolation on a quadtree; 3.4.1.3. Numerical integration; 3.4.2. Application of the boundary conditions - interface conditions; 3.4.2.1. Dirichlet-type boundary conditions: use of R-functions; 3.4.2.2. Neumann-type boundary conditions; 3.4.2.3. Partition of unity method; Chapter 4. Applications in the Mechanics of Structures and Processes; 4.1. Two- and three-dimensional elasticity 327 $a4.2. Indicators and estimators of error: adaptivity 330 $a"This book presents a recent state of the art on the foundations and applications of the meshless natural element method in computational mechanics, including structural mechanics and material forming processes involving solids and Newtonian and non-Newtonian fluids"--$cProvided by publisher. 410 0$aISTE 606 $aMaterials$xMechanical properties$xMathematical models 606 $aNumerical analysis 606 $aNumbers, Natural 615 0$aMaterials$xMechanical properties$xMathematical models. 615 0$aNumerical analysis. 615 0$aNumbers, Natural. 676 $a624.1/7015118 686 $aMAT003000$2bisacsh 701 $aChinesta$b Francisco$0720584 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910876846503321 996 $aNatural element method for the simulation of structures and processes$94188071 997 $aUNINA