Natural Element Method for the Simulation of Structures and Processes.

• Κύριος συγγραφέας: Chinesta, Francisco
• Άλλοι συγγραφείς: Cescotto, S. (Serge), Cueto, Elias, Lorong, Philippe
• Μορφή: Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: London : Wiley, 2013.
• Σειρά: ISTE.
• Θέματα: Materials > Mechanical properties > Mathematical models.; Numerical analysis.; Numbers, Natural.; MATHEMATICS > Applied.; TECHNOLOGY & ENGINEERING > Structural.; Electronic books.

Computational mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics. Before the emergence of computational science (also called scientific computing) as a ""third way"" besides theoretical and experi...

Πίνακας περιεχομένων:

• Cover; 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.
• 2.2.3. 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.
• 2.5.2. 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 ćx and cv.
• 3.2.2.1. 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.
• 3.3.3.2. 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.