Advances in Meshfree Techniques

C. Armando Duarte, Dae-Jin Kim, Ivo Babuška (auth.), V. M. A. Leitão, C. J. S. Alves, C. Armando Duarte (eds.)1402060947, 9781402060946, 9781402060953

In recent years meshless/meshfree methods have gained a considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues.

The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon. The list of contributors reveals a mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different mesh reduction methods and its range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Table of contents :
Front Matter….Pages i-viii
A Global-Local Approach for the Construction of Enrichment Functions for the Generalized FEM and Its Application to Three-Dimensional Cracks….Pages 1-26
Study of Some Optimal XFEM Type Methods….Pages 27-38
Generalized Finite Element Method in Mixed Variational Formulation: A Study of Convergence and Solvability….Pages 39-53
Stability in Lagrangian and Semi-Lagrangian Reproducing Kernel Discretizations Using Nodal Integration in Nonlinear Solid Mechanics….Pages 55-76
Simulation of Forming Processes by the α -Shapes-Based Natural Element Method….Pages 77-95
New Advances in Meshless Methods: Coupling Natural Element and Moving Least Squares Techniques….Pages 97-121
Eliminating Shear-Locking in Meshless Methods: A Critical Overview and a New Framework for Structural Theories….Pages 123-145
FEM/SPH Coupling Technique for High Velocity Impact Simulations….Pages 147-167
On the Construction of Mass Conservative and Meshless Adaptive Particle Advection Methods….Pages 169-186
Spectral-Like Accuracy in Space of a Meshless Vortex Method….Pages 187-197
A Hybrid Meshless/Spectral-Element Method for the Shallow Water Equations on the Sphere….Pages 199-219
Iterated Approximate Moving Least Squares Approximation….Pages 221-239
A Kansa Type Method Using Fundamental Solutions Applied to Elliptic PDEs….Pages 241-256
From Global to Local Radial Basis Function Collocation Method for Transport Phenomena….Pages 257-282
Computation of Static Deformations and Natural Frequencies of Shear Deformable Plates by an RBF-Pseudospectral Method with an Optimal Shape Parameter….Pages 283-310
Back Matter….Pages 311-314