This book contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported. Contents: Meshfree Shape Functions for Weak Formulation, Strong Formulation; Meshfree Methods for Smart Materials/Structures; Meshfree Methods for Fracture Analysis; Meshfree Methods for Membrances, Plates & Shells; Meshfree Methods for Soil; Meshfree Methods for CFD; Boundary Meshfree Methods; Coding, Error Estimation, Parallisation; Meshfree Particle Methods; X-FEM. Readership: Graduate and undergraduate students, reserchers, academics, lecturers and engineers in civil engineering, engineering mechanics and mechanical engineering.

This book is a collection of the papers from the proceedings of the 1st Asian Workshop on Meshfree Methods held in conjunction with the 2nd International Conference on Structural Stability & Dynamics (ICSSD02) on 16-18 December 2002 in Singapore. It contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported.

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

This is the first-ever book on smoothed particle hydrodynamics (SPH) and its variations, covering the theoretical background, numerical techniques, code implementation issues, and many novel and interesting applications.It contains many appealing and practical examples, including free surface flows, high explosive detonation and explosion, underwater explosion and water mitigation of explosive shocks, high velocity impact and penetration, and multiple scale simulations coupled with the molecular dynamics method. An SPH source code is provided, making this a friendly book for readers and SPH users.

Here are the printed proceedings of EPMESC X, held on August 21-23, 2006 in Sanya, Hainan Island of China. It includes 14 full papers of plenary and semi-plenary lectures and approximately 166 one-page summaries. The accompanying CD-ROM includes all 180 full papers presented at the conference.

The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations involved in phase change transitions of materials due to heat transfer. Boundary layer applications are widespread in research and industry. Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application equips the reader with information about heat transfer problems occurring during phase changes. The book covers several boundary element methods, including methods for phase changes, fixed and moving domains and new approaches. The contents are rounded off with chapters on numerical results and industrial applications. Key features: - Simple, didactic presentation of boundary layer problems for heat transfer problems - Covers a wide range of boundary element methods - Includes methods for fixed and moving domains - Explains industrial applications of the methods - Includes solutions to numerical problems The book serves as a textbook for students of advanced mathematics and engineering. It is also a handbook for researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.

The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon. The list of contributors is a mix of highly distinguished authors as well as promising young researchers. This means that the reader gets a varied and contemporary view on 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.

The First International Conference on Computational Methods (ICCM04), organized by the department of Mechanical Engineering, National University of Singapore, was held in Singapore, December 15-17, 2004, with great success. This conference proceedings contains some 290 papers from more than 30 countries/regions. The papers cover a broad range of topics such as meshfree particle methods, Generalized FE and Extended FE methods, inverse analysis and optimization methods. Computational methods for geomechanics, machine learning, vibration, shock, impact, health monitoring, material modeling, fracture and damage mechanics, multi-physics and multi-scales simulation, sports and environments are also included. All the papers are pre-reviewed before they are accepted for publication in this proceedings. The proceedings will provide an informative, timely and invaluable resource for engineers and scientists working in the important areas of computational methods.

Complex behavior models (plasticity, crack, visco-elascticity) are facing several theoretical difficulties in determining the behavior law at the continuous (macroscopic) scale. When homogenization fails to give the right behavior law, a solution is to simulate the material at a mesoscale using the discrete element model (DEM) in order to directly simulate a set of discrete properties that are responsible for the macroscopic behavior. Originally, the discrete element model was developed for granular material. This book, the second in the Discrete Element Model and Simulation of Continuous Materials Behavior set of books, shows how to choose the adequate coupling parameters to avoid spurious wave reflection and to allow the passage of all the dynamic information both from the fine to the coarse model and vice versa. The authors demonstrate the coupling method to simulate a highly nonlinear dynamical problem: the laser shock processing of silica glass.

The aim of this book is intended, through parallel expounding, to help readers comprehensively grasp the intrinsic features of typical advanced computational methods. These methods are created in recent three decades for the understanding of the post-failure of geo-materials accompanied with discontinuous and finite deformation/dislocation, as well as the violent fluid-structure interaction accompanied with strong distortion of water surface. The strong points and weak points of the formalisms for governing equations, the discretization schemes, the nodal interpolation /approximation of field variables, and their connectivity (via support domains, covers, or enrichments), the basic algorithms, etc., are clarified. Being aware of that the differences in these methods are not so large as at the first glance, this book will help readers to select appropriate methods, to improve the methods for their specific purpose, and to evaluate the reliability/applicability of the outcomes in the hazard evaluation of geotechnical (hydraulic) structures beyond extreme work situation. This book may be looked at as an advanced continuation of “Computational Geomechanics and Hydraulic Structures” by the author (2018) (Springer-Verlag, ISBN 978-981-10-8134-7) which elaborates the fundamental computational methods in geomechanics for the routine design of geotechnical (hydraulic) engineering.