Meshfree and Particle Methods

Ted Belytschko , J. S. Chen , Michael Hillman 지음

Wiley 2023년 12월 13일 출간

작품소개

책소개

Meshfree and Particle Methods Provides thorough coverage of essential concepts and state-of-the-art developments in the field Meshfree and Particle Methods is the first book of its kind to combine comprehensive, up-to-date information on the fundamental theories and applications of meshfree methods with systematic guidance on practical coding implementation. Broad in scope and content, this unique volume provides readers with the knowledge necessary to perform research and solve challenging problems in nearly all fields of science and engineering using meshfree computational techniques. The authors provide detailed descriptions of essential issues in meshfree methods, as well as specific techniques to address them, while discussing a wide range of subjects and use cases. Topics include approximations in meshfree methods, nonlinear meshfree methods, essential boundary condition enforcement, quadrature in meshfree methods, strong form collocation methods, and more. Throughout the book, topics are integrated with descriptions of computer implementation and an open-source code (with a dedicated chapter for users) to illustrate the connection between the formulations discussed in the text and their real-world implementation and application. This authoritative resource: Explains the fundamentals of meshfree methods, their constructions, and their unique capabilities as compared to traditional methods Features an overview of the open-source meshfree code RKPM2D, including code and numerical examples Describes all the variational concepts required to solve scientific and engineering problems using meshfree methods such as Nitsche’s method and the Lagrange multiplier method Includes comprehensive reviews of essential boundary condition enforcement, quadrature in meshfree methods, and nonlinear aspects of meshfree analysis Discusses other Galerkin meshfree methods, strong form meshfree methods, and thei

목차

Preface Glossary of Notation Chapter 1: Introduction to Meshfree and Particle Methods 1.1 Definition of Meshfree Method 1.2 Key Approximation Characteristics 1.3 Meshfree Computational Model 1.4 A Demonstration of Meshfree Analysis 1.5 Classes of Meshfree Methods 1.6 Applications of Meshfree Methods References Chapter 2: Preliminaries: Strong and Weak Forms of Diffusion, Elasticity and Solid Continua 2.1 Diffusion Equation 2.1.1 Strong Form of the Diffusion Equation 2.1.2 The Variational Principle for the Diffusion Equation 2.1.3 Constrained Principles for the Diffusion Equation 2.1.4 Weak Form of the Diffusion Equation by the Method of Weighted Residuals 2.2 Elasticity 2.2.1 Strong Form of Elasticity 2.2.2 The Variational Principle for Elasticity 2.2.3 Constrained Variational Principles for Elasticity 2.3 Nonlinear Continuum Mechanics 2.3.1 Strong Form for General Continua 2.3.2 Principle of Stationary Potential Energy 2.3.3 Standard Weak Form for Nonlinear Continua Appendix References Chapter 3: Meshfree Approximations 3.1 Moving Least Squares (MLS) Approximation 3.1.1 Weight Functions 3.1.2 MLS Approximation of Vectors in Multiple dimensions 3.1.3 Reproducing Properties 3.1.4 Continuity of Shape Functions 3.2 Reproducing Kernel Approximation 3.2.1 Continuous Reproducing Kernel Approximation 3.2.2 Discrete Reproducing Kernel Approximation 3.3 Differentiation of Meshfree Shape Functions and Derivative Completeness Conditions 3.4 Properties of the Moving Least Squares and Reproducing Kernel Approximations 3.5 Derivative Approximations in Mes

출판사 서평

작가정보

저자(글) Ted Belytschko

저자(글) J. S. Chen

저자(글) Michael Hillman