LEADER 03814nam 22005293 450 001 9911019903203321 005 20231217090316.0 010 $a9781119811138 010 $a1119811139 010 $a9781119811145 010 $a1119811147 035 $a(MiAaPQ)EBC31018027 035 $a(Au-PeEL)EBL31018027 035 $a(CKB)29364381400041 035 $a(Exl-AI)31018027 035 $a(Perlego)4311955 035 $a(OCoLC)1415897834 035 $a(EXLCZ)9929364381400041 100 $a20231217d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMeshfree and Particle Methods $eFundamentals and Applications 205 $a1st ed. 210 1$aNewark :$cJohn Wiley & Sons, Incorporated,$d2023. 210 4$dİ2024. 215 $a1 online resource (349 pages) 311 08$aPrint version: Belytschko, Ted Meshfree and Particle Methods Newark : John Wiley & Sons, Incorporated,c2023 9780470848005 327 $aCover -- Title Page -- Copyright Page -- Contents -- 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 -- 2.1.2.1 The Standard Variational Principle -- 2.1.2.2 The Variational Equation -- 2.1.2.3 Equivalence of the Variational Equation and the Strong Form -- 2.1.3 Constrained Variational Principles for the Diffusion Equation -- 2.1.3.1 The Penalty Method -- 2.1.3.2 The Lagrange Multiplier Method -- 2.1.3.3 Nitsche's Method -- 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$7Generated by AI. 330 $aThis book provides an in-depth exploration of meshfree and particle methods, which are advanced numerical techniques used in computational mechanics. It covers the fundamental principles and applications of these methods, including the construction and analysis of meshfree computational models. The authors discuss various approximation techniques such as the Moving Least Squares (MLS) and Reproducing Kernel approximations, and their applications in solving partial differential equations. The book also addresses the challenges of numerical integration and stability in meshfree methods, presenting solutions like nodal integration and stabilization techniques. Intended for researchers and practitioners in numerical analysis and computational mechanics, this text serves as a comprehensive resource for understanding and implementing meshfree and particle methods.$7Generated by AI. 606 $aMeshfree methods (Numerical analysis)$7Generated by AI 606 $aParticle methods (Numerical analysis)$7Generated by AI 615 0$aMeshfree methods (Numerical analysis) 615 0$aParticle methods (Numerical analysis) 676 $a518.2 700 $aBelytschko$b Ted$012929 701 $aChen$b J. S$01136887 701 $aHillman$b Michael$01842535 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019903203321 996 $aMeshfree and Particle Methods$94422705 997 $aUNINA