Since the method of fundamental solutions (MFS) was developed in 1964, meshless MFS has come to be used for a variety of physical and engineering problems, including potential, elastic, fracture, fluid, piezoelectric, antiplane, inverse, and free-boundary problems. The method has been extended to deal with inhomogeneous partial differential equations, partial differential equations with variable coefficients, and time-dependent problems. The significant advantage of the MFS over other numerical methods in solid mechanics, is that it is easy to program for engineering problems in two and three-dimensional regular and irregular domains. An Introduction to the Method of Fundamental Solutions with Applications in Solid Mechanics presents the fundamentals of continuum mechanics, the foundational concepts of the MFS, and methodologies and applications to various engineering problems. Eight chapters give an overview of meshless methods; the mechanics of solids and structures; the basics of fundamental solutions and radical basis functions; meshless analysis for thin beam bending, thin plate bending, two-dimensional elastic, and plane piezoelectric problems; and heat transfer in heterogenous media. The book presents a working knowledge of the MFS, aimed at solving real-world engineering problems through understanding the physical and mathematical characteristics of the MFS and its applications. Explains foundational concepts for the method of fundamental solutions (MFS) for the advanced numerical analysis of solid mechanics and heat transferExtends the application of the MFS for use with complex problemsConsiders the majority of engineering problems including beam bending, plate bending, elasticity, piezoelectricity, and heat transferGives detailed solution procedures for engineering problemsOffers a practical guide, complete with engineering examples, for the application of the MFS to real-world physical and engineering challenges INDICE: 1. Overview of meshless methods 2. Mechanics of solids and structures 3. Basics of fundamental solutions and radial basis functions 4. Meshless analysis for thin beam bending problems 5. Meshless analysis for thin plate bending problems 6. Meshless analysis for two-dimensional elastic problems 7. Meshless analysis for plane piezoelectric problems 8. Meshless analysis for heat transfer in heterogeneous media Appendix A. Derivatives of function in terms of radial variable r B. Transformations C. Derivatives of approximated particular solutions in inhomogeneous plane elasticity
- ISBN: 978-0-12-818283-3
- Editorial: Elsevier
- Encuadernacion: Rústica
- Páginas: 280
- Fecha Publicación: 01/11/2019
- Nº Volúmenes: 1
- Idioma: Inglés