Methods of Fundamental Solutions 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, plane piezoelectric problems, and heat transfer in heterogeneous media. The book presents a working knowledge of the MFS that is aimed at solving real-world engineering problems through an understanding of the physical and mathematical characteristics of the MFS and its applications.
1. 6.1. Introduction - p. 144 2. 6.2. Fundamental solutions for two-dimensional elasticity - p. 147 3. 6.3. Solution procedure for homogeneous elasticity - p. 150 4. 6.4. Solution procedure for inhomogeneous elasticity - p. 172 5. 6.5. Further analysis for functionally graded solids - p. 188 6. 6.6. Remarks - p. 208 7. Chapter 7. Meshless analysis for plane piezoelectric problems - p. 211 8. 7.1. Introduction - p. 211 9. 7.2. Fundamental solutions for plane piezoelectricity - p. 212 10. 7.3. Solution procedure for plane piezoelectricity - p. 219 11. 7.4. Results and discussion - p. 222 12. 7.5. Remarks - p. 234 13. Chapter 8. Meshless analysis of heat transfer in heterogeneous media - p. 237 14. Appendix A. Derivatives of functions in terms of radial variable r - p. 277 15. Appendix B. Transformations - p. 281 16. Appendix C. Derivatives of approximated particular solutions in inhomogeneous plane elasticity - p. 285 17. Index - p. 289
Methods of Fundamental Solutions 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, plane piezoelectric problems, and heat transfer in heterogeneous media. The book presents a working knowledge of the MFS that is aimed at solving real-world engineering problems through an understanding of the physical and mathematical characteristics of the MFS and its applications.
1. 6.1. Introduction - p. 144 2. 6.2. Fundamental solutions for two-dimensional elasticity - p. 147 3. 6.3. Solution procedure for homogeneous elasticity - p. 150 4. 6.4. Solution procedure for inhomogeneous elasticity - p. 172 5. 6.5. Further analysis for functionally graded solids - p. 188 6. 6.6. Remarks - p. 208 7. Chapter 7. Meshless analysis for plane piezoelectric problems - p. 211 8. 7.1. Introduction - p. 211 9. 7.2. Fundamental solutions for plane piezoelectricity - p. 212 10. 7.3. Solution procedure for plane piezoelectricity - p. 219 11. 7.4. Results and discussion - p. 222 12. 7.5. Remarks - p. 234 13. Chapter 8. Meshless analysis of heat transfer in heterogeneous media - p. 237 14. Appendix A. Derivatives of functions in terms of radial variable r - p. 277 15. Appendix B. Transformations - p. 281 16. Appendix C. Derivatives of approximated particular solutions in inhomogeneous plane elasticity - p. 285 17. Index - p. 289
