Description
Book Synopsis
This book is an introduction to numerical analysis in geomechanics and is intended for advanced undergraduate and beginning graduate study of the mechanics of porous, jointed rocks and soils. Although familiarity with the concepts of stress, strain and so on is assumed, a review of the fundamentals of solid mechanics including concepts of physical laws, kinematics and material laws is presented in an appendix. Emphasis is on the popular finite element method but brief explanations of the boundary element method, the distinct element method (also known as the discrete element method) and discontinuous deformation analysis are included. Familiarity with a computer programming language such as Fortran, C++ or Python is not required, although programming excerpts in Fortran are presented at the end of some chapters.
This work begins with an intuitive approach to interpolation over a triangular element and thus avoids making the simple complex by not doing energy minimizatio
Table of Contents
1. Introduction. 2. Interpolation Over a Triangle. 3. Derivatives of Interpolation Functions. 4. Linear Interpolation Over a Quadrilateral. 5. Derivatives for a Linear Displacement Quadrilateral. 6. Element Equilibrium and Stiffness. 7. Global Equilibrium and Global Stiffness. 8. Static Condensation and a 4CST Element. 9. Equation Solving. 10. Material Nonlinearity. 11. Time Integration. 12. Finite Element Seepage Formulation. 13. Hydro-mechanical Coupling. 14. Boundary Element Formulations. 15. Distinct Element Formulations. 16. Conclusion. Appendix A: Review of Fundamental Concepts. Appendix B: Study Questions. Appendix C: Question Replies.
