http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Notes on numerical modeling in geomechanics
1 online resource (x, 277 pages) : illustrations
"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 minimization via a calculus of variations approach so often found in reference books on the finite element method. The presentation then proceeds to a principal of virtual work via the well-known divergence theorem to obtain element equilibrium and then global equilibrium, both expressed as stiffness equations relating force to displacement. Solution methods for the finite element approach including elimination and iteration methods are discussed. Hydro-mechanical coupling is described and extension of the finite element method to accommodate fluid flow in porous geological media is made. Example problems illustrate important concepts throughout the text. Additional problems for a 15-week course of study are presented in an appendix; solutions are given in another appendix"--
1 Introduction 2 Interpolation Over a Triangle 2.1 Linear Theory 2.2 Explicit Formulas 2.3 Linear Strain Triangle 2.4 Programming Comments 3 Derivatives of Interpolation Functions 3.1 Strains 3.2 Hydraulic Gradient 3.3 Axial Symmetry 3.4 Programming Comment 4 Linear Interpolation Over a Quadrilateral 4.1 The Generic 4-Node Quadrilateral 4.2 The Isoparametric 4-Node Quadrilateral 4.3 Programming Comment 5 Derivatives for a Linear Displacement Quadrilateral 5.1 Chain Rule Application 5.2 Strain Displacement Matrix 5.3 Programming Comment 6 Element Equilibrium and Stiffness 6.1 Equations from Elasticity 6.2 Principle of Virtual Work 6.3 Element Equilibrium 7 Global Equilibrium and Stiffness 7.1 Global Equilibrium 7.2 Global Assembly 7.3 Programming Comment 8 Static Condensation and a 4CST Element 8.1 Static Condensation 8.2 Programming Comment 9 Equation Solving 9.1 Gauss Elimination 9.2 Elimination Boundary Conditions 9.3 Gauss-Seidel Iteration 9.4 Iteration Boundary Conditions 9.5 Programming Comments for Elimination 9.6 Programming Comments for Iteration 10 Material Non-linearity 10.1 Incremental (Tangent Stiffness) Approach 10.2 Iterative (Modified Newton-Raphson) Approach 10.3 Programming Comment 11 Time Integration 12 Finite Element Seepage Formulation 12.1 Incompressible flow through a Rigid, Porous Solid 12.2 Compressible Flow through a Deformable, Porous Solid 13 Hydro-mechanical Coupling 13.1 Effective Stress Concept 13.2 Finite Element Formulation 14 Boundary Element Formulations 14.1 Indirect Formulation 14.2 Direct Formulation 15 Distinct Element Formulations 15.1 DEM Formulation 15.2 DDA Formulation 16 Conclusion Appendix A: REVIEW OF FUNDAMENTAL CONCEPTS 1 Physical Laws 1.1 Conservation of Mass 1.2 Balance of Linear Momentum 1.3 Balance of Angular Momentum 1.4 Balance of Energy 2 Analysis of Stress 2.1 Surface Tractions and Stresses 2.2 Stress Vector and State of Stress 2.3 Cauchy Stress Formulas and Sign Convention 2.4 Equality of Shear Stresses 2.5 Rotation of Reference Axes 2.6 Principal Stresses 2.7 Maximum and Minimum Shear Stresses 2.8 Stress Invariants, Hydrostatic Stress and Deviatoric Stress 2.9 Mohr⁰́₉s Circle in Two Dimensions 2.10 Stress Equations of Motion 2.11 Initial Stress and Stress Change 3 Analysis of Strain 3.1 Normal Strain 3.2 Shear strain 3.3 Small Strain ⁰́₃ Displacement Relations 3.4 Geometric Interpretation of Small Strains 3.5 Change of Reference Axes 3.6 Principal Strains, Maximum Shear Strain and Mohr⁰́₉s Circle 4 Stress Strain Laws ⁰́₃ Elasticity 4.1 Hooke⁰́₉s Law in One Dimension ⁰́₃ Young⁰́₉s Modulus and Shear Modulus 4.2 Hooke⁰́₉s Law in Three Dimensions ⁰́₃ Other Elastic Moduli 4.3 More on Elastic Anisotropy 5 Plane Stress, Plane Strain and Axial Symmetry 5.1 Plane Stress and Plane Strain 5.2 Rock Weight and Gravity Stress 5.3 Axial Symmetry 6 Limits to Elasticity ⁰́₃ Strength 6.1 Mohr-Coulomb Failure 6.2 Hoek-Brown Failure 6.3 Drucker-Prager Failure 6.4 Compressive Strength Under Confining Pressure 6.5 Energy and Stability 6.6 A Statistical Strength Model 6.7 Strain Beyond the Elastic Limit Appendix B: Study Questions Appendix C: Question Replies Subject Index
William G. Pariseau, Professor Emeritus, Department of Mining Engineering, University of Utah, Salt Lake City, USA.
Includes bibliographical references and index.