Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Notes on numerical modeling in geomechanics
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
Notes on numerical modeling in geomechanics
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
Notes on numerical modeling in geomechanics
Pariseau, W. G. (Autor:in)
2022
1 online resource
Campusweiter Zugriff (Universität Hannover) - Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Keine Weitergabe an Dritte. Kein systematisches Downloaden durch Robots
Buch
Elektronische Ressource
Englisch
DDC:
624.1/51
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