Notes on numerical modeling in geomechanics. (2022)

• Record Type: Book
• Further Information: Note: William G. Pariseau.
• Authors: Pariseau, W. G
• Contents: 1 Introduction 2 Interpolation Over a Triangle 2.1 Linear Theory 2.2 Explicit Formulas 2.3 Linear Strain Triangles 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 for a Quadrilateral 4.1 The Generic 4-Node Quadrilateral 4.2 The Isoparametric 4-Node Quadrilateral 5 Derivatives for a Linear Displacement Quadrilateral 5.1 Chain Rule Application 5.2 Strain– Displacement Matrix 5.3 Programming Comments 6 Element Equilibrium and Stiffness 6.1 Equations from Elasticity 6.2 Principle of Virtual Work 6.3 Element Equilibrium 7 Global Equilibrium and Global 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 Nonlinearity 10.1 Incremental (Tangent Stiffness) Approach 10.2 Iterative (Modified Newton-Raphson) Approach 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 Appendix B: Study Questions Appendix C: Question Replies Index
• Edition: 1st
• Publisher Details: Boca Raton : CRC Press
• Publication Date: 2022
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 624.151; Geotechnical engineering -- Mathematics; Soil mechanics -- Mathematics; Rock mechanics -- Mathematics; Strains and stresses -- Mathematical models; Finite element method
• Languages: English
• ISBNs: 9781000546453; 9781000546439; 9781003166283
• Related ISBNs: 9780367762834; 9780367762872
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; resource not viewed.
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