Boundary Element Method in Geomechanics
Boundary Element Method in Geomechanics

Author: W.S. Venturini

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 255

ISBN-13: 3642820999

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Numerical techniques for solving many problems in continuum mechanics have experienced a tremendous growth in the last twenty years due to the development of large high speed computers. In particular, geomechanical stress analysis can now be modelled within a more realistic context. In spite of the fact that many applications in geomechanics are still being carried out applying linear theories, soil and rock materials have been demonstrated experimentally to be physically nonlinear. Soils do not recover their initial state after removal of temporary loads and rock does not deform in proportion to the loads applied. The search for a unified theory to model the real response of these materials is impossible due to the complexities involved in each case. Realistic solutions in geomechanical analysis must be provided by considering that material properties vary from point to point, in addition to other significant features such as non-homogeneous media, in situ stress condition, type of loading, time effects and discontinuities. A possible alternative to tackle such a problem is to inttoduce some simplified assumptions which at least can provide an approximate solution in each case. The validity or accuracy of the final solution obtained is always dependent upon the approach adopted. As a consequence, the choice of a reliable theory for each particular problem is another difficult decision which should be 2 taken by the analyst in geomechanical stress analysis.

Boundary Element Method in Geomechanics
Boundary Element Method in Geomechanics

Author: W.S. Venturini

Publisher: Springer

Published: 1983-08-01

Total Pages: 212

ISBN-13: 9783540126539

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Numerical techniques for solving many problems in continuum mechanics have experienced a tremendous growth in the last twenty years due to the development of large high speed computers. In particular, geomechanical stress analysis can now be modelled within a more realistic context. In spite of the fact that many applications in geomechanics are still being carried out applying linear theories, soil and rock materials have been demonstrated experimentally to be physically nonlinear. Soils do not recover their initial state after removal of temporary loads and rock does not deform in proportion to the loads applied. The search for a unified theory to model the real response of these materials is impossible due to the complexities involved in each case. Realistic solutions in geomechanical analysis must be provided by considering that material properties vary from point to point, in addition to other significant features such as non-homogeneous media, in situ stress condition, type of loading, time effects and discontinuities. A possible alternative to tackle such a problem is to inttoduce some simplified assumptions which at least can provide an approximate solution in each case. The validity or accuracy of the final solution obtained is always dependent upon the approach adopted. As a consequence, the choice of a reliable theory for each particular problem is another difficult decision which should be 2 taken by the analyst in geomechanical stress analysis.

2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics
2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics

Author: Nobuo Morita

Publisher: Elsevier

Published: 2020-11-17

Total Pages: 480

ISBN-13: 0128238399

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2D/3D Boundary Element Programming in Petroleum Engineering and Geomechanics, Volume 72, is designed to make it easy for researchers, engineers and students to begin writing boundary element programs. This reference covers the fundamentals, theoretical developments, programming and applications. Both fluid flow through porous media and structural problems are used for coding exercises. Included computer programs may be used as starting codes; after modifications, they can be applied to real world problems. The book covers topics around mesh generation, 3D boundary element coding, and interface coding for controlling mesh generation, and plotting results. - Includes interactive 2D and 3D coding exercises that readers can modify based on need - Features research on the most recent developments in indirect and dual boundary element methods - Contains case studies showing examples and applications of the theories presented in the book

The Isogeometric Boundary Element Method
The Isogeometric Boundary Element Method

Author: Gernot Beer

Publisher: Springer Nature

Published: 2019-09-21

Total Pages: 342

ISBN-13: 3030233391

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This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.

Boundary Element Techniques in Geomechanics
Boundary Element Techniques in Geomechanics

Author: George D. Manolis

Publisher:

Published: 1993

Total Pages: 558

ISBN-13:

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This text provides an understanding of the role of Boundary Element Methods (BEM) in the numerical analysis of problems in geomechanics. Topics covered include: computer implementation; wave propagation due to seismicity or to man-related causes; and soil-fluid-structure interaction.

Finite Element Analysis in Geotechnical Engineering
Finite Element Analysis in Geotechnical Engineering

Author: David M Potts

Publisher: Thomas Telford

Published: 2001

Total Pages: 456

ISBN-13: 9780727727831

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An insight into the use of the finite method in geotechnical engineering. The first volume covers the theory and the second volume covers the applications of the subject. The work examines popular constitutive models, numerical techniques and case studies.

Particulate Discrete Element Modelling
Particulate Discrete Element Modelling

Author: Catherine O'Sullivan

Publisher: CRC Press

Published: 2011-04-06

Total Pages: 574

ISBN-13: 1482266490

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The first single work on DEM providing the information to get started with this powerful numerical modelling approach. Provides the basic details of the numerical method and the approaches used to interpret the results of DEM simulations. It will be of use to professionals, researchers and higher level students, with a theoretical overview of DEM as well as practical guidance.Selected Contents: 1.Introduction 2.Use of DEM in Geomechanics 3.Calculation of Contact Forces 4.Particle Motion 5.Particle Types 6.Boundary Conditions 7.Initial Geometry and Specimen Generation 8.Time Integration and Discrete Element Modelling 9.DEM Interpretation: A Continuum Perspective 10.Postprocessing: Graphical Interpretation of DEM Simulations 11.Basic Statisti

Notes on Numerical Modeling in Geomechanics
Notes on Numerical Modeling in Geomechanics

Author: William G. Pariseau

Publisher: CRC Press

Published: 2022-03-31

Total Pages: 226

ISBN-13: 1000546454

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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.