Three-dimensional Finite Element Implementation for a Dynamic Solid-fluid Mixture at Finite Strain PDF Download
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Author: Davoud Ebrahimi
Publisher:
ISBN:
Category : Continuum mechanics
Languages : en
Pages : 134
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Book Description
Based on the mixture theory formulation of a fluid saturated porous solid subjected to dynamic large strain deformation, a 3D finite element implementation is presented. Under standard mixture theory assumptions, describing motion of the fluid phase relative to the solid phase and following solid phase motion, field equations in the u-p form are derived by applying balance of mass and balance of momentum of the continuum mixture. Solid and fluid volume fractions are used as evolving state parameters through the finite deformation analysis. A compressible neo-Hookean hyperelastic constitutive model with a Kelvin solid viscous enhancement for the solid phase is assumed, along with a generalized form of Darcy's law for the fluid phase. In turn, the governing nonlinear coupled partial differential equations are spatially discretized using a Bubnov-Galerkin method. An unconditionally stable finite differencing procedure is used for the time domain numerical integration. For efficient numerical solution of the 3D nonlinear time dependent coupled formulation which includes both geometric and material nonlinearities, a full consistent tangent matrix of the system of equations has been derived. A mixed hexahedral finite element, quadratic in solid displacement and linear in fluid pore pressure, and the associated consistent tangent matrix are implemented in a C++ finite element code, Tahoe. The implementation is verified with available 1D and 2D benchmark problems. New numerical solutions for 3D large strain dynamic behavior of saturated porous media will be presented. The computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated by means of several numerical examples.
Author: Davoud Ebrahimi
Publisher:
ISBN:
Category : Continuum mechanics
Languages : en
Pages : 134
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Book Description
Based on the mixture theory formulation of a fluid saturated porous solid subjected to dynamic large strain deformation, a 3D finite element implementation is presented. Under standard mixture theory assumptions, describing motion of the fluid phase relative to the solid phase and following solid phase motion, field equations in the u-p form are derived by applying balance of mass and balance of momentum of the continuum mixture. Solid and fluid volume fractions are used as evolving state parameters through the finite deformation analysis. A compressible neo-Hookean hyperelastic constitutive model with a Kelvin solid viscous enhancement for the solid phase is assumed, along with a generalized form of Darcy's law for the fluid phase. In turn, the governing nonlinear coupled partial differential equations are spatially discretized using a Bubnov-Galerkin method. An unconditionally stable finite differencing procedure is used for the time domain numerical integration. For efficient numerical solution of the 3D nonlinear time dependent coupled formulation which includes both geometric and material nonlinearities, a full consistent tangent matrix of the system of equations has been derived. A mixed hexahedral finite element, quadratic in solid displacement and linear in fluid pore pressure, and the associated consistent tangent matrix are implemented in a C++ finite element code, Tahoe. The implementation is verified with available 1D and 2D benchmark problems. New numerical solutions for 3D large strain dynamic behavior of saturated porous media will be presented. The computational efficiency of the implemented formulation in achieving quadratic convergence is illustrated by means of several numerical examples.
Author: Guido Dhondt
Publisher: John Wiley & Sons
ISBN: 0470857625
Category : Science
Languages : en
Pages : 362
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Book Description
Though many 'finite element' books exist, this book provides a unique focus on developing the method for three-dimensional, industrial problems. This is significant as many methods which work well for small applications fail for large scale problems, which generally: are not so well posed introduce stringent computer time conditions require robust solution techniques. Starting from sound continuum mechanics principles, derivation in this book focuses only on proven methods. Coverage of all different aspects of linear and nonlinear thermal mechanical problems in solids are described, thereby avoiding distracting the reader with extraneous solutions paths. Emphasis is put on consistent representation and includes the examination of topics which are not frequently found in other texts, such as cyclic symmetry, rigid body motion and nonlinear multiple point constraints. Advanced material formulations include anisotropic hyperelasticity, large strain multiplicative viscoplasticity and single crystal viscoplasticity. Finally, the methods described in the book are implemented in the finite element software CalculiX, which is freely available (www.calculix.de; the GNU General Public License applies). Suited to industry practitioners and academic researchers alike, The Finite Element Method for Three-Dimensional Thermomechanical Applications expertly bridges the gap between continuum mechanics and the finite element method.
Author: O. C. Zienkiewicz
Publisher: Butterworth-Heinemann
ISBN: 9780750650557
Category : Continuum mechanics
Languages : en
Pages : 482
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 160
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Book Description
This report provides a user's manual for NIKE3D, a fully implicit three-dimensional finite element code for analyzing the finite strain static and dynamic response of inelastic solids, shells, and beams. Spatial discretization is achieved by the use of 8-node solid elements, 2-node truss and beam elements, and 4-node membrane and shell elements. Over twenty constitutive models are available for representing a wide range of elastic, plastic, viscous, and thermally dependent material behavior. Contact-impact algorithms permit gaps, frictional sliding, and mesh discontinuities along material interfaces. Several nonlinear solution strategies are available, including Full-, Modified-, and Quasi-Newton methods. The resulting system of simultaneous linear equations is either solved iteratively by an element-by-element method, or directly by a factorization method, for which case bandwidth minimization is optional. Data may be stored either in or out of core memory to allow for large analyses.
Author: Klaus-Jürgen Bathe
Publisher:
ISBN:
Category : Fluid dynamics
Languages : en
Pages : 40
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Book Description
Author: J. N. Reddy
Publisher: CRC Press
ISBN: 1420085980
Category : Science
Languages : en
Pages : 515
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Book Description
As Computational Fluid Dynamics (CFD) and Computational Heat Transfer (CHT) evolve and become increasingly important in standard engineering design and analysis practice, users require a solid understanding of mechanics and numerical methods to make optimal use of available software. The Finite Element Method in Heat Transfer and Fluid Dynamics, Third Edition illustrates what a user must know to ensure the optimal application of computational procedures—particularly the Finite Element Method (FEM)—to important problems associated with heat conduction, incompressible viscous flows, and convection heat transfer. This book follows the tradition of the bestselling previous editions, noted for their concise explanation and powerful presentation of useful methodology tailored for use in simulating CFD and CHT. The authors update research developments while retaining the previous editions’ key material and popular style in regard to text organization, equation numbering, references, and symbols. This updated third edition features new or extended coverage of: Coupled problems and parallel processing Mathematical preliminaries and low-speed compressible flows Mode superposition methods and a more detailed account of radiation solution methods Variational multi-scale methods (VMM) and least-squares finite element models (LSFEM) Application of the finite element method to non-isothermal flows Formulation of low-speed, compressible flows With its presentation of realistic, applied examples of FEM in thermal and fluid design analysis, this proven masterwork is an invaluable tool for mastering basic methodology, competently using existing simulation software, and developing simpler special-purpose computer codes. It remains one of the very best resources for understanding numerical methods used in the study of fluid mechanics and heat transfer phenomena.
Author: Hoe I. Ling
Publisher: DEStech Publications, Inc
ISBN: 1605950068
Category : Science
Languages : en
Pages : 679
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Book Description
Based on the Biot conference, named after Maurice Biot and held at Columbia University, this book contains over 170 original papers on different phases of poromechanics in many materials from soils and minerals to human bone. It covers testing and modeling.
Author: O. C. Zienkiewicz
Publisher: Butterworth-Heinemann
ISBN: 0080951376
Category : Technology & Engineering
Languages : en
Pages : 581
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Book Description
The Finite Element Method for Fluid Dynamics offers a complete introduction the application of the finite element method to fluid mechanics. The book begins with a useful summary of all relevant partial differential equations before moving on to discuss convection stabilization procedures, steady and transient state equations, and numerical solution of fluid dynamic equations. The character-based split (CBS) scheme is introduced and discussed in detail, followed by thorough coverage of incompressible and compressible fluid dynamics, flow through porous media, shallow water flow, and the numerical treatment of long and short waves. Updated throughout, this new edition includes new chapters on: - Fluid-structure interaction, including discussion of one-dimensional and multidimensional problems - Biofluid dynamics, covering flow throughout the human arterial system Focusing on the core knowledge, mathematical and analytical tools needed for successful computational fluid dynamics (CFD), The Finite Element Method for Fluid Dynamics is the authoritative introduction of choice for graduate level students, researchers and professional engineers. - A proven keystone reference in the library of any engineer needing to understand and apply the finite element method to fluid mechanics - Founded by an influential pioneer in the field and updated in this seventh edition by leading academics who worked closely with Olgierd C. Zienkiewicz - Features new chapters on fluid-structure interaction and biofluid dynamics, including coverage of one-dimensional flow in flexible pipes and challenges in modeling systemic arterial circulation
Author: Vaughan R. Voller
Publisher: World Scientific
ISBN: 9812834990
Category : Mathematics
Languages : en
Pages : 185
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Book Description
The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems.
Author:
Publisher: ScholarlyEditions
ISBN: 146496453X
Category : Computers
Languages : en
Pages : 1318
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Book Description
Issues in Computation / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computation. The editors have built Issues in Computation: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computation in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
