Download or read book Mixed and Hybrid Finite Element Methods written by Franco Brezzi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity. The authors provide with this publication an analysis of the methods in order to understand their properties as thoroughly as possible.
Download or read book Mixed Finite Element Methods and Applications written by Daniele Boffi and published by Springer Science & Business Media. This book was released on 2013-07-02 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-standard finite element methods, in particular mixed methods, are central to many applications. In this text the authors, Boffi, Brezzi and Fortin present a general framework, starting with a finite dimensional presentation, then moving on to formulation in Hilbert spaces and finally considering approximations, including stabilized methods and eigenvalue problems. This book also provides an introduction to standard finite element approximations, followed by the construction of elements for the approximation of mixed formulations in H(div) and H(curl). The general theory is applied to some classical examples: Dirichlet's problem, Stokes' problem, plate problems, elasticity and electromagnetism.
Download or read book Hybrid and Incompatible Finite Element Methods written by Theodore H.H. Pian and published by CRC Press. This book was released on 2005-11-04 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods. Today, however, recent advances--many directly attributable to these authors--have allowed the development of the stability theory and abstract mathematics to useful tools. Hybrid and Incompatible Finite Element Methods introduces these advances in the theory and applications of incompatible and multivariable finite element methods. After an overview of the variation formulation of finite element methods in solid mechanics, the authors discuss the fundamental theory and systematically demonstrate the theoretical foundations of incompatible elements and their application to different problems in the theory of elasticity. They also introduce new ideas in the development of hybrid finite elements, study the numerical stability of the hybrid and mixed element, and establish the theory of zero energy deformation modes. The final chapters, explore applications to fracture problems, present a bound analysis for fracture parameters, and demonstrate an implementation of a finite element analysis program.
Download or read book Handbook of Numerical Analysis written by Philippe G. Ciarlet and published by Gulf Professional Publishing. This book was released on 1990 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hybrid and Incompatible Finite Element Methods written by Theodore H.H. Pian and published by CRC Press. This book was released on 2005-11-04 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of incompatible multivariable elements, along with a common perception of impracticality, have hindered the widespread implementation of these methods.
Download or read book A Simple Introduction to the Mixed Finite Element Method written by Gabriel N. Gatica and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.
Download or read book Mathematical Aspects of Finite Element Methods written by I. Galligani and published by Springer. This book was released on 2006-11-15 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hybrid and Mixed Finite Element Methods written by Satya N. Atluri and published by . This book was released on with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mixed Finite Elements Compatibility Conditions and Applications written by Daniele Boffi and published by Springer. This book was released on 2008-04-01 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.
Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.
Download or read book Finite Element Method for Solids and Structures written by Sung W. Lee and published by Cambridge University Press. This book was released on 2021-06-17 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the basic mathematics needed for a balanced understanding of finite element method theory and its implementation.
Download or read book Compatible Spatial Discretizations written by Douglas N. Arnold and published by Springer Science & Business Media. This book was released on 2007-01-26 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: The IMA Hot Topics workshop on compatible spatialdiscretizations was held in 2004. This volume contains original contributions based on the material presented there. A unique feature is the inclusion of work that is representative of the recent developments in compatible discretizations across a wide spectrum of disciplines in computational science. Abstracts and presentation slides from the workshop can be accessed on the internet.
Download or read book Mixed Finite Element Technologies written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2009-06-16 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixed finite element methods are a tool to solve complex engineering problems of different nature. This subject is treated in the volume from the engineering and the mathematical point. Different applications are considered which depict the value of mixed formulations in engineering on one side. On the other side the mathematical background is provided including proofs of convergence and stability of these methods and adequate solvers for mixed problems are discussed. This broad spectrum yields an indepth treatment of mixed methods from different perspectives.
Download or read book The Finite Element Method written by Zhu and published by John Wiley & Sons. This book was released on 2018-03-12 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines. Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.
Download or read book Hybrid Finite Element Method for Stress Analysis of Laminated Composites written by Suong Van Hoa and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has one single purpose: to present the development of the partial hybrid finite element method for the stress analysis of laminated composite structures. The reason for this presentation is because the authors believe that partial hybrid finite element method is more efficient that the displacement based finite element method for the stress analysis oflaminated composites. In fact, the examples in chapter 5 of this book show that the partial hybrid finite element method is about 5 times more efficient than the displacement based finite element method. Since there is a great need for accurate and efficient calculation of interlaminar stresses for the design using composites, the partial hybrid finite method does provide one possible solution. Hybrid finite method has been in existence since 1964 and a significant amount of work has been done on the topic. However, the authors are not aware of any systematic piece of literature that gives a detailed presentation of the method. Chapters of the displacement finite element method and the evolution 1 and 2 present a sununary of the hybrid finite element method. Hopefully, these two chapters can provide the readers with an appreciation for the difference between the displacement finite element method and the hybrid finite element. It also should prepare the readers for the introduction of partial hybrid finite element method presented in chapter 3.
Download or read book The Finite Element Method for Electromagnetic Modeling written by Gérard Meunier and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by specialists of modeling in electromagnetism, this book provides a comprehensive review of the finite element method for low frequency applications. Fundamentals of the method as well as new advances in the field are described in detail. Chapters 1 to 4 present general 2D and 3D static and dynamic formulations by the use of scalar and vector unknowns and adapted interpolations for the fields (nodal, edge, face or volume). Chapter 5 is dedicated to the presentation of different macroscopic behavior laws of materials and their implementation in a finite element context: anisotropy and hysteretic properties for magnetic sheets, iron losses, non-linear permanent magnets and superconductors. More specific formulations are then proposed: the modeling of thin regions when finite elements become misfit (Chapter 6), infinite domains by using geometrical transformations (Chapter 7), the coupling of 2D and 3D formulations with circuit equations (Chapter 8), taking into account the movement, particularly in the presence of Eddy currents (Chapter 9) and an original approach for the treatment of geometrical symmetries when the sources are not symmetric (Chapter 10). Chapters 11 to 13 are devoted to coupled problems: magneto-thermal coupling for induction heating, magneto-mechanical coupling by introducing the notion of strong and weak coupling and magneto-hydrodynamical coupling focusing on electromagnetic instabilities in fluid conductors. Chapter 14 presents different meshing methods in the context of electromagnetism (presence of air) and introduces self-adaptive mesh refinement procedures. Optimization techniques are then covered in Chapter 15, with the adaptation of deterministic and probabilistic methods to the numerical finite element environment. Chapter 16 presents a variational approach of electromagnetism, showing how Maxwell equations are derived from thermodynamic principles.
Download or read book Crystal Plasticity Finite Element Methods written by Franz Roters and published by John Wiley & Sons. This book was released on 2011-08-04 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.
