Download or read book Higher Order Finite Element Methods written by Pavel Solin and published by CRC Press. This book was released on 2003-07-28 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and

Download or read book Higher Order Finite Element Methods written by Pavel Solin and published by Chapman and Hall/CRC. This book was released on 2003-07-28 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales. Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity. Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.

Download or read book The Finite Element Method Its Basis and Fundamentals written by Olek C Zienkiewicz and published by Elsevier. This book was released on 2005-05-26 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. The classic introduction to the finite element method, by two of the subject's leading authors Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text

Download or read book TEXTBOOK OF FINITE ELEMENT ANALYSIS written by P. SESHU and published by PHI Learning Pvt. Ltd.. This book was released on 2003-01-01 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a one-semester course in Finite Element Method, this compact and well-organized text presents FEM as a tool to find approximate solutions to differential equations. This provides the student a better perspective on the technique and its wide range of applications. This approach reflects the current trend as the present-day applications range from structures to biomechanics to electromagnetics, unlike in conventional texts that view FEM primarily as an extension of matrix methods of structural analysis. After an introduction and a review of mathematical preliminaries, the book gives a detailed discussion on FEM as a technique for solving differential equations and variational formulation of FEM. This is followed by a lucid presentation of one-dimensional and two-dimensional finite elements and finite element formulation for dynamics. The book concludes with some case studies that focus on industrial problems and Appendices that include mini-project topics based on near-real-life problems. Postgraduate/Senior undergraduate students of civil, mechanical and aeronautical engineering will find this text extremely useful; it will also appeal to the practising engineers and the teaching community.

Download or read book Finite Elements and Approximation written by O. C. Zienkiewicz and published by Courier Corporation. This book was released on 2013-04-22 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.

Download or read book The Finite Element Method in Engineering written by Singiresu S. Rao and published by Pergamon. This book was released on 1989 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partial Differential Equations and the Finite Element Method written by Pavel Ŝolín and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM. A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM. Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science. Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.

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 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative approach to teaching the finite element method blends theoretical, textbook-based learning with practical application using online and video resources. This hybrid teaching package features computational software such as MATLAB®, and tutorials presenting software applications such as PTC Creo Parametric, ANSYS APDL, ANSYS Workbench and SolidWorks, complete with detailed annotations and instructions so students can confidently develop hands-on experience. Suitable for senior undergraduate and graduate level classes, students will transition seamlessly between mathematical models and practical commercial software problems, empowering them to advance from basic differential equations to industry-standard modelling and analysis. Complete with over 120 end-of chapter problems and over 200 illustrations, this accessible reference will equip students with the tools they need to succeed in the workplace.

Download or read book Finite Element Methods written by Jonathan Whiteley and published by Springer. This book was released on 2017-01-26 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

Download or read book The Finite Element Method Solid mechanics written by O. C. Zienkiewicz and published by Butterworth-Heinemann. This book was released on 2000 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Higher Order Finite Element Methods written by Pavel Solin and published by Chapman and Hall/CRC. This book was released on 2003-07-28 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales. Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity. Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.

Download or read book Lamb Wave Based Structural Health Monitoring in Polymer Composites written by Rolf Lammering and published by Springer. This book was released on 2017-08-30 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses especially on the application of SHM technology to thin walled structural systems made from carbon fiber reinforced plastics. Here, guided elastic waves (Lamb-waves) show an excellent sensitivity to structural damages so that they are in the center of this book. It is divided into 4 sections dealing with analytical, numerical and experimental fundamentals, and subsequently with Lamb-wave propagation in fiber reinforced composites, SHM-systems and signal processing. The book is designed for engineering students as well as for researchers in the field of structural health monitoring and for users of this technology.

Download or read book Finite Element Method written by Pin Tong and published by Dover Books on Engineering. This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces mathematical foundations, developing them coherently and rigorously to reveal the method's broad applications. It emphasizes use of the variational approach, providing appendixes on variational calculus and matrix algebra for a self-contained treatment. Detailed examples employ Poisson's equations and the general Sturm-Liouville problem. 1977 edition.

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 An Introduction to the Finite Element Method for Differential Equations written by Mohammad Asadzadeh and published by John Wiley & Sons. This book was released on 2020-08-27 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master the finite element method with this masterful and practical volume An Introduction to the Finite Element Method (FEM) for Differential Equations provides readers with a practical and approachable examination of the use of the finite element method in mathematics. Author Mohammad Asadzadeh covers basic FEM theory, both in one-dimensional and higher dimensional cases. The book is filled with concrete strategies and useful methods to simplify its complex mathematical contents. Practically written and carefully detailed, An Introduction to the Finite Element Method covers topics including: An introduction to basic ordinary and partial differential equations The concept of fundamental solutions using Green's function approaches Polynomial approximations and interpolations, quadrature rules, and iterative numerical methods to solve linear systems of equations Higher-dimensional interpolation procedures Stability and convergence analysis of FEM for differential equations This book is ideal for upper-level undergraduate and graduate students in natural science and engineering. It belongs on the shelf of anyone seeking to improve their understanding of differential equations.

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomee and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.