Hybrid And Incompatible Finite Element Methods

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Hybrid And Incompatible Finite Element Methods

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Author : Theodore H.H. Pian
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2005-11-04

Hybrid And Incompatible Finite Element Methods written by Theodore H.H. Pian and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-04 with Mathematics categories.

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.

Smoothed Point Interpolation Methods G Space Theory And Weakened Weak Forms

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Author : Gui-rong Liu
language : en
Publisher: World Scientific
Release Date : 2013-08-16

Smoothed Point Interpolation Methods G Space Theory And Weakened Weak Forms written by Gui-rong Liu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Technology & Engineering categories.

Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations — one of the most important features of the next generation methods. This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds.The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development.

Structural Analysis With Finite Elements

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Author : Friedel Hartmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-30

Structural Analysis With Finite Elements written by Friedel Hartmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-30 with Technology & Engineering categories.

This book provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at www.winfem.de.

Smoothed Point Interpolation Methods

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Author : Gui-Rong Liu
language : en
Publisher: World Scientific
Release Date : 2013

Smoothed Point Interpolation Methods written by Gui-Rong Liu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

This book describes the various Smoothed Point Interpolation Method (S-PIM) models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail.

Advanced Finite Element Method In Structural Engineering

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Author : Yu-Qiu Long
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-29

Advanced Finite Element Method In Structural Engineering written by Yu-Qiu Long and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-29 with Technology & Engineering categories.

Advanced Finite Element Method in Structural Engineering systematically introduces the research work on the Finite Element Method (FEM), which was completed by Prof. Yu-qiu Long and his research group in the past 25 years. Seven original theoretical achievements - for instance, the Generalized Conforming Element method, to name one - and their applications in the fields of structural engineering and computational mechanics are discussed in detail. The book also shows the new strategies for avoiding five difficulties that exist in traditional FEM (shear-locking problem of thick plate elements; sensitivity problem to mesh distortion; non-convergence problem of non-conforming elements; accuracy loss problem of stress solutions by displacement-based elements; stress singular point problem) by utilizing foregoing achievements.

Methods Of Fundamental Solutions In Solid Mechanics

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Author : Hui Wang
language : en
Publisher: Elsevier
Release Date : 2019-06-06

Methods Of Fundamental Solutions In Solid Mechanics written by Hui Wang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-06 with Technology & Engineering categories.

Methods of Fundamental Solutions in Solid Mechanics presents the fundamentals of continuum mechanics, the foundational concepts of the MFS, and methodologies and applications to various engineering problems. Eight chapters give an overview of meshless methods, the mechanics of solids and structures, the basics of fundamental solutions and radical basis functions, meshless analysis for thin beam bending, thin plate bending, two-dimensional elastic, plane piezoelectric problems, and heat transfer in heterogeneous media. The book presents a working knowledge of the MFS that is aimed at solving real-world engineering problems through an understanding of the physical and mathematical characteristics of the MFS and its applications. - Explains foundational concepts for the method of fundamental solutions (MFS) for the advanced numerical analysis of solid mechanics and heat transfer - Extends the application of the MFS for use with complex problems - Considers the majority of engineering problems, including beam bending, plate bending, elasticity, piezoelectricity and heat transfer - Gives detailed solution procedures for engineering problems - Offers a practical guide, complete with engineering examples, for the application of the MFS to real-world physical and engineering challenges

Meshfree Methods

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Author : G.R. Liu
language : en
Publisher: CRC Press
Release Date : 2009-10-06

Meshfree Methods written by G.R. Liu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-06 with Mathematics categories.

Understand How to Use and Develop Meshfree TechniquesAn Update of a Groundbreaking WorkReflecting the significant advances made in the field since the publication of its predecessor, Meshfree Methods: Moving Beyond the Finite Element Method, Second Edition systematically covers the most widely used meshfree methods. With 70% new material, this edit

Computational Modelling And Advanced Simulations

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Author : Justín Murín
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-25

Computational Modelling And Advanced Simulations written by Justín Murín and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-25 with Mathematics categories.

This book contains selected, extended papers presented at the thematic ECCOMAS conference on Computational Modelling and Advanced Simulations (CMAS2009) held in Bratislava, Slovakia, June 30 – July 3, 2009. Modelling and simulation of engineering problems play a very important role in the classic and new composite material sciences, and in design and computational prototyping of modern and advanced technologic parts and systems. According to this, the existing numerical methods have been improved and new numerical methods have been established for modelling and simulation of more and more complex and complicated engineering problems. The present book should contribute to the effort to make modelling and simulation more effective and accurate.

Mathematical Analysis And Its Applications

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Author : P. N. Agrawal
language : en
Publisher: Springer
Release Date : 2015-08-22

Mathematical Analysis And Its Applications written by P. N. Agrawal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-22 with Mathematics categories.

This book discusses recent developments in and the latest research on mathematics, statistics and their applications. All contributing authors are eminent academics, scientists, researchers and scholars in their respective fields, hailing from around the world. The book presents roughly 60 unpublished, high-quality and peer-reviewed research papers that cover a broad range of areas including approximation theory, harmonic analysis, operator theory, fixed-point theory, functional differential equations, dynamical and control systems, complex analysis, special functions, function spaces, summability theory, Fourier and wavelet analysis, and numerical analysis – all of which are topics of great interest to the research community – while further papers highlight important applications of mathematical analysis in science, engineering and related areas. This conference aims at bringing together experts and young researchers in mathematics from all over the world to discuss the latest advances in mathematical analysis and at promoting the exchange of ideas in various applications of mathematics in engineering, physics and biology. This conference encourages international collaboration and provides young researchers an opportunity to learn about the current state of the research in their respective fields.

Advances And Trends In Structural Engineering Mechanics And Computation

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Author : Alphose Zingoni
language : en
Publisher: CRC Press
Release Date : 2010-08-16

Advances And Trends In Structural Engineering Mechanics And Computation written by Alphose Zingoni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Technology & Engineering categories.

Advances and Trends in Structural Engineering, Mechanics and Computation features over 300 papers classified into 21 sections, which were presented at the Fourth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2010, Cape Town, South Africa, 6-8 September 2010). The SEMC conferences have been held every 3 years in