smoothed finite element methods

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Smoothed Finite Element Methods

Author : G.R. Liu
ISBN : 1439820287
Genre : Science
File Size : 67. 42 MB
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Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve more accurate results, a generally higher convergence rate in energy without increasing computational cost, and easier auto-meshing of the problem domain. Drawing on the authors’ extensive research results, Smoothed Finite Element Methods presents the theoretical framework and development of various S-FEM models. After introducing background material, basic equations, and an abstracted version of the FEM, the book discusses the overall modeling procedure, fundamental theories, error assessment matters, and necessary building blocks to construct useful S-FEM models. It then focuses on several specific S-FEM models, including cell-based (CS-FEM), node-based (NS-FEM), edge-based (ES-FEM), face-based (FS-FEM), and a combination of FEM and NS-FEM (αFEM). These models are then applied to a wide range of physical problems in solid mechanics, fracture mechanics, viscoelastoplasticity, plates, piezoelectric structures, heat transfer, and structural acoustics. Requiring no previous knowledge of FEM, this book shows how computational methods and numerical techniques like the S-FEM help in the design and analysis of advanced engineering systems in rapid and cost-effective ways since the modeling and simulation can be performed automatically in a virtual environment without physically building the system. Readers can easily apply the methods presented in the text to their own engineering problems for reliable and certified solutions.

Smoothed Finite Element Methods

Author : G.R. Liu
ISBN : 1439820279
Genre : Science
File Size : 66. 27 MB
Format : PDF, ePub
Download : 432
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Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve more accurate results, a generally higher convergence rate in energy without increasing computational cost, and easier auto-meshing of the problem domain. Drawing on the authors’ extensive research results, Smoothed Finite Element Methods presents the theoretical framework and development of various S-FEM models. After introducing background material, basic equations, and an abstracted version of the FEM, the book discusses the overall modeling procedure, fundamental theories, error assessment matters, and necessary building blocks to construct useful S-FEM models. It then focuses on several specific S-FEM models, including cell-based (CS-FEM), node-based (NS-FEM), edge-based (ES-FEM), face-based (FS-FEM), and a combination of FEM and NS-FEM (αFEM). These models are then applied to a wide range of physical problems in solid mechanics, fracture mechanics, viscoelastoplasticity, plates, piezoelectric structures, heat transfer, and structural acoustics. Requiring no previous knowledge of FEM, this book shows how computational methods and numerical techniques like the S-FEM help in the design and analysis of advanced engineering systems in rapid and cost-effective ways since the modeling and simulation can be performed automatically in a virtual environment without physically building the system. Readers can easily apply the methods presented in the text to their own engineering problems for reliable and certified solutions.

Smoothed Finite Element Methods

Author : G.R. Liu
ISBN : 1439820279
Genre : Science
File Size : 71. 40 MB
Format : PDF
Download : 933
Read : 1148

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Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve more accurate results, a generally higher convergence rate in energy without increasing computational cost, and easier auto-meshing of the problem domain. Drawing on the authors’ extensive research results, Smoothed Finite Element Methods presents the theoretical framework and development of various S-FEM models. After introducing background material, basic equations, and an abstracted version of the FEM, the book discusses the overall modeling procedure, fundamental theories, error assessment matters, and necessary building blocks to construct useful S-FEM models. It then focuses on several specific S-FEM models, including cell-based (CS-FEM), node-based (NS-FEM), edge-based (ES-FEM), face-based (FS-FEM), and a combination of FEM and NS-FEM (αFEM). These models are then applied to a wide range of physical problems in solid mechanics, fracture mechanics, viscoelastoplasticity, plates, piezoelectric structures, heat transfer, and structural acoustics. Requiring no previous knowledge of FEM, this book shows how computational methods and numerical techniques like the S-FEM help in the design and analysis of advanced engineering systems in rapid and cost-effective ways since the modeling and simulation can be performed automatically in a virtual environment without physically building the system. Readers can easily apply the methods presented in the text to their own engineering problems for reliable and certified solutions.

Smoothed Finite Element Methods

Author : G.R. Liu
ISBN : 1439820287
Genre : Science
File Size : 58. 43 MB
Format : PDF, ePub, Docs
Download : 508
Read : 312

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Generating a quality finite element mesh is difficult and often very time-consuming. Mesh-free methods operations can also be complicated and quite costly in terms of computational effort and resources. Developed by the authors and their colleagues, the smoothed finite element method (S-FEM) only requires a triangular/tetrahedral mesh to achieve more accurate results, a generally higher convergence rate in energy without increasing computational cost, and easier auto-meshing of the problem domain. Drawing on the authors’ extensive research results, Smoothed Finite Element Methods presents the theoretical framework and development of various S-FEM models. After introducing background material, basic equations, and an abstracted version of the FEM, the book discusses the overall modeling procedure, fundamental theories, error assessment matters, and necessary building blocks to construct useful S-FEM models. It then focuses on several specific S-FEM models, including cell-based (CS-FEM), node-based (NS-FEM), edge-based (ES-FEM), face-based (FS-FEM), and a combination of FEM and NS-FEM (αFEM). These models are then applied to a wide range of physical problems in solid mechanics, fracture mechanics, viscoelastoplasticity, plates, piezoelectric structures, heat transfer, and structural acoustics. Requiring no previous knowledge of FEM, this book shows how computational methods and numerical techniques like the S-FEM help in the design and analysis of advanced engineering systems in rapid and cost-effective ways since the modeling and simulation can be performed automatically in a virtual environment without physically building the system. Readers can easily apply the methods presented in the text to their own engineering problems for reliable and certified solutions.

A Smoothed Finite Element Method For The Static And Free Vibration Analysis Of Shells

Author : Nhon Thanh Nguyen
ISBN : OCLC:981950387
Genre :
File Size : 69. 20 MB
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Meshfree Methods

Author : G.R. Liu
ISBN : 1420082108
Genre : Science
File Size : 41. 93 MB
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Understand How to Use and Develop Meshfree Techniques An Update of a Groundbreaking Work Reflecting 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 edition addresses important new developments, especially on essential theoretical issues. New to the Second Edition Much more details on fundamental concepts and important theories for numerical methods Discussions on special properties of meshfree methods, including stability, convergence, accurate, efficiency, and bound property More detailed discussion on error estimation and adaptive analysis using meshfree methods Developments on combined meshfree/finite element method (FEM) models Comparison studies using meshfree and FEM Drawing on the author’s own research, this book provides a single-source guide to meshfree techniques and theories that can effectively handle a variety of complex engineering problems. It analyzes how the methods work, explains how to use and develop the methods, and explores the problems associated with meshfree methods. To access MFree2D (copyright, G. R. Liu), which accompanies MESHFREE METHODS: MOVING BEYOND THE FINITE ELEMENT METHOD, Second Edition (978-1-4200-8209-8) by Dr. G. R. Liu, please go to the website: www.ase.uc.edu/~liugr An access code is needed to use program – to receive it please email Dr. Liu directly at: [email protected] Dr. Liu will reply to you directly with the code, and you can then proceed to use the software.

The Finite Element Method

Author : G.R. Liu
ISBN : 9780080994413
Genre : Technology & Engineering
File Size : 56. 78 MB
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Written for practicing engineers and students alike, this book emphasizes the role of finite element modeling and simulation in the engineering design process. It provides the necessary theories and techniques of the FEM in a concise and easy-to-understand format and applies the techniques to civil, mechanical, and aerospace problems. Updated throughout for current developments in FEM and FEM software, the book also includes case studies, diagrams, illustrations, and tables to help demonstrate the material. Plentiful diagrams, illustrations and tables demonstrate the material Covers modeling techniques that predict how components will operate and tolerate loads, stresses and strains in reality Full set of PowerPoint presentation slides that illustrate and support the book, available on a companion website

Smoothed Point Interpolation Methods

Author : G R Liu
ISBN : 9789814452861
Genre : Technology & Engineering
File Size : 45. 6 MB
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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. Contents:PreliminariesG SpacesPIM Shape Function CreationStrain Field ConstructionWeak and Weakened Weak FormulationsNode-Based Smoothed Point Interpolation Method (NS-PIM)Edge-Based Smoothed Point Interpolation Method (ES-PIM)Cell-Based Smoothed Point Interpolation Method (CS-PIM)The Cell-Based Smoothed Alpha Radial Point Interpolation Method (CS-αRPIM)Strain-Constructed Point Interpolation Method (SC-PIM)S-PIM for Heat Transfer and Thermoelasticity ProblemsSingular CS-RPIM for Fracture Mechanics ProblemsAdaptive Analysis Using S-PIMsAppendices: Program Codes Library:Description of the SubroutinesA Demonstration Input FileSource Codes of Two ModulesSource Codes of the Common Subroutines Readership: Researchers, practitioners, academics, and graduate students in engineering mechanics, mechanical engineering, aerospace engineering, civil engineering and computational physics. Keywords:Numerical Method;Meshfree Method;Finite Element Method;Point Interpolation Method;G Space;Weakened Weak Form;Applied Mechanics;Adaptive Analysis;Radial Basis Functions;Radial Point Interpolation Method

Smoothed Point Interpolation Methods

Author : Gui-Rong Liu
ISBN : 9789814452854
Genre : Mathematics
File Size : 24. 57 MB
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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.

Structural Analysis With The Finite Element Method Linear Statics

Author : Eugenio Oñate
ISBN : 9781402087431
Genre : Computers
File Size : 20. 53 MB
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STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elastic foundations, stress smoothing, error estimation and adaptive mesh refinement techniques, among others. The text concludes with a chapter on the mesh generation and visualization of FEM results. The book will be useful for students approaching the finite element analysis of structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis. STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 2: Beams, Plates and Shells Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM).The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume 2 presents a detailed description of the finite element formulation for analysis of slender and thick beams, thin and thick plates, folded plate structures, axisymmetric shells, general curved shells, prismatic structures and three dimensional beams. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems Emphasis is put on the treatment of structures with layered composite materials. The book will be useful for students approaching the finite element analysis of beam, plate and shell structures for the first time, as well as for practising engineers interested in the details of the formulation and performance of the different finite elements for practical structural analysis.

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