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Extended Finite Element And Meshfree Methods

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Extended Finite Element and Meshfree Methods

Extended Finite Element and Meshfree Methods Book
Author : Timon Rabczuk,Jeong-Hoon Song,Xiaoying Zhuang,Cosmin Anitescu
Publisher : Academic Press
Release : 2019-11-13
ISBN : 0128141077
Language : En, Es, Fr & De

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Book Description :

Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. Explains all the important theory behind XFEM and meshfree methods Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods Introduces alternative modeling methods to help readers decide what is most appropriate for their work

Advances in Meshfree and X FEM Methods

Advances in Meshfree and X FEM Methods Book
Author : G R Liu
Publisher : World Scientific
Release : 2002-12-16
ISBN : 9814486884
Language : En, Es, Fr & De

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Book Description :

This book is a collection of the papers from the proceedings of the 1st Asian Workshop on Meshfree Methods held in conjunction with the 2nd International Conference on Structural Stability & Dynamics (ICSSD02) on 16-18 December 2002 in Singapore. It contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported. Contents:Meshfree FormulationsMeshfree Methods for Smart Materials/StructuresMeshfree Methods for Fracture AnalysisMeshfree Methods for Membranes, Plates & ShellsMeshfree Methods for SoilMeshfree Methods for CFDBoundary Meshfree MethodsCoding, Error Estimation, ParallisationMeshfree Particle MethodsX-FEM Readership: Graduate and undergraduate students, researchers, academics, lecturers and engineers in civil engineering, engineering mechanics and mechanical engineering. Keywords:Meshfree Method;Meshless Method;SPH;X-FEM;Computational Mechanics;Computational Science;Fluid Dynamics;Modified Variational Principle;Smart Materials

XFEM Fracture Analysis of Composites

XFEM Fracture Analysis of Composites Book
Author : Soheil Mohammadi
Publisher : John Wiley & Sons
Release : 2012-08-27
ISBN : 1118443381
Language : En, Es, Fr & De

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Book Description :

This book describes the basics and developments of the new XFEMapproach to fracture analysis of composite structures andmaterials. It provides state of the art techniques and algorithmsfor fracture analysis of structures including numeric examples atthe end of each chapter as well as an accompanying website whichwill include MATLAB resources, executables, data files, andsimulation procedures of XFEM. The first reference text for the extended finite element method(XFEM) for fracture analysis of structures and materials Includes theory and applications, with worked numericalproblems and solutions, and MATLAB examples on an accompanyingwebsite with further XFEM resources Provides a comprehensive overview of this new area of research,including a review of Fracture Mechanics, basic through to advancedXFEM theory, as well as current problems and applications Includes a chapter on the future developments in the field, newresearch areas and possible future applications of the method

Advances in Meshfree and X fem Methods

Advances in Meshfree and X fem Methods Book
Author : Gui-Rong Liu
Publisher : World Scientific
Release : 2003
ISBN : 9789812382474
Language : En, Es, Fr & De

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Book Description :

This book contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported. Contents: Meshfree Shape Functions for Weak Formulation, Strong Formulation; Meshfree Methods for Smart Materials/Structures; Meshfree Methods for Fracture Analysis; Meshfree Methods for Membrances, Plates & Shells; Meshfree Methods for Soil; Meshfree Methods for CFD; Boundary Meshfree Methods; Coding, Error Estimation, Parallisation; Meshfree Particle Methods; X-FEM. Readership: Graduate and undergraduate students, reserchers, academics, lecturers and engineers in civil engineering, engineering mechanics and mechanical engineering.

Extended Finite Element Method for Crack Propagation

Extended Finite Element Method for Crack Propagation Book
Author : Sylvie Pommier,Anthony Gravouil,Nicolas Moes,Alain Combescure
Publisher : John Wiley & Sons
Release : 2013-03-04
ISBN : 1118622693
Language : En, Es, Fr & De

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Book Description :

Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.

Error Estimates for Advanced Galerkin Methods

Error Estimates for Advanced Galerkin Methods Book
Author : Marcus Olavi Rüter
Publisher : Springer Nature
Release : 2019-11-07
ISBN : 3030061736
Language : En, Es, Fr & De

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Book Description :

This monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.

The Finite Element Method in Engineering

The Finite Element Method in Engineering Book
Author : Singiresu S. Rao
Publisher : Butterworth-Heinemann
Release : 2017-10-31
ISBN : 0128143649
Language : En, Es, Fr & De

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Book Description :

The Finite Element Method in Engineering, Sixth Edition, provides a thorough grounding in the mathematical principles behind the Finite Element Analysis technique—an analytical engineering tool originated in the 1960's by the aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. Rao shows how to set up finite element solutions in civil, mechanical and aerospace engineering applications. The new edition features updated real-world examples from MATLAB, Ansys and Abaqus, and a new chapter on additional FEM topics including extended FEM (X-FEM). Professional engineers will benefit from the introduction to the many useful applications of finite element analysis. Includes revised and updated chapters on MATLAB, Ansys and Abaqus Offers a new chapter, Additional Topics in Finite Element Method Includes discussion of practical considerations, errors and pitfalls in FEM singularity elements Features a brief presentation of recent developments in FEM including extended FEM (X-FEM), augmented FEM (A-FEM) and partition of unity FEM (POUFEM) Features improved pedagogy, including the addition of more design-oriented and practical examples and problems Covers real-life applications, sample review questions at the end of most chapters, and updated references

Extended Finite Element Method

Extended Finite Element Method Book
Author : Amir R. Khoei
Publisher : John Wiley & Sons
Release : 2015-02-23
ISBN : 1118457684
Language : En, Es, Fr & De

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Book Description :

Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Extended Finite Element Method: Theory and Applications introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics. The XFEM approach is based on an extension of standard finite element method based on the partition of unity method. Extended Finite Element Method: Theory and Applications begins by introducing the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. It then covers the theory and application of XFEM in large deformations, plasticity and contact problems. The implementation of XFEM in fracture mechanics, including the linear, cohesive, and ductile crack propagation is also covered. The theory and applications of the XFEM in multiphase fluid flow, including the hydraulic fracturing in soil saturated media and crack propagation in thermo-hydro-mechanical porous media, is also discussed in detail. Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples

Computational Modelling of Fracture with Local Maximum Entropy Approximations

Computational Modelling of Fracture with Local Maximum Entropy Approximations Book
Author : Fatemeh Amiri
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
Release : 2016-10-27
ISBN : 9783838153049
Language : En, Es, Fr & De

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Book Description :

The key objective of this research is to study fracture with a meshfree method, local maximum entropy approximations, and model fracture in thin shell structures with complex geometry and topology. This topic is of high relevance for real-world applications, for example in the automotive industry and in aerospace engineering. The shell structure can be described efficiently by meshless methods which are capable of describing complex shapes as a collection of points instead of a structured mesh. In order to find the appropriate numerical method to achieve this goal, the first part of the work was development of a method based on local maximum entropy (LME) shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method (XFEM) at a comparable computational cost. In addition, we keep the advantages of the LME shape functions,such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting. As extension of this method to three dimensional problems and complex thin shell structures with arbitrary crack growth is cumbersome, we developed a phase field model for fracture using LME. Phase field models provide a powerful tool to tackle moving interface problems, and have been extensively used in physics and materials science. Phase methods are gaining popularity in a wide set of applications in applied science and engineering, recently a second order phase field approximation for brittle fracture has gathered significant interest in computational fracture such that sharp cracks discontinuities are modeled by a diffusive crack. By minimizing the system energy with respect to the mechanical displacements and the phase-field, subject to an irreversibility condition to avoid crack healing, this model can describe crack nucleation, propagation, branching and merging. One of the main advantages of the phase field modeling of fractures is the unified treatment of the interfacial tracking and mechanics, which potentially leads to simple, robust, scalable computer codes applicable to complex systems. In other words, this approximation reduces considerably the implementation complexity because the numerical tracking of the fracture is not needed, at the expense of a high computational cost. We present a fourth-order phase field model for fracture based on local maximum entropy (LME) approximations. The higher order continuity of the meshfree LME approximation allows to directly solve the fourth-order phase field equations without splitting the fourth-order differential equation into two second order differential equations. Notably, in contrast to previous discretizations that use at least a quadratic basis, only linear completeness is needed in the LME approximation. We show that the crack surface can be captured more accurately in the fourth-order model than the second-order model. Furthermore, less nodes are needed for the fourth-order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation. In the last part of this research, we present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantageous over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.

Advances in Meshfree and X fem Methods

Advances in Meshfree and X fem Methods Book
Author : Liu Gui Rong
Publisher : Unknown
Release : 2003
ISBN : 9789812382474
Language : En, Es, Fr & De

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Book Description :

Annotation. This book contains 36 articles covering most of the topics in the rapidly developing areas of meshfree methods and extended finite element methods (X-FEM). These topics include domain discretization, boundary discretization, combined domain/boundary discretization, meshfree particle methods, collocation methods, X-FEM, etc. Papers on issues related to implementation and coding of meshfree methods are also presented. The areas of applications of meshfree methods include solving general partial differential equations, the mechanics of solids and structures, smart material/structures, soil-structures, fracture mechanics, fluid dynamics, impact, penetration, micro-fluidics, etc. In addition, techniques for field variable interpolation, such as the moving least squares (MLS) approximation, the point interpolation method (PIM), and radial PIM are reported. Contents: Meshfree Shape Functions for Weak Formulation, Strong Formulation; Meshfree Methods for Smart Materials/Structures; Meshfree Methods for Fracture Analysis; Meshfree Methods for Membrances, Plates & Shells; Meshfree Methods for Soil; Meshfree Methods for CFD; Boundary Meshfree Methods; Coding, Error Estimation, Parallisation; Meshfree Particle Methods; X-FEM. Readership: Graduate and undergraduate students, reserchers, academics, lecturers and engineers in civil engineering, engineering mechanics and mechanical engineering.

Finite Element Method Concepts and Applications

Finite Element Method  Concepts and Applications Book
Author : Connie Mcguire
Publisher : Unknown
Release : 2019-06-06
ISBN : 9781632408525
Language : En, Es, Fr & De

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Book Description :

Finite element method refers to the numerical method, which is used to solve problems in mathematical physics and engineering. The areas where finite element method is mostly applied are fluid flow, structural analysis, mass transport, heat transfer and electromagnetic potential problems. This method divides the problem into simpler and smaller parts called finite elements, in order to solve it. Algebraic equations are formulated for each element, which are then assembled into a larger set of equations that models the whole problem. Variational methods are then applied to find an approximate solution by minimizing the associated error function. The different finite element methods are applied element method (AEM), extended finite element method (XFEM), meshfree methods, Loubignac iteration, finite element limit analysis, spectral element method, etc. This book outlines the concepts and applications of finite element method in detail. It strives to provide a fair idea about this discipline and to help develop a better understanding of the latest advances within this area of mathematics. Those in search of information to further their knowledge will be greatly assisted by this book.

Advances in Meshfree Techniques

Advances in Meshfree Techniques Book
Author : V.M.A. Leitao,C.J.S. Alves,C. Armando Duarte
Publisher : Springer Science & Business Media
Release : 2007-05-26
ISBN : 1402060955
Language : En, Es, Fr & De

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Book Description :

The book collects extended original contributions presented at the first ECCOMAS Conference on Meshless Methods held in 2005 in Lisbon. The list of contributors is a mix of highly distinguished authors as well as promising young researchers. This means that the reader gets a varied and contemporary view on different mesh reduction methods and its range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Advances in Applied Mechanics

Advances in Applied Mechanics Book
Author : Daniel S. Balint,Stephane P.A. Bordas
Publisher : Academic Press
Release : 2020-11-01
ISBN : 0128209909
Language : En, Es, Fr & De

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Book Description :

Advances in Applied Mechanics, Volume 53 in this ongoing series, highlights new advances in the field, with this new volume presenting interesting chapters on Phase field modelling of fracture, Advanced geometry representations and tools for microstructural and multiscale modelling, The material point method: the past and the future, From Experimental Modeling of Shotcrete to Large Scale Numerical Simulations of Tunneling, and Material point method after 25 years: theory, implementation, applications. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Advances in Applied Mechanics series

An Extended Finite Element Method with Discontinuous Enrichment for Applied Mechanics

An Extended Finite Element Method with Discontinuous Enrichment for Applied Mechanics Book
Author : John Everett Dolbow
Publisher : Unknown
Release : 1999
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The modeling of a discontinuous field with a standard finite element approximation presents unique challenges. The construction of an approximating space which is discontinuous across a given line or surface places strict restrictions on the finite element mesh. The simulation of an evolution of the discontinuity is in turn burdened by the requirement to remesh at each stage of the calculation. This work approaches the problem by locally enriching the standard element-based approximation with discontinuous functions. The enriched basis is formed from a union of the set of nodal shape functions with a set of products of nodal shape functions and enrichment functions. The construction of the approximating space in this fashion places the formulation in the class of partition of unity methods. By aligning the discontinuities in the enrichment functions with a specified geometry, a discontinuous field is represented independently of the finite element mesh. This capability is shown to significantly extend the standard method for a number of applications in applied mechanics.

An Introduction to Meshfree Methods and Their Programming

An Introduction to Meshfree Methods and Their Programming Book
Author : G.R. Liu,Y.T. Gu
Publisher : Springer
Release : 2011-02-03
ISBN : 9789048168194
Language : En, Es, Fr & De

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Book Description :

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

Advances in Applied Mechanics

Advances in Applied Mechanics Book
Author : Anonim
Publisher : Academic Press
Release : 2014-11-21
ISBN : 0128003022
Language : En, Es, Fr & De

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Book Description :

Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. Covers all fields of the mechanical sciences Highlights classical and modern areas of mechanics that are ready for review Provides comprehensive coverage of the field in question

An Introduction to Meshfree Methods and Their Programming

An Introduction to Meshfree Methods and Their Programming Book
Author : G.R. Liu,Y.T. Gu
Publisher : Springer Science & Business Media
Release : 2005-12-05
ISBN : 9781402034688
Language : En, Es, Fr & De

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Book Description :

The finite difference method (FDM) hasbeen used tosolve differential equation systems for centuries. The FDM works well for problems of simple geometry and was widely used before the invention of the much more efficient, robust finite element method (FEM). FEM is now widely used in handling problems with complex geometry. Currently, we are using and developing even more powerful numerical techniques aiming to obtain more accurate approximate solutions in a more convenient manner for even more complex systems. The meshfree or meshless method is one such phenomenal development in the past decade, and is the subject of this book. There are many MFree methods proposed so far for different applications. Currently, three monographs on MFree methods have been published. Mesh Free Methods, Moving Beyond the Finite Element Method d by GR Liu (2002) provides a systematic discussion on basic theories, fundamentals for MFree methods, especially on MFree weak-form methods. It provides a comprehensive record of well-known MFree methods and the wide coverage of applications of MFree methods to problems of solids mechanics (solids, beams, plates, shells, etc.) as well as fluid mechanics. The Meshless Local Petrov-Galerkin (MLPG) Method d by Atluri and Shen (2002) provides detailed discussions of the meshfree local Petrov-Galerkin (MLPG) method and itsvariations. Formulations and applications of MLPG are well addressed in their book.

Advances in Discretization Methods

Advances in Discretization Methods Book
Author : Giulio Ventura,Elena Benvenuti
Publisher : Springer
Release : 2016-08-24
ISBN : 3319412469
Language : En, Es, Fr & De

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Book Description :

This book gathers selected contributions on emerging research work presented at the International Conference eXtended Discretization MethodS (X-DMS), held in Ferrara in September 2015. It highlights the most relevant advances made at the international level in the context of expanding classical discretization methods, like finite elements, to the numerical analysis of a variety of physical problems. The improvements are intended to achieve higher computational efficiency and to account for special features of the solution directly in the approximation space and/or in the discretization procedure. The methods described include, among others, partition of unity methods (meshfree, XFEM, GFEM), virtual element methods, fictitious domain methods, and special techniques for static and evolving interfaces. The uniting feature of all contributions is the direct link between computational methodologies and their application to different engineering areas.

Computational Modelling of Particulate Composites Using Meshless Methods

Computational Modelling of Particulate Composites Using Meshless Methods Book
Author : Md Islam
Publisher : Unknown
Release : 2011
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This thesis deals with the numerical simulation of particulate composites using one of the more stable and accurate meshless methods namely the element free Galerkin (EFG) method. To accurately describe the material inhomogeneities present in particulate composites, an extrinsic enrichment function is incorporated into the approximation of the EFG method which produces more versatile, robust and effective computational methodology. The effectiveness of the proposed numerical model is then investigated by employing the model to analyse different configurations of particulate composites. The accuracy and efficiency of this enriched EFG method are studied numerically by comparing the results obtained with the available analytical solutions and other numerical techniques. Further, it is demonstrated that the method developed in this work has the potential to efficiently model syntactic foam, a type of particulate composites. This is illustrated by performing multi-scale modelling using homogenisation technique which confirms satisfactory comparison of the numerical method with experimental results. To further explore the applicability of the developed methodology, an enriched or extended finite element method (XFEM) based technique, is applied to study crack inclusion and interaction of crack propagation with matrix and particles within particle reinforced composite material.