Download or read book A Generalized Finite Element Method for Three dimensional Branched Cracks written by Luziana Grillo Reno and published by . This book was released on 2006 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Extended Finite Element and Meshfree Methods written by Timon Rabczuk and published by Academic Press. This book was released on 2019-11-13 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Generalized Finite Element Methods for Three dimensional Crack Growth Simulations written by Jeronymo P. Pereira and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Three-dimensional (3-D) crack growth analysis is crucial for the assessment of structures such as aircrafts, rockets, engines and pressure vessels, which are subjected to extreme loading conditions. The analysis of 3-D arbitrary crack growth using the standard Finite Element Method (FEM) encounters several difficulties. The singularities at crack fronts require strongly refined finite element meshes that must fit the discontinuity surfaces while keeping the aspect ratio of the elements within acceptable bounds. Fully automatic generation of meshes in complex 3-D geometries satisfying these requirements is a daunting task. Partition-of-unity methods, such as the Generalized FEM (GFEM), are promising candidates to surmount the shortcomings of the standard FEM in crack growth simulations. These methods allow the representation of discontinuities and singularities in the solution via geometrical descriptions of crack surfaces, that are independent of the volume mesh, coupled with suitable enrichment functions. As a result, volume meshes need not fit crack surfaces. This work proposes an hp-version of the GFEM (hp-GFEM) for crack growth simulations. This method provides enough flexibility to build high-order discretizations for crack growth simulations. At each crack growth step, high-order approximations on locally refined meshes are automatically created in complex 3-D domains while preserving the aspect ratio of elements, regardless of crack geometry. The hp-GFEM uses explicit surface meshes composed of triangles to represent non-planar 3-D crack surfaces. By design, the proposed methodology allows the crack surface to be arbitrarily located within the GFEM mesh. To track the crack surface evolution, the proposed methodology considers an extension of the Face Offsetting Method (FOM). Based on the hp-GFEM solution, the FOM provides geometrically feasible crack front descriptions by updating the vertex positions and checking for self-intersections of the edges. The hp-GFEM with FOM allows the simulation of arbitrary crack growth independent of the volume mesh. Numerical simulations using the hp-GFEM coupled with the FOM are corroborated by experimental data and experimental observations. As an alternative to large-scale crack growth simulations, this work combines the proposed hp-GFEM with the generalized finite element method with global-local enrichment functions (GFEMgl). The proposed method allows crack growth simulations with arbitrary path in industrial level complexity problems while keeping the global mesh unchanged. Furthermore, this method allows crack growth simulations without solving the entire problem from scratch at each crack growth step. The GFEMgl for crack growth explores solutions from previous crack growth steps, hierarchical property of the enrichment functions as well as static condensation of the global-local degrees of freedom to expedite the solution process. Numerical examples demonstrate the robustness, efficiency and accuracy of the proposed GFEMgl for crack growth simulations.

Download or read book Fundamentals of Enriched Finite Element Methods written by Alejandro M. Aragón and published by Elsevier. This book was released on 2023-11-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Enriched Finite Element Methods provides an overview of the different enriched finite element methods, detailed instruction on their use, and also looks at their real-world applications, recommending in what situations they're best implemented. It starts with a concise background on the theory required to understand the underlying functioning principles behind enriched finite element methods before outlining detailed instruction on implementation of the techniques in standard displacement-based finite element codes. The strengths and weaknesses of each are discussed, as are computer implementation details, including a standalone generalized finite element package, written in Python. The applications of the methods to a range of scenarios, including multi-phase, fracture, multiscale, and immersed boundary (fictitious domain) problems are covered, and readers can find ready-to-use code, simulation videos, and other useful resources on the companion website to the book. - Reviews various enriched finite element methods, providing pros, cons, and scenarios forbest use - Provides step-by-step instruction on implementing these methods - Covers the theory of general and enriched finite element methods

Download or read book Analysis of Three Dimensional Fracture Mechanics Problems A Non Intrusive Approach Using ABAQUS and a Generalized Finite Element Method written by Piyush Gupta and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This report shows that the so-called generalized finite element method with global-local enrichment functions (GFEM g-l ) can be implemented non-intrusively in existing closed-source FEM software as an add-on module. The GFEM g-l is based on the solution of interdependent global (structural) and local (crack) scale problems. In the approach presented here, an initial global scale problem is solved by a commercial finite element analysis software like Abaqus, local problems containing 3-D fractures are solved by an hp-adaptive GFEM software and an enriched global scale problem is solved by a combination of the FEM and GFEM solvers. The interactions between the solvers are limited to the exchange of load and solution vectors and does not require the introduction of user subroutines to existing FEM software. As a results, the user can benefit from built-in features of available commercial grade FEM software while adding the benefits of the GFEM for this class of problems. Several three-dimensional fracture mechanics problems aimed at investigating the applicability and accuracy of the proposed two-solver methodology are presented.

Download or read book Meshfree Methods for Partial Differential Equations written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

Download or read book Meshfree Methods for Partial Differential Equations VII written by Michael Griebel and published by Springer. This book was released on 2014-12-02 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meshfree methods, particle methods, and generalized finite element methods have witnessed substantial development since the mid 1990s. The growing interest in these methods is due in part to the fact that they are extremely flexible numerical tools and can be interpreted in a number of ways. For instance, meshfree methods can be viewed as a natural extension of classical finite element and finite difference methods to scattered node configurations with no fixed connectivity. Furthermore, meshfree methods offer a number of advantageous features which are especially attractive when dealing with multiscale phenomena: a priori knowledge about particular local behavior of the solution can easily be introduced in the meshfree approximation space, and coarse-scale approximations can be seamlessly refined with fine-scale information. This volume collects selected papers presented at the Seventh International Workshop on Meshfree Methods, held in Bonn, Germany in September 2013. They address various aspects of this highly dynamic research field and cover topics from applied mathematics, physics and engineering.

Download or read book Convergence Analysis of the Generalized Finite Element Method with Global local Enrichments written by Varun Gupta and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The global-local analysis procedure in the Finite Element Method is broadly used in industry for the analysis of cracks or localized stress concentrations in large, complex, three-dimensional domains. However, the limitations of this technique are well-known. The global-local FEM (GL-FEM) involves two steps: First, the solution of the given problem is computed on a coarse, global, quasi-uniform mesh, in which the cracks or other local features need not be discretized. The solution of this problem is then used as boundary conditions to solve another Finite Element problem, which is basically a local sub-domain, comprised of localized features (like cracks), extracted from the global domain.The efficacy of the so-called Generalized Finite Element Method (GFEM) in solving such multi-scale problems has been quite well proven in past few years. Therefore, combining the two approaches, going one step further from Global-Local Finite Element Analysis, and using the local solution as an enrichment function for the global problem through the Partition of Unity framework of the Generalized Finite Element Method, gives rise to the Generalized Finite Element Method with global-local enrichments (or GFEMg-l). As these classes of methods are relatively new, there are many issues which need to be addressed to make these methods robust enough for their industrial applicability in a comprehensive manner. One of the issues surrounding this GFEMg-l approach concerns the domain size of the local problem containing the complex localized features of a structural problem, and the focus of this study is to provide guidance to address this issue. This study focuses on coming up with guidelines for selecting the size of the enrichment zone for three-dimensional fracture mechanics problems. A theoretical proof and rigorous convergence studies are presented here to provide the guidelines for selecting the size of enrichment zone for practical problems. The effect of inexact boundary conditions, applied to the local problem, on the solution is also investigated.

Download or read book Development of Domain Integral and Generalized Finite Element Methods for Three Dimensional Analysis of Near surface Cracking in Flexible Pavements written by Hasan Ozer and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Layered elastic theories and finite element method are among the most familiar and practiced mechanistic approaches. These approaches succeed to a certain extent in the analysis of classical bottom-up fatigue cracking of relatively thin flexible pavements, where tensile stresses and strains govern the behavior at the asphalt layer. However, elastic theories are incapable of predicting other pavement distresses, including near-surface cracking. Similarly, finite element method, which is equipped with fracture and continuum mechanics theories, also poses a significant challenge to the analysis of the near-surface cracking problem, where crack initiation and propagation planes are not easily predictable. Hence, the main objective of this study is to identify the effect of loading tire contact stresses on developing near-surface cracking potential. A numerical approach is chosen to analyze the problem, taking into account considering nonuniform tire-pavement contact stresses and multi-axial stress states in the proximity of tires. This study highlights the impact of novel computational methods, such as the Generalized Finite Element Method (GFEM), on the discovery and understanding of cracking mechanisms in pavements. GFEM allows for realistic modeling of complex phenomena that control fracture initiation and propagation. In this study, GFEM is adapted to analyze relatively thick flexible pavement structures to predict near-surface cracking. The three-dimensional (3-D) and highly multi-axial nature of the problem is successfully captured by this method, which is ideally designed for 3-D fracture problems for complex geometries and mixed loading conditions. This study proposes a high-order domain integral method for the computation of the crack front parameters such as energy release rate and stress intensity factors (SIFs). The method provides an approximation of the energy release rate function as a linear combination of Legendre polynomials. As a result, extracted functions are smoothly varying, which is crucial to obtain accurate crack propagation paths in 3-D for elastic or inelastic materials. Crack front directionality is captured by the proposed formulations and implementation using an energy release rate-based approach. The study also applies for the first time the domain integral techniques to pavement fracture problems utilizing the asphalt concrete viscoelastic characteristics. The GFEM, equipped with the tools developed in this study, is used as a computational platform to analyze near-surface cracking in relatively thick flexible pavement structures. Three-dimensional models of typical pavement structures are developed to analyze near-surface cracking and make predictions for potential critical locations for crack initiation and growth. Two potential scenarios become evident for crack growth in the vicinity of tires: Shear crack under compression and tensile crack. It is observed from the analysis that shear crack growth is the dominant mode of crack development due to loading in the proximity of tires, while tensile crack growth appears to develop within the pavement.

Download or read book Singular Phenomena and Scaling in Mathematical Models written by Michael Griebel and published by Springer Science & Business Media. This book was released on 2013-11-18 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book integrates theoretical analysis, numerical simulation and modeling approaches for the treatment of singular phenomena. The projects covered focus on actual applied problems, and develop qualitatively new and mathematically challenging methods for various problems from the natural sciences. Ranging from stochastic and geometric analysis over nonlinear analysis and modelling to numerical analysis and scientific computation, the book is divided into the three sections: A) Scaling limits of diffusion processes and singular spaces, B) Multiple scales in mathematical models of materials science and biology and C) Numerics for multiscale models and singular phenomena. Each section addresses the key aspects of multiple scales and model hierarchies, singularities and degeneracies, and scaling laws and self-similarity.

Download or read book The Scaled Boundary Finite Element Method written by Chongmin Song and published by John Wiley & Sons. This book was released on 2018-06-19 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.

Download or read book Extended Finite Element Method for Crack Propagation written by Sylvie Pommier and published by John Wiley & Sons. This book was released on 2013-03-04 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advanced Computational Methods and Geomechanics written by Shenghong Chen and published by Springer Nature. This book was released on 2023-01-01 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is intended, through parallel expounding, to help readers comprehensively grasp the intrinsic features of typical advanced computational methods. These methods are created in recent three decades for the understanding of the post-failure of geo-materials accompanied with discontinuous and finite deformation/dislocation, as well as the violent fluid-structure interaction accompanied with strong distortion of water surface. The strong points and weak points of the formalisms for governing equations, the discretization schemes, the nodal interpolation /approximation of field variables, and their connectivity (via support domains, covers, or enrichments), the basic algorithms, etc., are clarified. Being aware of that the differences in these methods are not so large as at the first glance, this book will help readers to select appropriate methods, to improve the methods for their specific purpose, and to evaluate the reliability/applicability of the outcomes in the hazard evaluation of geotechnical (hydraulic) structures beyond extreme work situation. This book may be looked at as an advanced continuation of “Computational Geomechanics and Hydraulic Structures” by the author (2018) (Springer-Verlag, ISBN 978-981-10-8134-7) which elaborates the fundamental computational methods in geomechanics for the routine design of geotechnical (hydraulic) engineering.

Download or read book Three Dimensional Crack Analysis by Finite Element Method with Boundary Integral Method at Crack Tip written by Tae Moon Kim and published by . This book was released on 1985 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Methods for Fracture written by Timon Rabczuk and published by MDPI. This book was released on 2019-10-28 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2. Continuous approaches to fracture based on, for instance, phase field models or continuum damage mechanics. On the other hand, the book also offers a wide range of applications where state-of-the-art techniques are employed to solve challenging engineering problems such as fractures in rock, glass, concrete. Also, larger systems such as fracture in subway stations due to fire, arch dams, or concrete decks are studied.

Download or read book A Special Crack Tip Element for Three dimensional Crack Problems written by R. Jones and published by . This book was released on 1978 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a finite element method for determining the stress intensity factors along the edge of a crack in an arbitrary three-dimensional body. A special element is placed around the crack front and in each special element the stresses and displacements are derived using the asymptotic nature of the stress and displacement fields near a crack tip. The method is based on the authors' previous technique for evaluating the stress intensity factors in cracked sheets, and coincides with this method in the case of a through crack in a thin sheet. As illustrative examples the problems of a semicircular surface flaw and an internal penny shaped crack are considered. In each case the computed values of the stress intensity factors are in excellent agreement with known analytical results.

Download or read book Dynamic Fracture Mechanics written by Arun Shukla and published by World Scientific. This book was released on 2006 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering a wide variety of topics in dynamic fracture mechanics, this volume presents state-of-the-art experimental techniques and theoretical analysis on dynamic fracture in standard and exotic materials. Written by world renowned researchers, this valuable compendium contains eleven chapters on crack initiation, crack propagation, crack arrest, crack-stress wave interactions, and experimental, analytical and numerical methods in dynamic fracture mechanics. Contents: Modeling Dynamic Fracture Using Large-Scale Atomistic Simulations (H-J Gao & M J Buehler); Dynamic Crack Initiation Toughness (D Rittel); The Dynamics of Rapidly Moving Tensile Cracks in Brittle Amorphous Material (J Fineberg); Optical Methods for Dynamic Fracture Mechanics (H V Tippur); On the Use of Strain Gages in Dynamic Fracture (V Parameswaran & A Shukla); Dynamic and Crack Arrest Fracture Toughness (R E Link & R Chona); Dynamic Fracture in Graded Materials (A Shukla & N Jain); Dynamic Fracture Initiation Toughness at Elevated Temperatures with Application to the New Generation of Titanium Aluminides Alloys (M Shazly et al.); Dynamic Fracture of Nanocomposite Materials (A Shukla et al.). Readership: Researchers, practitioners, and graduate students in fracture mechanics and materials science.