Download or read book Enriched Finite Element Methods and Their Application written by Hao Chen and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis consists of three parts. In each part, an enrichment method is introduced and numerical examples are provided.
Download or read book Finite Element Methods and Their Applications written by Zhangxin Chen and published by Springer Science & Business Media. This book was released on 2005-10-14 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.
Download or read book Extended Finite Element Method written by Amir R. Khoei and published by John Wiley & Sons. This book was released on 2015-02-23 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
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 Enriched Finite Element Methods written by Sundararajan Natarajan and published by . This book was released on 2011 with total page 0 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 The Finite Element Method written by Zhangxin Chen and published by World Scientific. This book was released on 2011 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental and practical introduction to the finite element method, its variants, and their applications in engineering.
Download or read book Enriched Finite Element Methods written by Sundararajan Natarajan and published by . This book was released on 2010 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents advances and applications of the eXtended Finite Element Method (XFEM). The novelty of the XFEM is the enrichment of the primary variables in the elements intersected by the discontinuity surface by appropriate functions. The enrichment scheme carries the local behaviour of the problem and the main advantage is that the method does not require themesh to conform to the internal boundaries. But this flexibility comes with associated difficulties: (1) Blending problem; (2) Numerical integration of enrichment functions and (3) sub-optimal rate of convergence. This thesis addresses the difficulty in the numerical integration of the enrichment functions in the XFEM by proposing two new numerical integration schemes. The first method relies on conformal mapping, where the regions intersected by the discontinuity surface are mapped onto a unit disk. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the interior of the finite elements is transformed into boundary integration, so that no sub-division into integration cells is required. The accuracy and the efficiency of both the methods are studied numerically with problems involving strong and weak discontinuities. The XFEM is applied to study the crack inclusion interaction in a particle reinforced composite material. The influence of the crack length, the number of inclusions and the geometry of the inclusions on the crack tip stress field is numerically studied. Linear natural frequencies of cracked functionally graded material plates are studied within the framework of the XFEM. The effect of the plate aspect ratio, the crack length, the crack orientation, the gradient index and the influence of cracks is numerically studied. LATEX-ed Friday, October 14, 2011; 10:55am © Sundararajan Natarajan.
Download or read book Finite Element Method with Applications in Engineering written by Y. M. Desai and published by Pearson Education India. This book was released on 2011 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book explains the finite element method with various engineering applications to help students, teachers, engineers and researchers. It explains mathematical modeling of engineering problems and approximate methods of analysis and different approaches.
Download or read book Enriched Space time Finite Element Methods for Structural Dynamics Applications written by David N. Alpert and published by . This book was released on 2013 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate prediction of structural responses under combined, extreme environments often involves a wide range of spatial and temporal scales. In the traditional analysis of structural response problems, time dependent problems are generally solved using a semi-discrete finite element method. These methods have difficulty simulating high frequency ranges, long time durations, and capturing sharp gradients and discontinuities. Some limitations include time step constraints or a lack of convergence. The space-time finite element method based on time-discontinuous formulation extends the discretization into the temporal domain and is able to address some of these concerns. The constraints on the time-step are relaxed and the method has had some success in accurately capturing sharp gradients and discontinuities. For applications featured by multiscale responses in both space and time, the regular space-time finite element method is unable to capture the full spectrum of the response. An enriched space-time finite element method is proposed based on a coupled space-time approximation. Enrichment is introduced into the space-time framework based on the extended finite element method (XFEM). The effects of continuous enrichment functions are explored for high frequency wave propagation. Previous works are based primarily on enrichment in time. Numerical solvers are developed and benchmarked for the space-time system on high-performance platform. The method's robustness is demonstrated by convergence studies using energy error norms. Improvements are observed in terms of the convergence properties of the enriched space-time finite element method over the traditional space-time finite element method for problems with fine scale features. As a result, enrichment may be considered an alternative to mesh refinement. The numerical instability associated with the high condition number of the enriched space-time analogous stiffness matrices is studied. The factors affecting the condition numbers are explored and a Jacobi preconditioner is applied to reduce the condition numbers. Programs to model example problems are developed using Fortran. The computational expense for these programs is reduced by using advanced programming libraries utilizing GPGPU. It is concluded that the proposed formulation is robust and accurate but the high condition number of the system can pose difficulties for its implementation.
Download or read book Finite Element Methods and Their Applications written by Mahboub Baccouch and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides several applications of the finite element method (FEM) for solving real-world problems. FEM is a widely used technique for numerical simulations in many areas of physics and engineering. It has gained increased popularity over recent years for the solution of complex engineering and science problems. FEM is now a powerful and popular numerical method for solving differential equations, with flexibility in dealing with complex geometric domains and various boundary conditions. The method has a wide range of applications in various branches of engineering such as mechanical engineering, thermal and fluid flows, electromagnetics, business management, and many others. This book describes the development of FEM and discusses and illustrates its specific applications.
Download or read book Partition of Unity Methods written by Stéphane P. A. Bordas and published by John Wiley & Sons. This book was released on 2023-10-19 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: PARTITION OF UNITY METHODS Master the latest tool in computational mechanics with this brand-new resource from distinguished leaders in the field While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice. Partition of Unity Methods explores all essential topics on this key new technology, including: Coverage of the difficulties faced by the finite element method and the impetus behind the development of XFEM The basics of the finite element method, with discussions of finite element formulation of linear elasticity and the calculation of the force vector An introduction to the fundamentals of enrichment A revisitation of the partition of unity enrichment A description of the geometry of enrichment features, with discussions of level sets for stationary interfaces Application of XFEM to bio-film, gradient theories, and three dimensional crack propagation Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.
Download or read book FINITE ELEMENT METHODS written by CHENNAKESAVA R. ALAVALA and published by PHI Learning Pvt. Ltd.. This book was released on 2008-11-10 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Methods form an indispensable part of engineering analysis and design. The strength of FEM is the ease and elegance with which it handles the boundary conditions. This compact and well-organized text presents a comprehensive analysis of Finite Element Methods (FEM). The book gives a clear picture of structural, torsion, free-vibration, heat transfer and fluid flow problems. It also provides detailed description of equations of equilibrium, stress-strain relations, interpolation functions and element design, symmetry and applications of FEM. The text is a synthesis of both the physical and the mathematical characteristics of finite element methods. A question bank at the end of each chapter comprises descriptive and objective type questions to drill the students in self-study. KEY FEATURES Includes step-by-step procedure to solve typical problems using ANSYS® software. Gives numerical problems in SI units. Elaborates shaper functions for higher-order elements. Furnishes a large number of worked-out examples and solved problems. This profusely illustrated, student-friendly text is intended primarily for undergraduate students of Mechanical/Production/Civil and Aeronautical Engineering. By a judicious selection of topics, it can also be profitably used by postgraduate students of these disciplines. In addition, practising engineers and scientists should find it very useful besides students preparing for competitive exams.
Download or read book Partition of Unity Methods written by St¿phane Bordas and published by John Wiley & Sons. This book was released on 2023-10-16 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: PARTITION OF UNITY METHODS Master the latest tool in computational mechanics with this brand-new resource from distinguished leaders in the field While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice. Partition of Unity Methods explores all essential topics on this key new technology, including: Coverage of the difficulties faced by the finite element method and the impetus behind the development of XFEM The basics of the finite element method, with discussions of finite element formulation of linear elasticity and the calculation of the force vector An introduction to the fundamentals of enrichment A revisitation of the partition of unity enrichment A description of the geometry of enrichment features, with discussions of level sets for stationary interfaces Application of XFEM to bio-film, gradient theories, and three dimensional crack propagation Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.
Download or read book Introduction to Finite Element Methods written by Dieter Dinkler and published by Springer Nature. This book was released on 2023-09-28 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: The textbook at hand offers an introduction to Finite Element Methods from an engineering point of view comprising the basic principles of virtual work, derivations of displacement-based, mixed and hybrid element formulations for 1-D and 2-D membrane as well as bending structures and heat conduction. Different element geometries, including triangular elements and the isoparametric concept, and related numerical integration schemes, are presented. The element matrices and load vectors are derived in detail, the assembly at the system level is discussed with respect to fulfillment of boundary conditions and numerical efficiency. Evaluation of errors and investigations concerning the quality of the elements complete the work flow.
Download or read book Advanced Finite Element Methods and Applications written by Thomas Apel and published by Springer. This book was released on 2012-07-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.
Download or read book Enriched Numerical Techniques written by Azher Jameel and published by Elsevier. This book was released on 2024-05-09 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Enriched Numerical Techniques: Implementation and Applications explores recent advances in enriched numerical techniques, including the extended finite element method, meshfree methods, extended isogeometric analysis and coupled numerical techniques. Techniques for implementation and programming issues are discussed, with other sections discussing applications for enriched numerical techniques in solving a range of engineering problems. The level set methodologies for complex shaped irregularities is presented, as are enriched numerical methodologies for various complex and advanced problems such as Nonlinear Structural Analysis, Fracture and Fatigue in Structures, Elasto-Plastic Crack Growth, Large Deformation Analysis, Frictional Contact Problems, Thermo-Mechanical Problems, Fluid Flow Investigations, Composite Materials and Bio-mechanics. - Features explanations on how to use enriched numerical techniques to model problems in fracture mechanics, continuum mechanics, fluid flow, and biomechanics - Explains methods through the use of worked examples throughout - Provides practical advice on how to tackle programming issues
