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

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 Numerical Methods in Contact Mechanics written by Vladislav A. Yastrebov and published by John Wiley & Sons. This book was released on 2013-02-13 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided. Contents: 1. Introduction to Computational Contact. 2. Geometry in Contact Mechanics. 3. Contact Detection. 4. Formulation of Contact Problems. 5. Numerical Procedures. 6. Numerical Examples. About the Authors Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricité de France.

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 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 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 The Proper Generalized Decomposition for Advanced Numerical Simulations written by Francisco Chinesta and published by Springer Science & Business Media. This book was released on 2013-10-08 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method. Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab© software used to generate these examples.

Download or read book Numerical Analysis of Wavelet Methods written by A. Cohen and published by Elsevier. This book was released on 2003-04-29 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are:1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions.2. Full treatment of the theoretical foundations that are crucial for the analysisof wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory.3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.

Download or read book Multiscale Modeling of Nonlinear Composite Materials Using Interface enriched Generalized Finite Element Method and Eigendeformation based Reduced Order Homogenization Models written by Min Lin and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composites have undergone significant growth in recent decades, primarily due to their exceptional strength-to-weight ratio. However, modeling the mechanical behavior of composites with complex microstructures still remains a great challenge. One approach to address this challenge is to utilize direct numerical modeling, which accounts for the intricate microscale details and nonlinear constitutive laws, and leverage advanced numerical techniques, such as the Interface-enriched Generalized Finite Element Method (IGFEM). Nevertheless, the high computational cost associated with this method often becomes a limiting factor. Reduced Order Modeling (ROM) has emerged as a technique to mitigate the computational cost by building upon the Eigendeformation-based reduced-order homogenization model (EHM). This approach significantly reduces the computational cost associated with the microscale problem by developing a reduced-order representation of the full field microscale problem, allowing flexible control of the model order to balance the accuracy and efficiency. This research advances EHM from multiple fronts. Inspired by the adaptive mesh refinement in the finite element method, both uniform and non-uniform adaptive ROMs have been developed. The idea is to start the modeling of microstructure with a coarse ROM, and gradually switch to a finer ROM when localized response starts. The adaptive ROM approach enhances the modeling of composite materials by providing greater flexibility in controlling the order of ROM to balance the computational cost and efficiency. We further developed a load-dependent ROM, which accounts for known characteristics of the loading the microstructure is going to experience, and construct the ROM accordingly. Numerical examples indicate that by incorporating load-dependent information into the EHM, more accurate stress-strain responses can be obtained. Additionally, we adopt the Physics-Informed Neural Network (PINN) to assist the pre-processing in EHM, where linear elastic analysis of the microstructure is needed for solving the so-called influence function problems. PINN could potentially utilize the similarities between a large number of microstructures generated from the same statistical distribution, providing a paradigm for efficient evaluation of the response envelops of statistical microstructures when used with EHM.

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 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 Guidelines for the Use of Advanced Numerical Analysis written by David Potts and published by Thomas Telford. This book was released on 2002 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is not easy for engineers to gain all the skills necessary to perform numerical analysis. This book is an authoritative guide that explains in detail the potential restrictions and pitfalls and so help engineers undertake advanced numerical analysis. It discusses the major approximations involved in nonlinear numerical analysis and describes some of the more popular constituitive models currently available and explores their strengths and weaknesses. It also discusses the determination of material parameters for defining soil behaviour, investigates the options for modelling structural components and their interface with the soil and the boundary conditions that are appropriate in geotechnical analysis and the assumptions implied when they are used. Guidelines for the use of Advanced Numerical Analysis also provides guidelines for best practice of specific types of soil-structure interaction that are common in urban development and discusses the role of benchmarking exercises. This authoritative book will be invaluable to practising engineers involved in urban development. It will also be useful tool for geotechnical and structural engineers.

Download or read book Progress on Meshless Methods written by A. J. M. Ferreira and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues. The book collects extended original contributions presented at the Second ECCOMAS Conference on Meshless Methods held in 2007 in Porto. The list of contributors reveals a fortunate mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different meshless approximation methods and their range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

Download or read book Extended Finite Element Method written by Soheil Mohammadi and published by John Wiley & Sons. This book was released on 2008-04-30 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications. One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been extended to nonlinear materials and other disciplines such as modelling contact and interface, simulation of inclusions and holes, moving and changing phase problems, and even to multiscale analyses. The book is self contained, with summaries of both classical and modern computational techniques. The main chapters include a comprehensive range of numerical examples describing various features of XFEM.

Download or read book Issues in Computation 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 1318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Computation / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computation. The editors have built Issues in Computation: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computation in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book IUTAM Symposium on Discretization Methods for Evolving Discontinuities written by Alain Combescure and published by Springer Science & Business Media. This book was released on 2010-04-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, discretization methods have been proposed which are more flexible and which have the potential of capturing (moving) discontinuities in a robust and efficient manner. This monograph assembles contributions of leading experts with the most recent developments in this rapidly evolving field. It provides the most comprehensive coverage of state-of-the art numerical methods for treating discontinuities in mechanics.