The Finite Element Method

The Finite Element Method
  • Author : Thomas J. R. Hughes
  • Publisher : Courier Corporation
  • Pages : 704
  • Relase : 2012-05-23
  • ISBN : 9780486135021

The Finite Element Method Book Review:

Designed for students without in-depth mathematical training, this text includes a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories. Solution guide available upon request.

The Finite Element Method in the Deformation and Consolidation of Porous Media

The Finite Element Method in the Deformation and Consolidation of Porous Media
  • Author : Roland Wynne Lewis,B. A. Schrefler
  • Publisher : John Wiley & Sons
  • Pages : 344
  • Relase : 1987
  • ISBN : UOM:39015012451665

The Finite Element Method in the Deformation and Consolidation of Porous Media Book Review:

Finite Elements in Structural Analysis

Finite Elements in Structural Analysis
  • Author : Horst Werkle
  • Publisher : Springer Nature
  • Pages : 709
  • Relase : 2021-05-27
  • ISBN : 9783030498405

Finite Elements in Structural Analysis Book Review:

The book introduces the basic concepts of the finite element method in the static and dynamic analysis of beam, plate, shell and solid structures, discussing how the method works, the characteristics of a finite element approximation and how to avoid the pitfalls of finite element modeling. Presenting the finite element theory as simply as possible, the book allows readers to gain the knowledge required when applying powerful FEA software tools. Further, it describes modeling procedures, especially for reinforced concrete structures, as well as structural dynamics methods, with a particular focus on the seismic analysis of buildings, and explores the modeling of dynamic systems. Featuring numerous illustrative examples, the book allows readers to easily grasp the fundamentals of the finite element theory and to apply the finite element method proficiently.

The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media

The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media
  • Author : Roland Wynne Lewis,Roland W. Lewis,B. A. Schrefler
  • Publisher : John Wiley & Sons
  • Pages : 492
  • Relase : 1998
  • ISBN : STANFORD:36105023417954

The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media Book Review:

The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media Second Edition Roland W. Lewis, University of Wales Swansea, UK Bernard A. Schrefler, University of Padua, Italy Following the highly successful first edition, this text deals with numerical solutions of coupled thermo-hydro-mechanical problems in porous media. Governing equations are newly derived in a general form using both averaging methods (hybrid mixture theory) and an engineering approach. Unique new features of the book include numerical solutions for fully and partially saturated consolidation, subsidence analysis including far field boundary conditions (Infinite Elements), new case studies and also petroleum reservoir simulation. Extended heat and mass transfer in partially saturated porous media, and consideration of phase change, are covered in detail. In addition, large strain, fully and partially saturated, soil dynamics problems are explained. Back analysis for consolidation problems is also included. Significantly, the reader is provided with access to a Finite Element code for coupled thermo-hydro-mechanical problems in partially saturated porous media with full two phase flow and phase change, written according to the theory outlined in the book and obtainable via the Network of the Italian Research Council (COMES). With a range of engineering applications from geotechnical and petroleum engineering through to bioengineering and materials science, this book represents an important resource for students, researchers and practising engineers in all these and related fields.

Finite-Element Modelling of Structural Concrete

Finite-Element Modelling of Structural Concrete
  • Author : Michael D. Kotsovos
  • Publisher : CRC Press
  • Pages : 381
  • Relase : 2015-05-20
  • ISBN : 9781498712316

Finite-Element Modelling of Structural Concrete Book Review:

A Powerful Tool for the Analysis and Design of Complex Structural Elements Finite-Element Modelling of Structural Concrete: Short-Term Static and Dynamic Loading Conditions presents a finite-element model of structural concrete under short-term loading, covering the whole range of short-term loading conditions, from static (monotonic and cyclic) to dynamic (seismic and impact) cases. Experimental data on the behavior of concrete at both the material and structural levels reveal the unavoidable development of triaxial stress conditions prior to failure which dictate the collapse and ductility of structural concrete members. Moreover, and in contrast with generally accepted tenets, it can be shown that the post-peak behavior of concrete as a material is realistically described by a complete and immediate loss of load-carrying capacity. Hence rational analysis and design of concrete components in accordance with the currently prevailing limit-state philosophy requires the use of triaxial material data consistent with the notion of a fully brittle material, and this approach is implemented in the book by outlining a finite-element method for the prediction of the strength, deformation, and cracking patterns of arbitrary structural concrete forms. Presents a Unified Approach to Structural Modeling Numerous examples are given that show both the unifying generality of this proposed approach and the reliability of the ensuing numerical procedure for which the sole input is the specified uniaxial cylinder compressive strength of concrete and the yield stress of the steel. This not only offers a better understanding of the phenomenology of structural concrete behavior but also illustrates, by means of suitable examples, the type of revision required for improving design methods in terms of both safety and economy. This book: Highlights the significance of valid experimental information on the behavior of concrete under triaxial stress conditions for interpreting structural behavior Describes the techniques used for obtaining valid test data and modeling concrete behavior Discusses the modeling of steel properties as well as the interaction between concrete and steel Presents numerical techniques for incorporating the material models into nonlinear finite-element analysis for the case of short-term static loading Provides numerical techniques adopted for extending the use of the numerical analysis scheme for the solution of dynamic problems Predicts the response of a wide range of structural-concrete configurations to seismic and impact excitations Using relevant case studies throughout, Finite-Element Modelling of Structural Concrete: Short-Term Static and Dynamic Loading Conditions focuses on the realistic modeling of structural concrete on the basis of existing and reliable material data and aids in the research and study of structural concrete and concrete materials.

Structural Dynamics

Structural Dynamics
  • Author : Mario Paz
  • Publisher : Springer Science & Business Media
  • Pages : 650
  • Relase : 2012-12-06
  • ISBN : 9781468400182

Structural Dynamics Book Review:

The use of COSMOS for the analysis and solution of structural dynamics problems is introduced in this new edition. The COSMOS program was selected from among the various professional programs available because it has the capability of solving complex problems in structures, as well as in other engin eering fields such as Heat Transfer, Fluid Flow, and Electromagnetic Phenom ena. COSMOS includes routines for Structural Analysis, Static, or Dynamics with linear or nonlinear behavior (material nonlinearity or large displacements), and can be used most efficiently in the microcomputer. The larger version of COSMOS has the capacity for the analysis of structures modeled up to 64,000 nodes. This fourth edition uses an introductory version that has a capability limited to 50 nodes or 50 elements. This version is included in the supplement, STRUCTURAL DYNAMICS USING COSMOS 1. The sets of educational programs in Structural Dynamics and Earthquake Engineering that accompanied the third edition have now been extended and updated. These sets include programs to determine the response in the time or frequency domain using the FFf (Fast Fourier Transform) of structures modeled as a single oscillator. Also included is a program to determine the response of an inelastic system with elastoplastic behavior and a program for the development of seismic response spectral charts. A set of seven computer programs is included for modeling structures as two-dimensional and three dimensional frames and trusses.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Numerical Solution of Partial Differential Equations by the Finite Element Method
  • Author : Claes Johnson
  • Publisher : Courier Corporation
  • Pages : 288
  • Relase : 2012-05-23
  • ISBN : 9780486131597

Numerical Solution of Partial Differential Equations by the Finite Element Method Book Review:

An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Engineering Computation of Structures: The Finite Element Method

Engineering Computation of Structures: The Finite Element Method
  • Author : Maria Augusta Neto,Ana Amaro,Luis Roseiro,José Cirne,Rogério Leal
  • Publisher : Springer
  • Pages : 314
  • Relase : 2015-09-29
  • ISBN : 9783319177106

Engineering Computation of Structures: The Finite Element Method Book Review:

This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It uses straightforward examples to demonstrate a complete and detailed finite element procedure, emphasizing the differences between exact and numerical procedures.

Nonlinear Solid Mechanics for Finite Element Analysis: Dynamics

Nonlinear Solid Mechanics for Finite Element Analysis: Dynamics
  • Author : Javier Bonet,Antonio J. Gil,Richard D. Wood
  • Publisher : Cambridge University Press
  • Pages : 348
  • Relase : 2021-03-18
  • ISBN : 9781107115620

Nonlinear Solid Mechanics for Finite Element Analysis: Dynamics Book Review:

The perfect introduction to the theory and computer programming for the dynamic simulation of nonlinear solid mechanics.

Static and Dynamic Analysis of Engineering Structures

Static and Dynamic Analysis of Engineering Structures
  • Author : Levon G. Petrosian,Vladimir A. Ambartsumian
  • Publisher : John Wiley & Sons
  • Pages : 528
  • Relase : 2020-05-11
  • ISBN : 9781119592839

Static and Dynamic Analysis of Engineering Structures Book Review:

An authoritative guide to the theory and practice of static and dynamic structures analysis Static and Dynamic Analysis of Engineering Structures examines static and dynamic analysis of engineering structures for methodological and practical purposes. In one volume, the authors – noted engineering experts – provide an overview of the topic and review the applications of modern as well as classic methods of calculation of various structure mechanics problems. They clearly show the analytical and mechanical relationships between classical and modern methods of solving boundary value problems. The first chapter offers solutions to problems using traditional techniques followed by the introduction of the boundary element methods. The book discusses various discrete and continuous systems of analysis. In addition, it offers solutions for more complex systems, such as elastic waves in inhomogeneous media, frequency-dependent damping and membranes of arbitrary shape, among others. Static and Dynamic Analysis of Engineering Structures is filled with illustrative examples to aid in comprehension of the presented material. The book: Illustrates the modern methods of static and dynamic analysis of structures; Provides methods for solving boundary value problems of structural mechanics and soil mechanics; Offers a wide spectrum of applications of modern techniques and methods of calculation of static, dynamic and seismic problems of engineering design; Presents a new foundation model. Written for researchers, design engineers and specialists in the field of structural mechanics, Static and Dynamic Analysis of Engineering Structures provides a guide to analyzing static and dynamic structures, using traditional and advanced approaches with real-world, practical examples.

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
  • Author : Shen R. Wu,Lei Gu
  • Publisher : John Wiley & Sons
  • Pages : 352
  • Relase : 2012-07-30
  • ISBN : 9781118382073

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics Book Review:

A systematic introduction to the theories and formulations ofthe explicit finite element method As numerical technology continues to grow and evolve withindustrial applications, understanding the explicit finite elementmethod has become increasingly important, particularly in the areasof crashworthiness, metal forming, and impact engineering.Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is the first book to addressspecifically what is now accepted as the most successful numericaltool for nonlinear transient dynamics. The book aids readers inmastering the explicit finite element method and programming codewithout requiring extensive background knowledge of the generalfinite element. The authors present topics relating to the variationalprinciple, numerical procedure, mechanical formulation, andfundamental achievements of the convergence theory. In addition,key topics and techniques are provided in four clearly organizedsections: • Fundamentals explores a framework of the explicitfinite element method for nonlinear transient dynamics andhighlights achievements related to the convergence theory • Element Technology discusses four-node,three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity andother nonlinear materials as well as the mechanics model of ductiledamage • Contact and Constraint Conditions covers subjectsrelated to three-dimensional surface contact, with examples solvedanalytically, as well as discussions on kinematic constraintconditions Throughout the book, vivid figures illustrate the ideas and keyfeatures of the explicit finite element method. Examples clearlypresent results, featuring both theoretical assessments andindustrial applications. Introduction to the Explicit Finite Element Method forNonlinear Transient Dynamics is an ideal book for bothengineers who require more theoretical discussions and fortheoreticians searching for interesting and challenging researchtopics. The book also serves as an excellent resource for courseson applied mathematics, applied mechanics, and numerical methods atthe graduate level.

The Finite Element Method in Heat Transfer and Fluid Dynamics, Second Edition

The Finite Element Method in Heat Transfer and Fluid Dynamics, Second Edition
  • Author : J. N. Reddy,D.K. Gartling
  • Publisher : CRC Press
  • Pages : 469
  • Relase : 2000-12-20
  • ISBN : 084932355X

The Finite Element Method in Heat Transfer and Fluid Dynamics, Second Edition Book Review:

The numerical simulation of fluid mechanics and heat transfer problems is now a standard part of engineering practice. The widespread availability of capable computing hardware has led to an increased demand for computer simulations of products and processes during their engineering design and manufacturing phases. The range of fluid mechanics and heat transfer applications of finite element analysis has become quite remarkable, with complex, realistic simulations being carried out on a routine basis. The award-winning first edition of The Finite Element Method in Heat Transfer and Fluid Dynamics brought this powerful methodology to those interested in applying it to the significant class of problems dealing with heat conduction, incompressible viscous flows, and convection heat transfer. The Second Edition of this bestselling text continues to provide the academic community and industry with up-to-date, authoritative information on the use of the finite element method in the study of fluid mechanics and heat transfer. Extensively revised and thoroughly updated, new and expanded material includes discussions on difficult boundary conditions, contact and bulk nodes, change of phase, weighted-integral statements and weak forms, chemically reactive systems, stabilized methods, free surface problems, and much more. The Finite Element Method in Heat Transfer and Fluid Dynamics offers students a pragmatic treatment that views numerical computation as a means to an end and does not dwell on theory or proof. Mastering its contents brings a firm understanding of the basic methodology, competence in using existing simulation software, and the ability to develop some simpler, special purpose computer codes.

The Finite Element Method: Its Basis and Fundamentals

The Finite Element Method: Its Basis and Fundamentals
  • Author : Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu
  • Publisher : Elsevier
  • Pages : 752
  • Relase : 2005-05-26
  • ISBN : 008047277X

The Finite Element Method: Its Basis and Fundamentals Book Review:

The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. The classic introduction to the finite element method, by two of the subject's leading authors Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text

Dynamic and Static Problems Using Finite Element Method

Dynamic and Static Problems Using Finite Element Method
  • Author : Douadji Lyes,Du WeiWei,Shi MingQuan
  • Publisher :
  • Pages : 80
  • Relase : 2017-09-10
  • ISBN : 3330353244

Dynamic and Static Problems Using Finite Element Method Book Review:

The Finite Element Method in Heat Transfer and Fluid Dynamics

The Finite Element Method in Heat Transfer and Fluid Dynamics
  • Author : J. N. Reddy,D.K. Gartling
  • Publisher : CRC Press
  • Pages : 524
  • Relase : 2010-04-06
  • ISBN : 9781439882573

The Finite Element Method in Heat Transfer and Fluid Dynamics Book Review:

As Computational Fluid Dynamics (CFD) and Computational Heat Transfer (CHT) evolve and become increasingly important in standard engineering design and analysis practice, users require a solid understanding of mechanics and numerical methods to make optimal use of available software. The Finite Element Method in Heat Transfer and Fluid Dynamics, Th

Computational Techniques of Rotor Dynamics with the Finite Element Method

Computational Techniques of Rotor Dynamics with the Finite Element Method
  • Author : Arne Vollan,Louis Komzsik
  • Publisher : CRC Press
  • Pages : 296
  • Relase : 2012-03-13
  • ISBN : 9781439847701

Computational Techniques of Rotor Dynamics with the Finite Element Method Book Review:

For more than a century, we have had a firm grasp on rotor dynamics involving rigid bodies with regular shapes, such as cylinders and shafts. However, to achieve an equally solid understanding of the rotational behavior of flexible bodies—especially those with irregular shapes, such as propeller and turbine blades—we require more modern tools and methods. Computational Techniques of Rotor Dynamics with the Finite Element Method explores the application of practical finite element method (FEM)-based computational techniques and state-of-the-art engineering software. These are used to simulate behavior of rotational structures that enable the function of various types of machinery—from generators and wind turbines to airplane engines and propellers. The book’s first section focuses on the theoretical foundation of rotor dynamics, and the second concentrates on the engineering analysis of rotating structures. The authors explain techniques used in the modeling and computation of the forces involved in the rotational phenomenon. They then demonstrate how to interpret and apply the results to improve fidelity and performance. Coverage includes: Use of FEM to achieve the most accurate computational simulation of all gyroscopic forces occurring in rotational structures Details of highly efficient and accurate computational and numerical techniques for dynamic simulations Interpretation of computational results, which is instrumental to developing stable rotating machinery Practical application examples of rotational structures’ dynamic response to external and internal excitations An FEM case study that illustrates the computational complexities associated with modeling and computation of forces of rotor dynamics Assessment of propellers and turbines that are critical to the transportation and energy industries Useful to practicing engineers and graduate-level students alike, this self-contained volume also serves as an invaluable reference for researchers and instructors in this field. CRC Press Authors Speak Louis Komzsik introduces you to two books that share a common mathematical foundation, the finite element analysis technique. Watch the video.

The Scaled Boundary Finite Element Method

The Scaled Boundary Finite Element Method
  • Author : Chongmin Song
  • Publisher : John Wiley & Sons
  • Pages : 504
  • Relase : 2018-06-19
  • ISBN : 9781119388456

The Scaled Boundary Finite Element Method Book Review:

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.

Numerical Methods in Mechanics of Materials, 3rd ed

Numerical Methods in Mechanics of Materials, 3rd ed
  • Author : Ken P. Chong,Arthur P. Boresi,Sunil Saigal,James D. Lee
  • Publisher : CRC Press
  • Pages : 318
  • Relase : 2017-11-27
  • ISBN : 9781351380980

Numerical Methods in Mechanics of Materials, 3rd ed Book Review:

In the dynamic digital age, the widespread use of computers has transformed engineering and science. A realistic and successful solution of an engineering problem usually begins with an accurate physical model of the problem and a proper understanding of the assumptions employed. With computers and appropriate software we can model and analyze complex physical systems and problems. However, efficient and accurate use of numerical results obtained from computer programs requires considerable background and advanced working knowledge to avoid blunders and the blind acceptance of computer results. This book provides the background and knowledge necessary to avoid these pitfalls, especially the most commonly used numerical methods employed in the solution of physical problems. It offers an in-depth presentation of the numerical methods for scales from nano to macro in nine self-contained chapters with extensive problems and up-to-date references, covering: Trends and new developments in simulation and computation Weighted residuals methods Finite difference methods Finite element methods Finite strip/layer/prism methods Boundary element methods Meshless methods Molecular dynamics Multiphysics problems Multiscale methods

An Introduction to the Mathematical Theory of Finite Elements

An Introduction to the Mathematical Theory of Finite Elements
  • Author : J. T. Oden,J. N. Reddy
  • Publisher : Courier Corporation
  • Pages : 448
  • Relase : 2012-05-23
  • ISBN : 9780486142210

An Introduction to the Mathematical Theory of Finite Elements Book Review:

This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.

Structural Dynamics

Structural Dynamics
  • Author : Einar N. Strømmen
  • Publisher : Springer Science & Business Media
  • Pages : 510
  • Relase : 2013-09-25
  • ISBN : 9783319018027

Structural Dynamics Book Review:

This book introduces to the theory of structural dynamics, with focus on civil engineering structures that may be described by line-like beam or beam-column type of systems, or by a system of rectangular plates. Throughout this book the mathematical presentation contains a classical analytical description as well as a description in a discrete finite element format, covering the mathematical development from basic assumptions to the final equations ready for practical dynamic response predictions. Solutions are presented in time domain as well as in frequency domain. Structural Dynamics starts off at a basic level and step by step brings the reader up to a level where the necessary safety considerations to wind or horizontal ground motion induced dynamic design problems can be performed. The special theory of the tuned mass damper has been given a comprehensive treatment, as this is a theory not fully covered elsewhere. For the same reason a chapter on the problem of moving loads on beams has been included.