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Advanced Mechanics of Continua

Advanced Mechanics of Continua Author Karan S. Surana
ISBN-10 9781498708111
Release 2016-04-27
Pages 786
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Explore the Computational Methods and Mathematical Models That Are Possible through Continuum Mechanics Formulations Mathematically demanding, but also rigorous, precise, and written using very clear language, Advanced Mechanics of Continua provides a thorough understanding of continuum mechanics. This book explores the foundation of continuum mechanics and constitutive theories of materials using understandable notations. It does not stick to one specific form, but instead provides a mix of notations that while in many instances are different than those used in current practice, are a natural choice for the information that they represent. The book places special emphasis on both matrix and vector notations, and presents material using these notations whenever possible. The author explores the development of mathematical descriptions and constitutive theories for deforming solids, fluids, and polymeric fluids—both compressible and incompressible with clear distinction between Lagrangian and Eulerian descriptions as well as co- and contravariant bases. He also establishes the tensorial nature of strain measures and influence of rotation of frames on various measures, illustrates the physical meaning of the components of strains, presents the polar decomposition of deformation, and provides the definitions and measures of stress. Comprised of 16 chapters, this text covers: Einstein’s notation Index notations Matrix and vector notations Basic definitions and concepts Mathematical preliminaries Tensor calculus and transformations using co- and contra-variant bases Differential calculus of tensors Development of mathematical descriptions and constitutive theories Advanced Mechanics of Continua prepares graduate students for fundamental and basic research work in engineering and sciences, provides detailed and consistent derivations with clarity, and can be used for self-study.



Advances in Applied Mechanics

Advances in Applied Mechanics Author
ISBN-10 9780128051740
Release 2016-10-20
Pages 228
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Advances in Applied Mechanics draws together recent, significant advances in various topics in applied mechanics. Published since 1948, the book aims to provide authoritative review articles on topics in the mechanical sciences. While the book is ideal for scientists and engineers working in various branches of mechanics, it is also beneficial to professionals who use the results of investigations in mechanics in various applications, such as aerospace, chemical, civil, environmental, mechanical, and nuclear engineering. Includes contributions from world-leading experts that are acquired by invitation only Beneficial to scientists, engineers, and professionals who use the results of investigations in mechanics in various applications, such as aerospace, chemical, civil, environmental, mechanical, and nuclear engineering Covers not only traditional topics, but also important emerging fields



An Introduction to Computational Micromechanics

An Introduction to Computational Micromechanics Author Tarek I. Zohdi
ISBN-10 9783540323600
Release 2008-03-15
Pages 195
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In this, its second corrected printing, Zohdi and Wriggers’ illuminating text presents a comprehensive introduction to the subject. The authors include in their scope basic homogenization theory, microstructural optimization and multifield analysis of heterogeneous materials. This volume is ideal for researchers and engineers, and can be used in a first-year course for graduate students with an interest in the computational micromechanical analysis of new materials.



Multiscale Modeling of Heterogeneous Structures

Multiscale Modeling of Heterogeneous Structures Author Jurica Sorić
ISBN-10 9783319654638
Release 2017-11-30
Pages 381
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This book provides an overview of multiscale approaches and homogenization procedures as well as damage evaluation and crack initiation, and addresses recent advances in the analysis and discretization of heterogeneous materials. It also highlights the state of the art in this research area with respect to different computational methods, software development and applications to engineering structures. The first part focuses on defects in composite materials including their numerical and experimental investigations; elastic as well as elastoplastic constitutive models are considered, where the modeling has been performed at macro- and micro levels. The second part is devoted to novel computational schemes applied on different scales and discusses the validation of numerical results. The third part discusses gradient enhanced modeling, in particular quasi-brittle and ductile damage, using the gradient enhanced approach. The final part addresses thermoplasticity, solid-liquid mixtures and ferroelectric models. The contents are based on the international workshop “Multiscale Modeling of Heterogeneous Structures” (MUMO 2016), held in Dubrovnik, Croatia in September 2016.



Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics

Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics Author Kai Hormann
ISBN-10 9781498763615
Release 2017-10-30
Pages 316
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In Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, eminent computer graphics and computational mechanics researchers provide a state-of-the-art overview of generalized barycentric coordinates. Commonly used in cutting-edge applications such as mesh parametrization, image warping, mesh deformation, and finite as well as boundary element methods, the theory of barycentric coordinates is also fundamental for use in animation and in simulating the deformation of solid continua. Generalized Barycentric Coordinates is divided into three sections, with five chapters each, covering the theoretical background, as well as their use in computer graphics and computational mechanics. A vivid 16-page insert illustrates the stunning applications of this fascinating research area.



An Introduction to Continuum Mechanics

An Introduction to Continuum Mechanics Author J. N. Reddy
ISBN-10 9781107025431
Release 2013-07-29
Pages 470
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This best-selling textbook presents the concepts of continuum mechanics, and the second edition includes additional explanations, examples and exercises.



Applied Mechanics of Solids

Applied Mechanics of Solids Author Allan F. Bower
ISBN-10 1439802483
Release 2009-10-05
Pages 820
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Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based. Develop Intuitive Ability to Identify and Avoid Physically Meaningless Predictions Applied Mechanics of Solids is a powerful tool for understanding how to take advantage of these revolutionary computer advances in the field of solid mechanics. Beginning with a description of the physical and mathematical laws that govern deformation in solids, the text presents modern constitutive equations, as well as analytical and computational methods of stress analysis and fracture mechanics. It also addresses the nonlinear theory of deformable rods, membranes, plates, and shells, and solutions to important boundary and initial value problems in solid mechanics. The author uses the step-by-step manner of a blackboard lecture to explain problem solving methods, often providing the solution to a problem before its derivation is presented. This format will be useful for practicing engineers and scientists who need a quick review of some aspect of solid mechanics, as well as for instructors and students. Select and Combine Topics Using Self-Contained Modules and Subsections Borrowing from the classical literature on linear elasticity, plasticity, and structural mechanics, this book: Introduces concepts, analytical techniques, and numerical methods used to analyze deformation, stress, and failure in materials or components Discusses the use of finite element software for stress analysis Assesses simple analytical solutions to explain how to set up properly posed boundary and initial-value problems Provides an understanding of algorithms implemented in software code Complemented by the author’s website, which features problem sets and sample code for self study, this book offers a crucial overview of problem solving for solid mechanics. It will help readers make optimal use of commercial finite element programs to achieve the most accurate prediction results possible.



A First Course in Continuum Mechanics

A First Course in Continuum Mechanics Author Oscar Gonzalez
ISBN-10 9780521886802
Release 2008-01-17
Pages 394
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A concise account of classic theories of fluids and solids, for graduate and advanced undergraduate courses in continuum mechanics.



Smooth Particle Applied Mechanics

Smooth Particle Applied Mechanics Author William Graham Hoover
ISBN-10 UCSD:31822035332352
Release 2006-01-01
Pages 300
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This book takes readers through all the steps necessary for solving hard problems in continuum mechanics with smooth particle methods. Pedagogical problems clarify the generation of initial conditions, the treatment of boundary conditions, the integration of the equations of motion, and the analysis of the results. Particular attention is paid to the parallel computing necessary for large problems and to the graphic displays, including debugging software, required for the efficient completion of computational projects. The book is self-contained, with summaries of classical particle mechanics and continuum mechanics for both fluids and solids, computer languages, the stability of numerical methods, Lyapunov spectra, and message-passing parallel computing. The main difficulties faced by meshless particle methods are discussed and the means of overcoming them are illustrated with worked examples.



Computational Modeling of Polymer Composites

Computational Modeling of Polymer Composites Author Samit Roy
ISBN-10 9781466586505
Release 2013-09-05
Pages 300
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Computational Modeling of Polymer Composites: A Study of Creep and Environmental Effects details the development of polymeric materials and their use in smart materials and composite structures in aerospace and automotive industries. Based on the authors' work during the past 30 years, this book provides a strong understanding of the theories and associated finite element life-prediction models for elastic and viscoelastic response of polymers and polymer composites in aggressive environments. The subject is an interdisciplinary one where chemists, material scientists, and chemical, mechanical, and structural engineers contribute to the overall product. Books on polymer composites are usually of three types: material science, mechanics, and computational. This book combines mechanics of materials with the computational element. The authors suggest an introductory course on mechanics of materials to cover all bases. The book begins with mathematical preliminaries, equations of anisotropic elasticity, virtual work principles, and variational methods. It provides an introduction to the finite element method and finite element analysis of viscoelastic materials, and then moves on to the solvent diffusion process in polymers and polymeric composites, as well as the linear and nonlinear viscoelastic models and the implementation of finite element models of viscoelastic materials. Computational Modeling of Polymer Composites: A Study of Creep and Environmental Effects delves into both uniaxial and multiaxial cases and delayed failure before discussing the finite element analysis of the nonlinear diffusion process in polymers. It also includes non-Fickean diffusion of polymers, the coupled hygrothermal cohesive layer model for simulating debond growth in bimaterial interfaces, and the viscoelastic cohesive layer model for the prediction of interlaminar shear strength of carbon/epoxy composites. The final chapter covers a multi-scale viscoelastic cohesive layer model for predicting delamination in high temperature polymer composites. This book can be used as a reference or as a graduate course textbook on theory and/or finite element analysis of polymers and polymeric composites.



Advances in Applied Mechanics

Advances in Applied Mechanics Author Erik Van Der Giessen
ISBN-10 0120020386
Release 2001-09
Pages 372
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Mechanics is defined as a branch of physics that focuses on motion and the reaction of physical systems to internal and external forces. This highly acclaimed series provides survey articles on the present state and future direction of research in important branches of applied solid and fluid mechanics.



Nonlinear Solid Mechanics

Nonlinear Solid Mechanics Author Gerhard A. Holzapfel
ISBN-10 0471823198
Release 2000-04-07
Pages 470
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Nonlinear Solid Mechanics a Continuum Approach for Engineering Gerhard A. Holzapfel Graz University of Technology, Austria With a modern, comprehensive approach directed towards computational mechanics, this book covers a unique combination of subjects at present unavailable in any other text. It includes vital information on 'variational principles' constituting the cornerstone of the finite element method. In fact this is the only method by which Nonlinear Solid Mechanics is utilized in engineering practice. The book opens with a fundamental chapter on vectors and tensors. The following chapters are based on nonlinear continuum mechanics - an inevitable prerequisite for computational mechanicians. In addition, continuum field theory (applied to a representative sample of hyperelastic materials currently used in nonlinear computations such as incompressible and compressible materials) is presented, as are transversely isotropic materials, composite materials, viscoelastic materials and hyperelastic materials with isotropic damage. Another central chapter is devoted to the thermodynamics of materials, covering both finite thermoelasticity and finite thermoviscoelasticity. Also included are: * an up-to-date list of almost 300 references and a comprehensive index * useful examples and exercises for the student * selected topics of statistical and continuum thermodynamics. Furthermore, the principle of virtual work (in both the material and spatial descriptions) is compared with two and three-field variational principles particularly designed to capture kinematic constraints such as incompressibility. All of the features combined result in an essential text for final year undergraduates, postgraduates and researchers in mechanical, civil and aerospace engineering and applied maths and physics.



Computational Methods for Plasticity

Computational Methods for Plasticity Author Eduardo A. de Souza Neto
ISBN-10 9781119964544
Release 2011-09-21
Pages 814
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The subject of computational plasticity encapsulates the numerical methods used for the finite element simulation of the behaviour of a wide range of engineering materials considered to be plastic – i.e. those that undergo a permanent change of shape in response to an applied force. Computational Methods for Plasticity: Theory and Applications describes the theory of the associated numerical methods for the simulation of a wide range of plastic engineering materials; from the simplest infinitesimal plasticity theory to more complex damage mechanics and finite strain crystal plasticity models. It is split into three parts - basic concepts, small strains and large strains. Beginning with elementary theory and progressing to advanced, complex theory and computer implementation, it is suitable for use at both introductory and advanced levels. The book: Offers a self-contained text that allows the reader to learn computational plasticity theory and its implementation from one volume. Includes many numerical examples that illustrate the application of the methodologies described. Provides introductory material on related disciplines and procedures such as tensor analysis, continuum mechanics and finite elements for non-linear solid mechanics. Is accompanied by purpose-developed finite element software that illustrates many of the techniques discussed in the text, downloadable from the book’s companion website. This comprehensive text will appeal to postgraduate and graduate students of civil, mechanical, aerospace and materials engineering as well as applied mathematics and courses with computational mechanics components. It will also be of interest to research engineers, scientists and software developers working in the field of computational solid mechanics.



The Mechanics and Thermodynamics of Continua

The Mechanics and Thermodynamics of Continua Author Morton E. Gurtin
ISBN-10 9781139482158
Release 2010-04-19
Pages
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The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.



Extended Finite Element Method

Extended Finite Element Method Author Amir R. Khoei
ISBN-10 9781118457689
Release 2015-02-23
Pages 584
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Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Extended Finite Element Method: Theory and Applications introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics. The XFEM approach is based on an extension of standard finite element method based on the partition of unity method. Extended Finite Element Method: Theory and Applications begins by introducing the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. It then covers the theory and application of XFEM in large deformations, plasticity and contact problems. The implementation of XFEM in fracture mechanics, including the linear, cohesive, and ductile crack propagation is also covered. The theory and applications of the XFEM in multiphase fluid flow, including the hydraulic fracturing in soil saturated media and crack propagation in thermo-hydro-mechanical porous media, is also discussed in detail. Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples



IUTAM IACM IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method

IUTAM IACM IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method Author Tadeusz Burczynski
ISBN-10 9789401597937
Release 2013-03-14
Pages 428
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During the last two decades the boundary element method has experienced a remarkable evolution. Contemporary concepts and techniques leading to the advancements of capabilities and understanding of the mathematical and computational aspects of the method in mechanics are presented. The special emphasis on theoretical and numerical issues, as well as new formulations and approaches for special and important fields of solid and fluid mechanics are considered. Several important and new mathematical aspects are presented: singularity and hypersingular formulations, regularity, errors and error estimators, adaptive methods, Galerkin formulations, coupling of BEM-FEM and non-deterministic (stochastic and fuzzy) BEM formulations. Novel developments and applications of the boundary element method in various fields of mechanics of solids and fluids are considered: heat conduction, diffusion and radiation, non-linear problems, dynamics and time-depending problems, fracture mechanics, thermoelasticity and poroelasticity, aerodynamics and acoustics, contact problems, biomechanics, optimization and sensitivity analysis problems, ill posed and inverse problems, and identification problems.



The Finite Element Method for Boundary Value Problems

The Finite Element Method for Boundary Value Problems Author Karan S. Surana
ISBN-10 9781498780513
Release 2016-11-17
Pages 824
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Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as self-adjoint, non-self-adjoint, and non-linear, thus addressing totality of all BVPs in various areas of engineering, applied mathematics, and physical sciences. These classes of operators are utilized in various methods of approximation: Galerkin method, Petrov-Galerkin Method, weighted residual method, Galerkin method with weak form, least squares method based on residual functional, etc. to establish unconditionally stable finite element computational processes using calculus of variations. Readers are able to grasp the mathematical foundation of finite element method as well as its versatility of applications. h-, p-, and k-versions of finite element method, hierarchical approximations, convergence, error estimation, error computation, and adaptivity are additional significant aspects of this book.