Partial Differential Equations Of Classical Structural Members
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Partial Differential Equations Of Classical Structural Members
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Author : Andreas Öchsner
language : en
Publisher: Springer Nature
Release Date : 2019-11-07
Partial Differential Equations Of Classical Structural Members written by Andreas Öchsner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-07 with Science categories.
The derivation and understanding of Partial Differential Equations relies heavily on the fundamental knowledge of the first years of scientific education, i.e., higher mathematics, physics, materials science, applied mechanics, design, and programming skills. Thus, it is a challenging topic for prospective engineers and scientists. This volume provides a compact overview on the classical Partial Differential Equations of structural members in mechanics. It offers a formal way to uniformly describe these equations. All derivations follow a common approach: the three fundamental equations of continuum mechanics, i.e., the kinematics equation, the constitutive equation, and the equilibrium equation, are combined to construct the partial differential equations.
Harmonic Wave Systems Partial Differential Equations Of The Helmholtz Decomposition
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Author : Victor A. Miroshnikov
language : en
Publisher: Scientific Research Publishing, Inc. USA
Release Date : 2017-12-15
Harmonic Wave Systems Partial Differential Equations Of The Helmholtz Decomposition written by Victor A. Miroshnikov and has been published by Scientific Research Publishing, Inc. USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Science categories.
Harmonic Wave Systems is the first textbook about the computational method of Decomposition in Invariant Structures (DIS) that generalizes the analytical methods of separation of variables, undetermined coefficients, asymptotic expansions, and series expansions. In recent years, there has been a boom in publications on propagation of nonlinear waves described by a fascinating list of partial differential equations (PDEs). The vast majority of wave problems are reducible to one-dimensional ones in propagation variables. However, a list of publications with two- and three-dimensional applications of the DIS method is brief. The book offers a comprehensive and rigorous treatment of the DIS method in two and three dimensions using the PDE approach to the Helmholtz decomposition that provides the most general background for mathematical modelling of harmonic waves in fluid dynamics, electrodynamics, heat transfer, and other numerous areas of science and engineering, which are dealing with propagation and interaction of N internal waves.
Advanced Topics In Computational Partial Differential Equations
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Author : Hans Petter Langtangen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-22
Advanced Topics In Computational Partial Differential Equations written by Hans Petter Langtangen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-22 with Mathematics categories.
This book is about solving partial differential equations (PDEs). Such equa tions are used to model a wide range ofphenomena in virtually all fields ofsci ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.
A Project Based Introduction To Computational Statics
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Author : Andreas Öchsner
language : en
Publisher: Springer Nature
Release Date : 2020-11-13
A Project Based Introduction To Computational Statics written by Andreas Öchsner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-13 with Science categories.
This book uses a novel concept to teach the finite element method, applying it to solid mechanics. This major conceptual shift takes away lengthy theoretical derivations in the face-to-face interactions with students and focuses on the summary of key equations and concepts; and to practice these on well-chosen example problems. For this new, 2nd edition, many examples and design modifications have been added, so that the learning-by-doing features of this book make it easier to understand the concepts and put them into practice. The theoretical derivations are provided as additional reading and students must study and review the derivations in a self-study approach. The book provides the theoretical foundations to solve a comprehensive design project in tensile testing. A classical clip-on extensometer serves as the demonstrator on which to apply the provided concepts. The major goal is to derive the calibration curve based on different approaches, i.e., analytical mechanics and based on the finite element method, and to consider further design questions such as technical drawings, manufacturing, and cost assessment. Working with two concepts, i.e., analytical and computational mechanics strengthens the vertical integration of knowledge and allows the student to compare and understand the different concepts, as well as highlighting the essential need for benchmarking any numerical result.
Structural Mechanics With A Pen
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Author : Andreas Öchsner
language : en
Publisher: Springer Nature
Release Date : 2021-02-09
Structural Mechanics With A Pen written by Andreas Öchsner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-09 with Science categories.
This book is focused on the introduction of the finite difference method based on the classical one-dimensional structural members, i.e., rods/bars and beams. It is the goal to provide a first introduction to the manifold aspects of the finite difference method and to enable the reader to get a methodical understanding of important subject areas in structural mechanics. The reader learns to understand the assumptions and derivations of different structural members. Furthermore, she/he learns to critically evaluate possibilities and limitations of the finite difference method. Additional comprehensive mathematical descriptions, which solely result from advanced illustrations for two- or three-dimensional problems, are omitted. Hence, the mathematical description largely remains simple and clear.
Advanced Partial Differential Equations
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Author : Sameer Kulkarni
language : en
Publisher: Educohack Press
Release Date : 2025-02-28
Advanced Partial Differential Equations written by Sameer Kulkarni and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-28 with Science categories.
Embark on an in-depth exploration of partial differential equations (PDEs) with "Advanced Partial Differential Equations." Our comprehensive guide provides a thorough overview of the theory, numerical methods, and practical applications of PDEs across various scientific and engineering fields. This resource is designed for both graduate-level students and professionals seeking to deepen their understanding of PDEs. We cover a wide range of topics, from classical PDEs and numerical methods to applications in physics, engineering, biology, and finance. Additionally, we delve into advanced topics such as nonlinear equations and stochastic processes, presenting each subject with rigorous mathematical treatment and clear explanations. Our guide includes detailed discussions on numerical techniques for solving PDEs, featuring finite difference, finite element, spectral, and boundary integral methods. Real-world examples and case studies illustrate the practical relevance of PDEs in disciplines like fluid dynamics, heat transfer, electromagnetics, structural mechanics, and mathematical biology. To enhance your learning experience, we offer thought-provoking exercises and problems at the end of each chapter, along with MATLAB and Python code snippets for implementing numerical algorithms. Whether you're a student, researcher, or practitioner, "Advanced Partial Differential Equations" equips you with the knowledge and tools to tackle complex problems in science and engineering.
Mechanics Of Composite Structural Elements
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Author : Holm Altenbach
language : en
Publisher: Springer
Release Date : 2018-04-10
Mechanics Of Composite Structural Elements written by Holm Altenbach and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-10 with Technology & Engineering categories.
This second edition of the textbook presents a systematic introduction to the structural mechanics of composite components. The book focusses on modeling and calculation of sandwiches and laminated composites i.e. anisotropic material. The new edition includes an additional chapter covering the latest advances in both research and applications, which are highly relevant for readers. The textbook is written for use not only in engineering curricula of aerospace, civil and mechanical engineering, but also for materials science and applied mechanics. Furthermore, it addresses practicing engineers and researchers. No prior knowledge of composite materials and structures is required for the understanding of its content. The book is close to classical courses of "Strength of Materials" and "Theory of Beams, Plates and Shells" but it extends the classic content on two topics: the linear elastic material behavior of isotropic and non-isotropic structural elements, and inhomogeneous material properties in the thickness direction. The Finite Element Analysis of laminate and sandwich structures is briefly presented. Many solved examples illustrate the application of the techniques learned.
Advanced Methods Of Structural Analysis Ii
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Author : Mr. Rohit Manglik
language : en
Publisher: EduGorilla Publication
Release Date : 2024-09-24
Advanced Methods Of Structural Analysis Ii written by Mr. Rohit Manglik and has been published by EduGorilla Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-24 with Technology & Engineering categories.
This book offers a detailed exploration of advanced methods of structural analysis - ii, focusing on key concepts, methodologies, and practical implementations relevant to modern engineering and technology practices.
Composite Mechanics
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Author : Andreas Öchsner
language : en
Publisher: Springer Nature
Release Date : 2023-08-03
Composite Mechanics written by Andreas Öchsner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-03 with Science categories.
This book in the advanced structured materials series provides first an introduction to the mircomechanics of fiber-reinforced laminae, which deals with the prediction of the macroscopic mechanical lamina properties based on the mechanical properties of the constituents, i.e., fibers and matrix. Composite materials, especially fiber-reinforced composites, are gaining increasing importance since they can overcome the limits of many structures based on classical metals. Particularly, the combination of a matrix with fibers provides far better properties than the constituents alone. Despite their importance, many engineering degree programs do not treat the mechanical behavior of this class of advanced structured materials in detail, at least on the bachelor’s degree level. Thus, some engineers are not able to thoroughly apply and introduce these modern engineering materials in their design process. The second part of this book provides a systematic and thorough introduction to the classical laminate theory based on the theory for plane elasticity elements and classical (shear-rigid) plate elements. The focus is on unidirectional lamina which can be described based on orthotropic constitutive equations and their composition to layered laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. The introduced classical laminate theory provides a simplified stress analysis, and a subsequent failure analysis, without the solution of the system of coupled differential equations for the unknown displacements in the three coordinate directions. The book concludes with a short introduction to a calculation program, the so-called Composite Laminate Analysis Tool (CLAT), which allows the application of the classical laminate based on a sophisticated Python script.
Fundamentals Of Structural Dynamics
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Author : Keith D. Hjelmstad
language : en
Publisher: Springer Nature
Release Date : 2022-01-05
Fundamentals Of Structural Dynamics written by Keith D. Hjelmstad and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-05 with Technology & Engineering categories.
This text closes the gap between traditional textbooks on structural dynamics and how structural dynamics is practiced in a world driven by commercial software, where performance-based design is increasingly important. The book emphasizes numerical methods, nonlinear response of structures, and the analysis of continuous systems (e.g., wave propagation). Fundamentals of Structural Dynamics: Theory and Computation builds the theory of structural dynamics from simple single-degree-of-freedom systems through complex nonlinear beams and frames in a consistent theoretical context supported by an extensive set of MATLAB codes that not only illustrate and support the principles, but provide powerful tools for exploration. The book is designed for students learning structural dynamics for the first time but also serves as a reference for professionals throughout their careers.