A Project-Based Introduction to Computational Statics
A Project-Based Introduction to Computational Statics

Author: Andreas Öchsner

Publisher: Springer Nature

Published: 2020-11-13

Total Pages: 273

ISBN-13: 3030587711

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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.

Computational Statics and Dynamics
Computational Statics and Dynamics

Author: Andreas Öchsner

Publisher: Springer Nature

Published: 2023-02-08

Total Pages: 723

ISBN-13: 3031096738

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This book is the 3rd edition of an introduction to modern computational mechanics based on the finite element method. This third edition is largely extended, adding many new examples to let the reader understand the principles better by performing calculations by hand, as well as numerical example to practice the finite element approach to engineering problems. The new edition comes together with a set of digital flash cards with questions and answers that improve learning success. Featuring over 100 more pages, the new edition will help students succeed in mechanics courses by showing them how to apply the fundamental knowledge they gained in the first years of their engineering education to more advanced topics. In order to deepen readers’ understanding of the equations and theories discussed, each chapter also includes supplementary problems. These problems start with fundamental knowledge questions on the theory presented in the respective chapter, followed by calculation problems. In total, over 80 such calculation problems are provided, along with brief solutions for each. Test your knowledge with questions and answers about the book in the Springer Nature Flashcards app.

Introductory Statistics with R
Introductory Statistics with R

Author: Peter Dalgaard

Publisher: Springer Science & Business Media

Published: 2008-06-27

Total Pages: 370

ISBN-13: 0387790543

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This book provides an elementary-level introduction to R, targeting both non-statistician scientists in various fields and students of statistics. The main mode of presentation is via code examples with liberal commenting of the code and the output, from the computational as well as the statistical viewpoint. Brief sections introduce the statistical methods before they are used. A supplementary R package can be downloaded and contains the data sets. All examples are directly runnable and all graphics in the text are generated from the examples. The statistical methodology covered includes statistical standard distributions, one- and two-sample tests with continuous data, regression analysis, one-and two-way analysis of variance, regression analysis, analysis of tabular data, and sample size calculations. In addition, the last four chapters contain introductions to multiple linear regression analysis, linear models in general, logistic regression, and survival analysis.

Finite Elements for Truss and Frame Structures
Finite Elements for Truss and Frame Structures

Author: Andreas Öchsner

Publisher: Springer

Published: 2018-07-03

Total Pages: 129

ISBN-13: 3319949411

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This book is intended as an essential study aid for the finite element method. Based on the free computer algebra system Maxima, the authors offer routines for symbolically or numerically solving problems in the context of plane truss and frame structures, allowing readers to check classical ‘hand calculations’ on the one hand and to understand the computer implementation of the method on the other. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler–Bernoulli and Timoshenko beams, and their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework, and the resulting matrix equations can be displayed with all components and not merely in the form of a symbolic representation. In addition, the use of a computer algebra system and the incorporated functions, e.g. for equation solving, allows readers to focus more on the methodology of the finite element method and not on standard procedures.

Plane Finite Elements for Two-Dimensional Problems
Plane Finite Elements for Two-Dimensional Problems

Author: Andreas Öchsner

Publisher: Springer Nature

Published: 2022-01-01

Total Pages: 257

ISBN-13: 3030895505

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This book is intended as a study aid for the finite element method. Based on the free computer algebra system Maxima, we offer routines to symbolically or numerically solve problems from the context of two-dimensional problems. For this rather advanced topic, classical ‘hand calculations’ are difficult to perform and the incorporation of a computer algebra system is a convenient approach to handle, for example, larger matrix operations. The mechanical theories focus on the classical two-dimensional structural elements, i.e., plane elements, thin or classical plates, and thick or shear deformable plate elements. The use of a computer algebra system and the incorporated functions, e.g., for matrix operations, allows to focus more on the methodology of the finite element method and not on standard procedures. Furthermore, we offer a graphical user interface (GUI) to facilitate the model definition. Thus, the user may enter the required definitions in a source code manner directly in wxMaxima or use the GUI which is able to execute wxMaxime to perform the calculations.

Finite Elements Using Maxima
Finite Elements Using Maxima

Author: Andreas Öchsner

Publisher: Springer

Published: 2019-05-21

Total Pages: 263

ISBN-13: 303017199X

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This book provides a study aid on the finite element method. Based on the free computer algebra system “Maxima”, it presents routines to symbolically or numerically solve problems in the context of plane truss and frame structures. This allows readers to not only check classical “hand calculations” but also understand the computer implementation of the method. The mechanical theories focus on the classical one-dimensional structural elements, i.e. bars, Euler–Bernoulli and Timoshenko beams as well as their combination to generalized beam elements. Focusing on one-dimensional elements reduces the complexity of the mathematical framework and the resulting matrix equations can still be displayed with all components, and not only in a symbolic representation. The use of a computer algebra system and the incorporated functions, e.g. for equation solving, highlights the methodology of the finite element method rather than standard procedures. The book is based on the Springer Brief “Finite Elements for Truss and Frame Structures” (978-3-319-94940-6) by the same authors.

A First Introduction to the Finite Element Analysis Program MSC Marc/Mentat
A First Introduction to the Finite Element Analysis Program MSC Marc/Mentat

Author: Andreas Öchsner

Publisher: Springer

Published: 2017-11-28

Total Pages: 165

ISBN-13: 3319719157

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This book offers a brief introduction to the general-purpose finite element program MSC Marc, focusing on providing simple examples, often single-element problems, which can easily be related to the theory that is discussed in finite element lectures. As such, it is an ideal companion book to classical introductory courses on the finite element method. MSC Marc is a specialized program for non-linear problems (implicit solver), which is distributed by the MSC Software Corporation and commonly used in academia and industry. The documentation of all finite element programs now includes a variety of step-by-step examples of differing complexity, and all software companies offer professional workshops on different topics. Since the first edition of the book, there have been several new releases of Marc/Mentat and numerous changes. This new edition incorporates the latest Marc/Mentat software developments and new examples.

Mechanics of Classical Sandwich Structures
Mechanics of Classical Sandwich Structures

Author: Andreas Öchsner

Publisher: Springer Nature

Published: 2023-03-29

Total Pages: 150

ISBN-13: 3031251067

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This book treats the mechanical behavior of one-dimensional sandwich structures, a typicaloncept in the context of lightweight design. Such structures are composed of different constituent (e.g., layers) in order to achieve overall properties, which are better than for a single component alone. This book covers the basic mechanical load cases, i.e., tension/compression, bending, and shear. Based on this knowledge, different failure modes, i.e., plastic yielding, and global and local instabilities are investigated. In addition, an introduction to classic optimization problems, i.e., the formulation of an objective function (e.g., the weight of a structure) and corresponding restrictions, is included. The consideration here is limited to one- or two-dimensional design spaces, i.e., with a maximum of two design variables. For such simple cases, the minimum of the objective function can often be determined using analytical or graphical methods.

Numerical Engineering Optimization
Numerical Engineering Optimization

Author: Andreas Öchsner

Publisher: Springer Nature

Published: 2020-04-08

Total Pages: 232

ISBN-13: 3030433889

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This study aid on numerical optimization techniques is intended for university undergraduate and postgraduate mechanical engineering students. Optimization procedures are becoming more and more important for lightweight design, where weight reduction can, for example in the case of automotive or aerospace industry, lead to lower fuel consumption and a corresponding reduction in operational costs as well as beneficial effects on the environment. Based on the free computer algebra system Maxima, the authors present procedures for numerically solving problems in engineering mathematics as well as applications taken from traditional courses on the strength of materials. The mechanical theories focus on the typical one-dimensional structural elements, i.e., springs, bars, and Euler–Bernoulli beams, in order to reduce the complexity of the numerical framework and limit the resulting design to a low number of variables. The use of a computer algebra system and the incorporated functions, e.g., for derivatives or equation solving, allows a greater focus on the methodology of the optimization methods and not on standard procedures. The book also provides numerous examples, including some that can be solved using a graphical approach to help readers gain a better understanding of the computer implementation.

Composite Mechanics
Composite Mechanics

Author: Andreas Öchsner

Publisher: Springer Nature

Published: 2023-08-03

Total Pages: 214

ISBN-13: 3031323904

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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.