Andreas Öchsner

This exercise book contains an extensive collection of exercises on the subject of lightweight design. In particular, the basics of strength theory, lightweight material design and molded lightweight design as well as sandwich elements are covered.

Dieses Lehrbuch stellt die unterschiedlichen Leichtbaukonzepte anhand einfacher eindimensionaler Strukturen in sehr verständlicher Weise dar und ermöglicht einen leichten Einstieg in das Thema. Es werden nachvollziehbare Informationen und Hinweise zur Werkstoffauswahl und geometrischen Gestaltung von Bauteilen gegeben. Studierende werden zudem durch eine Vielzahl an Übungsaufgaben und deren ausführlichen Lösungen unterstützt. Neben allgemeinen Korrekturen und Ergänzungen wurde die vorliegende dritte Auflage vor allem durch zusätzliche Übungsaufgaben erweitert.

This book provides a systematic introduction to composite materials, which are obtained by a layer-wise stacking of one-dimensional bar/beam elements. Each layer may have different mechanical properties, but each single layer is considered as isotropic. The major idea is to provide a simplified theory to easily understand the classical two-dimensional laminate theory for composites based on laminae with unidirectional fibers. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. Partial differential equations lay the foundation to mathematically describe the mechanical behavior of any classical structural member known in engineering mechanics, including composite materials. The so-called 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. The procedure provides the solution of a statically indeterminate system based on a generalized stress–strain relationship under consideration of the constitutive relationship and the definition of the so-called stress resultants. This laminate theory is typically provided for two-dimensional plane problems, where the basic structural element is a simple superposition of a classical plane elasticity element with a thin plate element under the consideration of an orthotropic constitutive law. This two-dimensional approach and the underlying advanced continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory, has been developed. The idea is to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understanding this simplified theory is much easier and the final step it to highlight the differences when moving to the general two-dimensional case.

This textbook presents the various lightweight design concepts using simple one-dimensional structures in a very understandable way and provides an easy introduction to the subject. It provides comprehensible information and advice on material selection and the geometric design of components. Students are also supported by a large number of exercises and their detailed solutions. It is the translation of the current third German edition.

This book covers all the standard introductory topics in classical mechanics, for the first part: Statics (the analysis of forces and moments acting on a mechanical system in equilibrium with its environment). Starting from Newton's laws, the necessary and sufficient conditions are formulated for a point/rigid/system to remain in equilibrium. The main problems that may arise in engineering practice are analyzed and numerous problems illustrate the presentation. It is well known that classical mechanics, viewed as a theoretical discipline, possesses an inherent beauty, depth and richness and presents coherence and elegance. This book tries to highlight this beauty and harmony that classical mechanics offers. The long experience of the authors means that the way of presentation is intensively tested in the decades of contact with students. The textbook is mainly addressed to advanced undergraduate and beginning graduate students who are interested in the engineering application of modern methods in classical mechanics. The authors try to use a clear and systematic style to promote a good understanding of the subject. For this part of mechanics, statics, the authors motivated and illustrated each concept, with worked examples. The book intends to provide a thorough coverage of the fundamental principles and techniques of classical mechanics. The text is based on the authors' many years of experience delivering lectures and seminars. Most of the problems are original and will be useful not only for those studying mechanics, but also for those who teach it.

This book focuses on beam and plate elements, essential components found across various fields from automotive and aerospace engineering to civil engineering structures. It offers a comparative exploration of the fundamental equations governing thin and thick beams, as well as thin and thick plates, providing readers with a clear understanding of these foundational structural elements. By explaining the three fundamental equations of continuum mechanics—equilibrium, kinematics, and constitution—the text culminates in a unified differential equation framework, offering both beginners and experienced practitioners a fresh perspective on structural member modeling.

A typical approach to treat composite materials, which are composed of layered unidirectional lamina, is the so-called classical laminate theory (CLT). This theory is based on the theory for plane elasticity elements and classical (shear-rigid) plate elements under the assumption of orthotropic constitutive equations. The solution of the fundamental equations of the classical laminate theory is connected with extensive matrix operations and many problems require in addition iteration loops.This two-dimensional approach and the underlying advanced continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory (SCLT), has been recently proposed. The idea was to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understandingthis simplified theory is much easier and the final step it to highlight the differences when moving to the general two-dimensional case.This monograph first provides a systematic and thorough introduction to the simplified laminate theory based on the theory for bars and classical beam plate elements. The focus is on stacking of isotropic layers to simplified laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. We provide a Python-based computational tool, the so-called Composite Laminate Analysis Tool (CLAT 1D) to easily solve some standard questions from the context of fiber reinforced composites. The tool runs in any standard web browser and offers a user-friendly interface with many post-processing options. The functionality comprises stress and strain analysis of simplified lamina and laminates and the failure analysis based on different criteria.

This book treats the micromechanics of laminae, i.e., the prediction of the macroscopic mechanical lamina properties based on the mechanical properties of the constituents, i.e., fibers and matrix. The focus is on unidirectional lamina which can be described based on orthotropic constitutive equations. In detail, predictions for the modulus of elasticity in and transverse to the fiber direction, the major Poisson’s ratio, as wells as the in-plane shear modulus are provided. The mechanics of materials approach, the elasticity solutions with contiguity after Tsai, and the Halpin-Tsai relationships, are presented in detail. Composite materials, especially fiber-reinforced composites, are gaining increasing importance since they can overcome the limits of many structures based on classical engineering materials. Particularly the combination of a matrix with fibers provides far better properties than the single constituents alone. A typical basic layer, the so-called lamina, can be composed of unidirectional fibers which are embedded in a matrix. In a second step, layers of laminae may be stacked under different fiber angles to a so-called laminate, which reveals—depending on the stacking sequence—different types of anisotropy/isotropy. A Python-based computational tool is provided, the so-called Micromechanics Analysis Tool (MMAT v1.0) to easily predict the elastic properties. The tool runs in any standard web browser and offers a user-friendly interface with many graphical representations of the elastic properties as a function of the fiber volume fraction.

This book provides a systematic introduction to composite materials, which are obtained by a layer-wise stacking of one-dimensional bar/beam elements. Each layer may have different mechanical properties but each single layer is considered as isotropic. The major idea is to provide a simplified theory to easier understand the classical two-dimensional laminate theory for composites based on laminae with unidirectional fibers. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. Partial differential equations lay the foundation to mathematically describe the mechanical behavior of any classical structural member known in engineering mechanics, including composite materials. The so-called 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. Theprocedure provides the solution of a statically indeterminate system based on a generalized stress–strain relationship under consideration of the constitutive relationship and the definition of the so-called stress resultants. This laminate theory is typically provided for two-dimensional plane problems, where the basic structural element is a simple superposition of a classical plane elasticity element with a thin plate element under the consideration of an orthotropic constitutive law. This two-dimensional approach and the underlying advanced continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory, has been developed. The idea is to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understanding this simplified theory is much easier and the final step it to highlight the differences when moving to the general two-dimensional case.

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.

This book first provides a systematic and thorough introduction to the classical laminate theory for composite materials 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 solution of the fundamental equations of the classical laminate theory is connected with extensive matrix operations, and many problems require in addition iteration loops. Thus, a classical hand calculation of related problems is extremely time consuming. In order to facilitate the application of the classical laminate theory, we decided to provide a Python-based computational tool, the so-called Composite Laminate Analysis Tool (CLAT) to easily solve somestandard questions from the context of fiber-reinforced composites. The tool runs in any standard web browser and offers a user-friendly interface with many post-processing options. The functionality comprises stress and strain analysis of lamina and laminates, derivation of off-axis elastic properties of lamina, and the failure analysis based on different criteria.

This book provides a comprehensive exploration of the fundamentals, experimental techniques, and simulation methodologies related to advanced engineering materials. It addresses the challenges posed by these materials, introduces the concept of stress invariants, and demonstrates their implementation in finite element programs for accurate simulations. The book serves as a valuable resource for researchers, engineers, and students interested in the cutting-edge developments in materials science and engineering.

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.

A typical approach to treat composite materials, which are composed of layered unidirectional lamina, is the so-called classical laminate theory (CLT). This theory is based on the theory for plane elasticity elements and classical (shear-rigid) plate elements under the assumption of orthotropic constitutive equations. The solution of the fundamental equations of the classical laminate theory is connected with extensive matrix operations and many problems require in addition iteration loops.This two-dimensional approach and the underlying advanced continuum mechanical modeling might be very challenging for some students, particularly at universities of applied sciences. Thus, a reduced approach, the so-called simplified classical laminate theory (SCLT), has been recently proposed. The idea was to use solely isotropic one-dimensional elements, i.e., a superposition of bar and beam elements, to introduce the major calculation steps of the classical laminate theory. Understandingthis simplified theory is much easier and the final step it to highlight the differences when moving to the general two-dimensional case.This monograph first provides a systematic and thorough introduction to the simplified laminate theory based on the theory for bars and classical beam plate elements. The focus is on stacking of isotropic layers to simplified laminates. In addition to the elastic behavior, failure is investigated based on the maximum stress, maximum strain, Tsai-Hill, and the Tsai-Wu criteria. We provide a Python-based computational tool, the so-called Composite Laminate Analysis Tool (CLAT 1D) to easily solve some standard questions from the context of fiber reinforced composites. The tool runs in any standard web browser and offers a user-friendly interface with many post-processing options. The functionality comprises stress and strain analysis of simplified lamina and laminates and the failure analysis based on different criteria.

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.

Dieses Übungsbuch beinhaltet eine umfangreiche Sammlung von Aufgaben zum Themenkomplex Leichtbau. Insbesondere werden die Grundlagen der Festigkeitslehre, Stoffleichtbau und Formleichtbau sowie Sandwichelemente behandelt. Dabei wird vor allem auf Grenzbeanspruchung und Optimierung der Strukturen eingegangen. Das Buch zeichnet sich durch detaillierte Müsterlösungen aus, sodass Studierende von Bachelor- und Masterstudiengängen die Lösungswege einfach nachvollziehen können. Das Werk ist dadurch auch für das Selbststudium bestens geeignet.

The basic idea of this introduction to the finite element method is based on the concept of explaining the complex method using only one-dimensional elements. Thus, the mathematical description remains largely simple and straightforward. The emphasis in each chapter is on explaining the method and understanding it itself. The reader learns to understand the assumptions and derivations in various physical problems in structural mechanics and to critically assess the possibilities and limitations of the finite element method.The restriction to one-dimensional elements thus enables the methodical understanding of important topics (e.g. plasticity or composite materials), which a prospective computational engineer encounters in professional practice, but which are rarely treated in this form at universities. Thus, an easy entry - also into more advanced application areas - is ensured by the concept of (a) introduction to the basics (b) exact derivation with restriction to one-dimensional elements (and in many cases also to one-dimensional problems) (c) extensive examples and advanced tasks (with short solution in the appendix).For illustration purposes, each chapter is deepened with extensively calculated and commented examples as well as with further tasks including short solutions

This monograph provides a compact introduction into the classical, i.e. rate-independent, plasticity theory. Starting from the engineering stress-strain diagram, the concept of elastic and elasto-plastic material behavior is introduced, as well as the concept of uniaxial and multiaxial stress states. Continuum mechanical modeling in the elasto-plastic range requires, in regards to the constitutive equation, in addition to the elastic law (e.g. Hooke’s law), a yield condition, a flow rule and a hardening rule. These basic equations are thoroughly introduced and explained for one-dimensional stress states. Considering three-dimensional plasticity, different sets of stress invariants to characterize the stress matrix and the decomposition of the stress matrix in its hydrostatic and deviatoric part are introduced. Furthermore, the concept of the yield condition, flow rule and hardening rule is generalized for multiaxial stress states. Some typical yield conditions are introduced and theirgraphical representation in different stress spaces is discussed in detail. The book concludes with an introduction in the elasto-plastic finite element simulation of mechanical structures. In the context of numerical approximation methods, the so-called predictor-corrector methods are used to integrate the constitutive equations. This is again introduced in detail based on one-dimensional stress states and afterwards generalized to the three-dimensional case. Test your knowledge with questions and answers about the book in the Springer Nature Flashcards app.