The book contains the basics of tensor algebra as well as a comprehensive description of tensor calculus, both in Cartesian and curvilinear coordinates. Some recent developments in representation theorems and differential forms are included. The last part of the book presents a detailed introduction to differential geometry of surfaces and curves which is based on tensor calculus. By solving numerous exercises, the reader is equipped to properly understand the theoretical background and de...

This book provides a comprehensive treatment of the virtual element method (VEM) for engineering applications, focusing on its application in solid mechanics. Starting with a continuum mechanics background, the book establishes the necessary foundation for understanding the subsequent chapters. It then delves into the VEM's Ansatz functions and projection techniques, both for solids and the Poisson equation, which are fundamental to the method. The book explores the virtual element formula...

Dieser vierte Band, Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, schließt die Lehrbuchreihe Technische Mechanik ab. Der dargestellte Stoff orientiert sich an gängigen Kursen deutschsprachiger Hochschulen und ist für Bachelor-, Master- und Diplomstudiengänge hervorragend geeignet.In der 10. Auflage wurden deutliche Ergänzungen und eine Vielzahl von Verbesserungen vorgenommen.Das Werk enthält zahlreiche durchgerechnete Beispiele, die das...

Dieser vierte Band, Hydromechanik, Elemente der Höheren Mechanik, Numerische Methoden, schließt die Lehrbuchreihe Technische Mechanik ab. Der dargestellte Stoff orientiert sich an gängigen Kursen deutschsprachiger Hochschulen und ist für Bachelor-, Master- und Diplomstudiengänge hervorragend geeignet.In der 10. Auflage wurden deutliche Ergänzungen und eine Vielzahl von Verbesserungen vorgenommen.Das Werk enthält zahlreiche durchgerechnete Beispiele, die das...

New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitu...

The book conveys modern techniques and the latest state-of-the-art with regard to the most fundamental aspects of computational contact mechanics. However, since contact can readily be interpreted as a special type of interface problem, it seems advisable not to isolate contact mechanics, but rather to address it in the context of a broader class of problems denoted as computational interface mechanics. The book gives a clear understanding of the underlying physics of interfaces, and a com...

This book provides an overview of new mathematical models, computational simulations and experimental tests in the field of biomedical technology, and covers a wide range of current research and challenges. The first part focuses on the virtual environment used to study biological systems at different scales and under multiphysics conditions. In turn, the second part is devoted to modeling and computational approaches in the field of cardiovascular medicine, e.g. simulation of turbulence i...

This book provides an overview of the experimental characterization of materials and their numerical modeling, as well as the development of new computational methods for virtual design. Its 17 contributions are divided into four main sections: experiments and virtual design, composites, fractures and fatigue, and uncertainty quantification. The first section explores new experimental methods that can be used to more accurately characterize material behavior. Furthermore, it presents a com...

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 numerica...

During the last years computational methods lead to new approaches that can be applied within medical practice. Based on the tremendous advances in medical imaging and high-performance computing, virtual testing is able to help in medical decision processes or implant designs. Current challenges in medicine and engineering are related to the application of computational methods to clinical medicine and the study of biological systems at different scales.Additionally manufacturers w...

This edited volume summarizes research being pursued within the DFG Priority Programme 1748: "Reliable Simulation Methods in Solid Mechanics. Development of non-standard discretisation methods, mechanical and mathematical analysis", the aim of which was to develop novel discretisation methods based e.g. on mixed finite element methods, isogeometric approaches as well as discontinuous Galerkin formulations, including a sound mathematical analysis for geometrically as well as physically nonl...

The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of mode...