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Proposed in the early 1990s, the enhanced assumed strain (EAS) method is one of the probably most successful mixed finite element methods for solid mechanics. This cumulative dissertation gives a comprehensive overview of previous publications on that method and covers recent improvements for EAS elements. In particular, we describe three key issues of standard EAS elements and develop corresponding solutions.
This work is about the inverse dynamics of underactuated flexible mechanical systems governed by quasi-linear hyperbolic partial differential equations subjected to time-varying Dirichlet boundary conditions that are enforced by unknown, spatially disjunct, hence non-collocated Neumann boundary conditions.
PARTITION OF UNITY METHODS Master the latest tool in computational mechanics with this brand-new resource from distinguished leaders in the field While it is the number one tool for computer aided design and engineering, the finite element method (FEM) has difficulties with discontinuities, singularities, and moving boundaries. Partition of unity methods addresses these challenges and is now increasingly implemented in commercially available software. Partition of Unity Methods delivers a detailed overview of its fundamentals, in particular the extended finite element method for applications in solving moving boundary problems. The distinguished academics and authors introduce the XFEM as a natural extension of the traditional finite element method (FEM), through straightforward one-dimensional examples which form the basis for the subsequent introduction of higher dimensional problems. This book allows readers to fully understand and utilize XFEM just as it becomes ever more crucial to industry practice. Partition of Unity Methods explores all essential topics on this key new technology, including: Coverage of the difficulties faced by the finite element method and the impetus behind the development of XFEM The basics of the finite element method, with discussions of finite element formulation of linear elasticity and the calculation of the force vector An introduction to the fundamentals of enrichment A revisitation of the partition of unity enrichment A description of the geometry of enrichment features, with discussions of level sets for stationary interfaces Application of XFEM to bio-film, gradient theories, and three dimensional crack propagation Perfect for researchers and postdoctoral candidates working in the field of computational mechanics, Partition of Unity Methods also has a place in the libraries of senior undergraduate and graduate students working in the field. Finite element and CFD analysts and developers in private industry will also greatly benefit from this book.
This book examines optimization problems that in practice involve random model parameters. It details the computation of robust optimal solutions, i.e., optimal solutions that are insensitive with respect to random parameter variations, where appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the probabilities and expectations involved, the book also shows how to apply approximative solution techniques. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures and differentiation formulas for probabilities and expectations. In the third edition, this book further develops stochastic optimization methods. In particular, it now shows how to apply stochastic optimization methods to the approximate solution of important concrete problems arising in engineering, economics and operations research.
The book in hand grew out of the authors' current research and their long-continued experience in teaching mathematics and mechanics. In a wide sense, it aims at mathematical modeling of mechanical objects and their exploitation. This is done in a bit unconventional way by concentrating on the special object class worm-like locomotion systems and in proceeding with no use of recent sophisticated mathematical tools which most likely cannot be handled by freshmen in engineering or mathematics. Nevertheless, this does not harm the stringent line the physical object to the analytical interpretation of the final mathematical model. The basic model spiked worm in a straight line enables the authors to come up with a fairly self-contained theory which then allows one to study effects of friction and control. The considered system class has its importance in practice (motion in narrow canals, e.g.), but this book is not with an orientation to design and application, the theory developed here should rather be seen as a contribution to bionics.
A first Symposium on Dynamics of Multibody Systems was held August 29 September 3, 1977, under the chairmanship of - Prof. Dr. K. Magnus in Munich, FRG. Since that -time considerable progress has been made in the dynamics of multibody systems, a discipline renderin~ essential services to the fields of robotics, biomechanics, spacecraft control, road and rail vehicle design, and dynamics of machinery. Therefore, the International Union of Theoretical and Applied Mechanics (IUTAM) has initiated and sponsored, in cooperation with the International 'c Federation for Theory of Machines and Mechanisms (IFToMM), a Symposium on Dynamics of Multibody Systems, held at the International Centre of Mechanical Sciences (CISM) in Udine, Italy, ~eptember 16-20, 1985. The aims of the symposium were to generate knowledge, to stimulate research, to disseminate new ideas, and to acquaint the scientific community in general with the work currently in progress in the area of multibody dynamics. A Scientific Committee has been appointed consisting of G. Bianch~ (Co-Chairman), Italy; T.R. Kane, USA; R. Kawai, Japan; D.M. Klimov, USSR; K. Magnus, FRG; F. Niordson, Denmark; A.D. de Pater, The Netherlands; B. Roth, U~A; W. Schiehlen (Co-Chairman), FRG; J. Wittenburg, FRG.