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Author: A.M. Khludnev
Publisher: Birkhäuser
ISBN: 3034889844
Category : Mathematics
Languages : en
Pages : 380
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Book Description
New trends in free boundary problems and new mathematical tools together with broadening areas of applications have led to attempts at presenting the state of art of the field in a unified way. In this monograph we focus on formal models representing contact problems for elastic and elastoplastic plates and shells. New approaches open up new fields for research. For example, in crack theory a systematic treatment of mathematical modelling and optimization of problems with cracks is required. Similarly, sensitivity analysis of solutions to problems subjected to perturbations, which forms an important part of the problem solving process, is the source of many open questions. Two aspects of sensitivity analysis, namely the behaviour of solutions under deformations of the domain of integration and perturbations of surfaces seem to be particularly demanding in this context. On writing this book we aimed at providing the reader with a self-contained study of the mathematical modelling in mechanics. Much attention is given to modelling of typical constructions applied in many different areas. Plates and shallow shells which are widely used in the aerospace industry provide good exam ples. Allied optimization problems consist in finding the constructions which are of maximal strength (endurance) and satisfy some other requirements, ego weight limitations. Mathematical modelling of plates and shells always requires a reasonable compromise between two principal needs. One of them is the accuracy of the de scription of a physical phenomenon (as required by the principles of mechanics).
Author: A.M. Khludnev
Publisher: Birkhäuser
ISBN: 3034889844
Category : Mathematics
Languages : en
Pages : 380
Get Book Here
Book Description
New trends in free boundary problems and new mathematical tools together with broadening areas of applications have led to attempts at presenting the state of art of the field in a unified way. In this monograph we focus on formal models representing contact problems for elastic and elastoplastic plates and shells. New approaches open up new fields for research. For example, in crack theory a systematic treatment of mathematical modelling and optimization of problems with cracks is required. Similarly, sensitivity analysis of solutions to problems subjected to perturbations, which forms an important part of the problem solving process, is the source of many open questions. Two aspects of sensitivity analysis, namely the behaviour of solutions under deformations of the domain of integration and perturbations of surfaces seem to be particularly demanding in this context. On writing this book we aimed at providing the reader with a self-contained study of the mathematical modelling in mechanics. Much attention is given to modelling of typical constructions applied in many different areas. Plates and shallow shells which are widely used in the aerospace industry provide good exam ples. Allied optimization problems consist in finding the constructions which are of maximal strength (endurance) and satisfy some other requirements, ego weight limitations. Mathematical modelling of plates and shells always requires a reasonable compromise between two principal needs. One of them is the accuracy of the de scription of a physical phenomenon (as required by the principles of mechanics).
Author: Ugo Galvanetto
Publisher: Imperial College Press
ISBN: 1848163088
Category : Science
Languages : en
Pages : 349
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Book Description
This unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear Homogenisation as well as various nonlinear approaches. It then presents advanced applications of multiscale approaches applied to nonlinear mechanical problems. Finally, the novel topic of materials with self-similar structure is discussed. Sample Chapter(s). Chapter 1: Computational Homogenisation for Non-Linear Heterogeneous Solids (808 KB). Contents: Computational Homogenisation for Non-Linear Heterogeneous Solids (V G Kouznetsova et al.); Two-Scale Asymptotic Homogenisation-Based Finite Element Analysis of Composite Materials (Q-Z Xiao & B L Karihaloo); Multi-Scale Boundary Element Modelling of Material Degradation and Fracture (G K Sfantos & M H Aliabadi); Non-Uniform Transformation Field Analysis: A Reduced Model for Multiscale Non-Linear Problems in Solid Mechanics (J-C Michel & P Suquet); Multiscale Approach for the Thermomechanical Analysis of Hierarchical Structures (M J Lefik et al.); Recent Advances in Masonry Modelling: Micro-Modelling and Homogenisation (P B Louren o); Mechanics of Materials with Self-Similar Hierarchical Microstructure (R C Picu & M A Soare). Readership: Researchers and academics in the field of heterogeneous materials and mechanical engineering; professionals in aeronautical engineering and materials science.
Author: A M Khludnev
Publisher:
ISBN: 9783034889858
Category :
Languages : en
Pages : 388
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Book Description
Author: Robert Seifried
Publisher: Springer Science & Business Media
ISBN: 3319012282
Category : Technology & Engineering
Languages : en
Pages : 257
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Book Description
Underactuated multibody systems are intriguing mechatronic systems, as they posses fewer control inputs than degrees of freedom. Some examples are modern light-weight flexible robots and articulated manipulators with passive joints. This book investigates such underactuated multibody systems from an integrated perspective. This includes all major steps from the modeling of rigid and flexible multibody systems, through nonlinear control theory, to optimal system design. The underlying theories and techniques from these different fields are presented using a self-contained and unified approach and notation system. Subsequently, the book focuses on applications to large multibody systems with multiple degrees of freedom, which require a combination of symbolical and numerical procedures. Finally, an integrated, optimization-based design procedure is proposed, whereby both structural and control design are considered concurrently. Each chapter is supplemented by illustrated examples.
Author: Francesco dell'Isola
Publisher: Springer Science & Business Media
ISBN: 3709109833
Category : Technology & Engineering
Languages : en
Pages : 363
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Book Description
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Author: S. Krenk
Publisher: Cambridge University Press
ISBN: 0521830540
Category : Mathematics
Languages : en
Pages : 361
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Book Description
Finite element analysis for non-linear solids and structure porblems.
Author: Bernard Brogliato
Publisher: Springer Science & Business Media
ISBN: 1447105575
Category : Technology & Engineering
Languages : en
Pages : 565
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Book Description
Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.
Author: Peter Howell
Publisher: Cambridge University Press
ISBN: 052185489X
Category : Mathematics
Languages : en
Pages : 467
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Book Description
Emphasises the power of mathematics to provide quantitative insights across the whole area of solid mechanics; accessible and comprehensive.
Author: Jorgen S Bergstrom
Publisher: William Andrew
ISBN: 0323322964
Category : Technology & Engineering
Languages : en
Pages : 524
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Book Description
Very few polymer mechanics problems are solved with only pen and paper today, and virtually all academic research and industrial work relies heavily on finite element simulations and specialized computer software. Introducing and demonstrating the utility of computational tools and simulations, Mechanics of Solid Polymers provides a modern view of how solid polymers behave, how they can be experimentally characterized, and how to predict their behavior in different load environments. Reflecting the significant progress made in the understanding of polymer behaviour over the last two decades, this book will discuss recent developments and compare them to classical theories. The book shows how best to make use of commercially available finite element software to solve polymer mechanics problems, introducing readers to the current state of the art in predicting failure using a combination of experiment and computational techniques. Case studies and example Matlab code are also included. As industry and academia are increasingly reliant on advanced computational mechanics software to implement sophisticated constitutive models – and authoritative information is hard to find in one place - this book provides engineers with what they need to know to make best use of the technology available. - Helps professionals deploy the latest experimental polymer testing methods to assess suitability for applications - Discusses material models for different polymer types - Shows how to best make use of available finite element software to model polymer behaviour, and includes case studies and example code to help engineers and researchers apply it to their work
Author: Roger Temam
Publisher: Cambridge University Press
ISBN: 1139443216
Category : Science
Languages : en
Pages : 356
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Book Description
Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
