Non Standard Discretisation Methods In Solid Mechanics

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Non-standard Discretisation Methods in Solid Mechanics

Jörg Schröder,Peter Wriggers
Non standard Discretisation Methods in Solid Mechanics Book PDF

Author : Jörg Schröder,Peter Wriggers
Publisher : Springer Nature
Page : 561 pages
File Size : 44,6 Mb
Release : 2022-04-14
Category : Technology & Engineering
ISBN : 9783030926724

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Non-standard Discretisation Methods in Solid Mechanics by Jörg Schröder,Peter Wriggers Pdf

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 nonlinear problems. The Priority Programme has established an international framework for mechanical and applied mathematical research to pursue open challenges on an inter-disciplinary level. The compiled results can be understood as state of the art in the research field and show promising ways of further research in the respective areas. The book is intended for doctoral and post-doctoral students in civil engineering, mechanical engineering, applied mathematics and physics, as well as industrial researchers interested in the field.

Trends in Applications of Mathematics to Mechanics

Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin
Trends in Applications of Mathematics to Mechanics Book PDF

Author : Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin
Publisher : Springer
Page : 373 pages
File Size : 45,7 Mb
Release : 2018-04-27
Category : Mathematics
ISBN : 9783319759401

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Trends in Applications of Mathematics to Mechanics by Elisabetta Rocca,Ulisse Stefanelli,Lev Truskinovsky,Augusto Visintin Pdf

This volume originates from the INDAM Symposium on Trends on Applications of Mathematics to Mechanics (STAMM), which was held at the INDAM headquarters in Rome on 5–9 September 2016. It brings together original contributions at the interface of Mathematics and Mechanics. The focus is on mathematical models of phenomena issued from various applications. These include thermomechanics of solids and gases, nematic shells, thin films, dry friction, delamination, damage, and phase-field dynamics. The papers in the volume present novel results and identify possible future developments. The book is addressed to researchers involved in Mathematics and its applications to Mechanics.

Mathematical Analysis of Continuum Mechanics and Industrial Applications II

Patrick van Meurs,Masato Kimura,Hirofumi Notsu
Mathematical Analysis of Continuum Mechanics and Industrial Applications II Book PDF

Author : Patrick van Meurs,Masato Kimura,Hirofumi Notsu
Publisher : Springer
Page : 193 pages
File Size : 52,7 Mb
Release : 2017-11-16
Category : Science
ISBN : 9789811062834

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Mathematical Analysis of Continuum Mechanics and Industrial Applications II by Patrick van Meurs,Masato Kimura,Hirofumi Notsu Pdf

As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.

Discretization Methods in Structural Mechanics

Günther Kuhn,Herbert Mang
Discretization Methods in Structural Mechanics Book PDF

Author : Günther Kuhn,Herbert Mang
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 41,8 Mb
Release : 2013-03-08
Category : Technology & Engineering
ISBN : 9783642493737

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Discretization Methods in Structural Mechanics by Günther Kuhn,Herbert Mang Pdf

The advent of the digital computer has given great impetus to the development of modern discretization methods in structural mechanics. The young history of the finite element method (FEM) reflects the dramatic increase of computing speed and storage capacity within a relatively short period of time. The history of the boundary element method (BEM) is still younger. Presently, intense scientific efforts aimed at extending the range of application of the BEM can be observed. More than 10 years ago, O.C. Zienkiewicz and his co-workers published the first papers on the coupling of FE and BE discretizations of subregions of solids for the purpose of exploiting the complementary advantages of the two discretization methods and reducing their disadvantages. The FEM has revolutionized structural analysis in industry as well as academia. The BEM has a fair share in the continuation of this revolution. Both discretization methods have become a domain of vigorous, world-wide research activities. The rapid increase of the number of specialized journals and scientific meetings indicates the remarkable increase of research efforts in this important subdolll.ain of computational ulechanics. Several discussions of this situation in the Committee for Discretization Methods ill Solid Mechanics of the Society for Applied Mathematics and Mechanics (GAMM) resulted in the plan to submit a proposal to the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM) to sponsor a pertinent IUTAM Symposium.

Error-controlled Adaptive Finite Elements in Solid Mechanics

Ekkehard Ramm,E. Rank,R. Rannacher,K. Schweizerhof,E. Stein,W. Wendland,G. Wittum,Peter Wriggers,Walter Wunderlich
Error controlled Adaptive Finite Elements in Solid Mechanics Book PDF

Author : Ekkehard Ramm,E. Rank,R. Rannacher,K. Schweizerhof,E. Stein,W. Wendland,G. Wittum,Peter Wriggers,Walter Wunderlich
Publisher : John Wiley & Sons
Page : 422 pages
File Size : 44,7 Mb
Release : 2003-08-01
Category : Technology & Engineering
ISBN : 9780470857977

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Error-controlled Adaptive Finite Elements in Solid Mechanics by Ekkehard Ramm,E. Rank,R. Rannacher,K. Schweizerhof,E. Stein,W. Wendland,G. Wittum,Peter Wriggers,Walter Wunderlich Pdf

Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. * First book to go beyond the Finite Element Method in itself * Covers material from a new research area * Presents benchmarks of 2D- and 3D- applications * Fits with the new trend for genetic strategies in engineering

Model Reduction of Parametrized Systems

Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban
Model Reduction of Parametrized Systems Book PDF

Author : Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban
Publisher : Springer
Page : 504 pages
File Size : 53,7 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9783319587868

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Model Reduction of Parametrized Systems by Peter Benner,Mario Ohlberger,Anthony Patera,Gianluigi Rozza,Karsten Urban Pdf

The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).

Meshless Methods in Solid Mechanics

Youping Chen,James Lee,Azim Eskandarian
Meshless Methods in Solid Mechanics Book PDF

Author : Youping Chen,James Lee,Azim Eskandarian
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 43,8 Mb
Release : 2006-04-28
Category : Science
ISBN : 9780387307367

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Meshless Methods in Solid Mechanics by Youping Chen,James Lee,Azim Eskandarian Pdf

This book covers the fundamentals of continuum mechanics, the integral formulation methods of continuum problems, the basic concepts of finite element methods, and the methodologies, formulations, procedures, and applications of various meshless methods. It also provides general and detailed procedures of meshless analysis on elastostatics, elastodynamics, non-local continuum mechanics and plasticity with a large number of numerical examples. Some basic and important mathematical methods are included in the Appendixes. For readers who want to gain knowledge through hands-on experience, the meshless programs for elastostatics and elastodynamics are provided on an included disc.

Spatial and Material Forces in Nonlinear Continuum Mechanics

Paul Steinmann
Spatial and Material Forces in Nonlinear Continuum Mechanics Book PDF

Author : Paul Steinmann
Publisher : Springer Nature
Page : 418 pages
File Size : 54,9 Mb
Release : 2022-03-28
Category : Science
ISBN : 9783030890704

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Spatial and Material Forces in Nonlinear Continuum Mechanics by Paul Steinmann Pdf

This monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the related configurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes.

Multiscale Modeling in Solid Mechanics

Ugo Galvanetto,M. H. Ferri Aliabadi
Multiscale Modeling in Solid Mechanics Book PDF

Author : Ugo Galvanetto,M. H. Ferri Aliabadi
Publisher : Imperial College Press
Page : 349 pages
File Size : 42,6 Mb
Release : 2010
Category : Science
ISBN : 9781848163089

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Multiscale Modeling in Solid Mechanics by Ugo Galvanetto,M. H. Ferri Aliabadi Pdf

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.

Numerical Methods for Nonsmooth Dynamical Systems

Vincent Acary,Bernard Brogliato
Numerical Methods for Nonsmooth Dynamical Systems Book PDF

Author : Vincent Acary,Bernard Brogliato
Publisher : Springer Science & Business Media
Page : 529 pages
File Size : 43,5 Mb
Release : 2008-01-30
Category : Technology & Engineering
ISBN : 9783540753926

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Numerical Methods for Nonsmooth Dynamical Systems by Vincent Acary,Bernard Brogliato Pdf

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

Spectral Methods for Non-Standard Eigenvalue Problems

Călin-Ioan Gheorghiu
Spectral Methods for Non Standard Eigenvalue Problems Book PDF

Author : Călin-Ioan Gheorghiu
Publisher : Springer Science & Business
Page : 130 pages
File Size : 49,5 Mb
Release : 2014-04-22
Category : Mathematics
ISBN : 9783319062303

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Spectral Methods for Non-Standard Eigenvalue Problems by Călin-Ioan Gheorghiu Pdf

This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions. The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems. In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows. This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.

Fluid-Structure Interaction

Hans-Joachim Bungartz,Michael Schäfer
Fluid Structure Interaction Book PDF

Author : Hans-Joachim Bungartz,Michael Schäfer
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 43,7 Mb
Release : 2007-06-24
Category : Technology & Engineering
ISBN : 9783540345961

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Fluid-Structure Interaction by Hans-Joachim Bungartz,Michael Schäfer Pdf

This volume in the series Lecture Notes in Computational Science and Engineering presents a collection of papers presented at the International Workshop on FSI, held in October 2005 in Hohenwart and organized by DFG's Research Unit 493 "FSI: Modeling, Simulation, and Optimization". The papers address partitioned and monolithic coupling approaches, methodical issues and applications, and discuss FSI from the mathematical, informatics, and engineering points of view.

Efficient High-Order Discretizations for Computational Fluid Dynamics

Martin Kronbichler,Per-Olof Persson
Efficient High Order Discretizations for Computational Fluid Dynamics Book PDF

Author : Martin Kronbichler,Per-Olof Persson
Publisher : Springer
Page : 311 pages
File Size : 55,8 Mb
Release : 2021-02-05
Category : Technology & Engineering
ISBN : 3030606090

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Efficient High-Order Discretizations for Computational Fluid Dynamics by Martin Kronbichler,Per-Olof Persson Pdf

The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to teach the basics of the discontinuous Galerkin (DG) method in terms of its finite volume and finite element ingredients. It also discusses the computational efficiency of high-order methods versus state-of-the-art low order methods in the finite difference context, given that accuracy requirements in engineering are often not overly strict. The book mainly addresses researchers and doctoral students in engineering, applied mathematics, physics and high-performance computing with a strong interest in the interdisciplinary aspects of computational fluid dynamics. It is also well-suited for practicing computational engineers who would like to gain an overview of discontinuous Galerkin methods, modern algorithmic realizations, and high-performance implementations.

Mechanics of Solid Deformable Body

Michael Zhuravkov,Yongtao Lyu,Eduard Starovoitov
Mechanics of Solid Deformable Body Book PDF

Author : Michael Zhuravkov,Yongtao Lyu,Eduard Starovoitov
Publisher : Springer Nature
Page : 317 pages
File Size : 50,7 Mb
Release : 2023-02-21
Category : Science
ISBN : 9789811984105

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Mechanics of Solid Deformable Body by Michael Zhuravkov,Yongtao Lyu,Eduard Starovoitov Pdf

This textbook contains sections with fundamental, classical knowledge in solid mechanics, as well as original modern mathematical models to describe the state and behavior of solid deformable bodies. It has original sections with the basics of mathematical modeling in the solid mechanics, material on the basic principles, and features of mathematical formulation of model problems of solid mechanics. For successful mastering of the material, it is necessary to have basic knowledge of the relevant sections of the courses of mathematical analysis, linear algebra and tensor analysis, differential equations, and equations of mathematical physics. Each section contains a list of test questions and exercises to check the level of assimilation of the material. The textbook is intended for senior university students, postgraduates, and research fellows. It can be used in the study of general and special disciplines in various sections of solid mechanics, applied mechanics for students and undergraduates of various specializations and specialties, such as mechanics and mathematical modeling, applied mathematics, solid physics, and engineering mechanics.

Numerical Methods in Geotechnical Engineering IX

António S. Cardoso,José L. Borges,Pedro A. Costa,António T. Gomes,José C. Marques,Castorina S. Vieira
Numerical Methods in Geotechnical Engineering IX Book PDF

Author : António S. Cardoso,José L. Borges,Pedro A. Costa,António T. Gomes,José C. Marques,Castorina S. Vieira
Publisher : CRC Press
Page : 2563 pages
File Size : 42,5 Mb
Release : 2018-06-19
Category : Technology & Engineering
ISBN : 9781351003605

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Numerical Methods in Geotechnical Engineering IX by António S. Cardoso,José L. Borges,Pedro A. Costa,António T. Gomes,José C. Marques,Castorina S. Vieira Pdf

Numerical Methods in Geotechnical Engineering IX contains 204 technical and scientific papers presented at the 9th European Conference on Numerical Methods in Geotechnical Engineering (NUMGE2018, Porto, Portugal, 25—27 June 2018). The papers cover a wide range of topics in the field of computational geotechnics, providing an overview of recent developments on scientific achievements, innovations and engineering applications related to or employing numerical methods. They deal with subjects from emerging research to engineering practice, and are grouped under the following themes: Constitutive modelling and numerical implementation Finite element, discrete element and other numerical methods. Coupling of diverse methods Reliability and probability analysis Large deformation – large strain analysis Artificial intelligence and neural networks Ground flow, thermal and coupled analysis Earthquake engineering, soil dynamics and soil-structure interactions Rock mechanics Application of numerical methods in the context of the Eurocodes Shallow and deep foundations Slopes and cuts Supported excavations and retaining walls Embankments and dams Tunnels and caverns (and pipelines) Ground improvement and reinforcement Offshore geotechnical engineering Propagation of vibrations Following the objectives of previous eight thematic conferences, (1986 Stuttgart, Germany; 1990 Santander, Spain; 1994 Manchester, United Kingdom; 1998 Udine, Italy; 2002 Paris, France; 2006 Graz, Austria; 2010 Trondheim, Norway; 2014 Delft, The Netherlands), Numerical Methods in Geotechnical Engineering IX updates the state-of-the-art regarding the application of numerical methods in geotechnics, both in a scientific perspective and in what concerns its application for solving practical boundary value problems. The book will be much of interest to engineers, academics and professionals involved or interested in Geotechnical Engineering.