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Non-standard Discretisation Methods in Solid Mechanics

2022-04-14 Technology & Engineering
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Release : 2022-04-14
Genre : Technology & Engineering
Kind : eBook
Book Rating : 729/5 ( reviews)

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Book Synopsis Non-standard Discretisation Methods in Solid Mechanics by : Jörg Schröder

Download or read book Non-standard Discretisation Methods in Solid Mechanics written by Jörg Schröder. This book was released on 2022-04-14. Available in PDF, EPUB and Kindle. Book excerpt: 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

2018-04-27 Mathematics
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Release : 2018-04-27
Genre : Mathematics
Kind : eBook
Book Rating : 40X/5 ( reviews)

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Book Synopsis Trends in Applications of Mathematics to Mechanics by : Elisabetta Rocca

Download or read book Trends in Applications of Mathematics to Mechanics written by Elisabetta Rocca. This book was released on 2018-04-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Isogeometric Analysis and Applications 2014

2015-12-21 Mathematics
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Release : 2015-12-21
Genre : Mathematics
Kind : eBook
Book Rating : 157/5 ( reviews)

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Book Synopsis Isogeometric Analysis and Applications 2014 by : Bert Jüttler

Download or read book Isogeometric Analysis and Applications 2014 written by Bert Jüttler. This book was released on 2015-12-21. Available in PDF, EPUB and Kindle. Book excerpt: Isogeometric Analysis is a groundbreaking computational approach that promises the possibility of integrating the finite element method into conventional spline-based CAD design tools. It thus bridges the gap between numerical analysis and geometry, and moreover it allows to tackle new cutting edge applications at the frontiers of research in science and engineering. This proceedings volume contains a selection of outstanding research papers presented at the second International Workshop on Isogeometric Analysis and Applications, held at Annweiler, Germany, in April 2014.

Model Reduction of Parametrized Systems

2017-09-05 Mathematics
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Release : 2017-09-05
Genre : Mathematics
Kind : eBook
Book Rating : 862/5 ( reviews)

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Book Synopsis Model Reduction of Parametrized Systems by : Peter Benner

Download or read book Model Reduction of Parametrized Systems written by Peter Benner. This book was released on 2017-09-05. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Spatial and Material Forces in Nonlinear Continuum Mechanics

2022-03-28 Science
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Release : 2022-03-28
Genre : Science
Kind : eBook
Book Rating : 708/5 ( reviews)

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Book Synopsis Spatial and Material Forces in Nonlinear Continuum Mechanics by : Paul Steinmann

Download or read book Spatial and Material Forces in Nonlinear Continuum Mechanics written by Paul Steinmann. This book was released on 2022-03-28. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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