Kategoria BISAC: Mathematics >> Numerical Analysis

ECM2 is a completely updated and expanded Second Edition of the well-established Encyclopedia of Computational Mechanics. The project has once again been prepared under the guidance of three of the world's foremost experts in the field:

• Erwin Stein, Professor Emeritus, Stein Institut fUr Baumechanik und Numerische Mechanik, Leibniz UniversitAt, Hannover, Germany
• RenE de Borst, Centenary Professor of Civil Engineering, University of Sheffield, UK
• Thomas J. R. Hughes, Peter O'Donnell Jr. Chair in Computational and Applied Mathematics and Professor of Aerospace...

Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems.
This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of...

This book contains theoretical and application-oriented methods to treat models of dynamical systems involving non-smooth nonlinearities.
The theoretical approach that has been retained and underlined in this work is associated with differential inclusions of mainly finite dimensional dynamical systems and the introduction of maximal monotone operators (graphs) in order to describe models of impact or friction. The authors of this book master the mathematical, numerical and modeling tools in a particular way so that they can propose all aspects of the approach, in both a...

This book presents the derivations of the equations of motion for all structure foundations using either the continuous model or the discrete model. This mathematical display is a strong feature of the book as it helps to explain in full detail how calculations are reached and interpreted. In addition to the simple 'uniform' and 'straight' beams, the book introduces solution techniques...

All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered only as far as it gives insight into the construction of algorithms. In the exercises, a complete FE-solver for stationary 2D problems is implemented in Matlab/Octave.

Contents:
Finite Element Fundamentals
Grids and Finite Elements
Assembly
Solvers
Error Estimation
Mesh Refinement
Multigrid
Elastomechanics
Fluid Mechanics
Grid Data...

This book is dedicated to the general study of the dynamics of mechanical structures with consideration of uncertainties. The goal is to get the appropriate forms of a part in minimizing a given criterion. In all fields of structural mechanics, the impact of good design of a room is very important to its strength, its life and its use in service. The development of the engineer's art requires considerable effort to constantly improve structural design techniques.

The purpose of this book is to clarify the issues related to the environment of mechanical vibrations in the material life profile. In particular, through their simulation testing laboratory, through a better understanding of the physical phenomenon, means to implement to simulate, measurements and interpretations associated results. It is aimed at development of technical consultants, quality and services primarily to those testing laboratories, as well as to all those who are faced with supply reference to the environmental test calls and particularly here, vibration tests. Furthermore...

"Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems.

This book incorporates diverse perspectives from broad-ranging areas of research including,...

The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced...

The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another.

Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of...

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a...

This Series provides the necessary elements to the development and validation of numerical prediction models for hydrodynamic bearings. This book describes the rheological models and the equations of lubrication. It also presents the numerical approaches used to solve the above equations by finite differences, finite volumes and finite elements methods.