Search Results for: differential geometry and kinematics of continua

Differential Geometry And Kinematics Of Continua

Differential Geometry and Kinematics of Continua PDF
Author: John D Clayton
Publisher: World Scientific
Size: 32.90 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 192
View: 5829

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Differential Geometry And Kinematics Of Continua Book Description

by John D Clayton, Differential Geometry And Kinematics Of Continua Books available in PDF, EPUB, Mobi Format. Download Differential Geometry And Kinematics Of Continua books, This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided. Contents: IntroductionGeometric FundamentalsKinematics of Integrable DeformationGeometry of Anholonomic DeformationKinematics of Anholonomic DeformationList of SymbolsBibliographyIndex Readership: Researchers in mathematical physics and engineering mechanics. Key Features:Presentation of mathematical operations and examples in anholonomic space associated with a multiplicative decomposition (e.g., of the gradient of motion) is more general and comprehensive than any given elsewhere and contains original ideas and new resultsLine-by-line derivations are frequent and exhaustive, to facilitate practice and enable verification of final resultsGeneral analysis is given in generic curvilinear coordinates; particular sections deal with applications and examples in Cartesian, cylindrical, spherical, and convected coordinates. Indicial and direct notations of tensor calculus enable connections with historic and modern literature, respectivelyKeywords:Differential Geometry;Tensor Analysis;Continuum Mechanics;Kinematics;Deformation;Anholonomic Coordinates


A Geometric Approach To Thermomechanics Of Dissipating Continua

A Geometric Approach to Thermomechanics of Dissipating Continua PDF
Author: Lalao Rakotomanana
Publisher: Springer Science & Business Media
Size: 30.60 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 265
View: 4885

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A Geometric Approach To Thermomechanics Of Dissipating Continua Book Description

by Lalao Rakotomanana, A Geometric Approach To Thermomechanics Of Dissipating Continua Books available in PDF, EPUB, Mobi Format. Download A Geometric Approach To Thermomechanics Of Dissipating Continua books, Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in space. Vector algebra theory was not sufficient to compare the different velocities of a particle in the course of time. There was a need to (parallel) transport these velocities at a single point before any vector algebraic operation. The appropriate mathematical structure for this transport was the connection. I The Euclidean connection derived from the metric tensor of the referential body was the only connection used in mechanics for over two centuries. Then, major steps in the evolution of spacetime concepts were made by Einstein in 1905 (special relativity) and 1915 (general relativity) by using Riemannian connection. Slightly later, nonrelativistic spacetime which includes the main features of general relativity I It took about one and a half centuries for connection theory to be accepted as an independent theory in mathematics. Major steps for the connection concept are attributed to a series of findings: Riemann 1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918, Cartan 1923, Eshermann 1950.


Generalized Continua From The Theory To Engineering Applications

Generalized Continua   from the Theory to Engineering Applications PDF
Author: Holm Altenbach
Publisher: Springer Science & Business Media
Size: 53.31 MB
Format: PDF, ePub, Docs
Category : Technology & Engineering
Languages : en
Pages : 387
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Generalized Continua From The Theory To Engineering Applications Book Description

by Holm Altenbach, Generalized Continua From The Theory To Engineering Applications Books available in PDF, EPUB, Mobi Format. Download Generalized Continua From The Theory To Engineering Applications books, On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.


Defects And Anelasticity In The Characterization Of Crystalline Solids

Defects and Anelasticity in the Characterization of Crystalline Solids PDF
Author: American Society of Mechanical Engineers. Winter Meeting
Publisher: American Society of Mechanical Engineers
Size: 46.99 MB
Format: PDF, Kindle
Category : Continuum mechanics
Languages : en
Pages : 169
View: 2483

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Defects And Anelasticity In The Characterization Of Crystalline Solids Book Description

by American Society of Mechanical Engineers. Winter Meeting, Defects And Anelasticity In The Characterization Of Crystalline Solids Books available in PDF, EPUB, Mobi Format. Download Defects And Anelasticity In The Characterization Of Crystalline Solids books,


Differential Geometry And Continuum Mechanics

Differential Geometry and Continuum Mechanics PDF
Author: Gui-Qiang G. Chen
Publisher: Springer
Size: 30.66 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 387
View: 6804

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Differential Geometry And Continuum Mechanics Book Description

by Gui-Qiang G. Chen, Differential Geometry And Continuum Mechanics Books available in PDF, EPUB, Mobi Format. Download Differential Geometry And Continuum Mechanics books, This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.


Boundary Control And Boundary Variations

Boundary Control and Boundary Variations PDF
Author: J.P. Zolesio
Publisher: Springer
Size: 29.27 MB
Format: PDF, ePub, Docs
Category : Technology & Engineering
Languages : en
Pages : 401
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Boundary Control And Boundary Variations Book Description

by J.P. Zolesio, Boundary Control And Boundary Variations Books available in PDF, EPUB, Mobi Format. Download Boundary Control And Boundary Variations books, This volume comprises the proceedings of the Working Conference "Boundary variations and boundary control" held in Nice (France), June 10-13, 1986. The aim of this Conference was to stimulate exchange of ideas between the group working on shape optimization (including free boundary problems) and the group working on boundary control of hyperbolic systems (including stabilization). An important remark is that if one considers a dynamical system governed by linear elasticity the choice of Lagrangian coordinates leads to discuss boundary conditions, or boundary control (for example to stabilize), while the choice of Eulerian coordinates lead to a moving boundary and moving domain . This remark challenges us to consider the domain (or its boundary) as a control.


Reviews In Global Analysis 1980 86 As Printed In Mathematical Reviews

Reviews in Global Analysis  1980 86 as Printed in Mathematical Reviews PDF
Author:
Publisher:
Size: 57.19 MB
Format: PDF, ePub, Mobi
Category : Global analysis (Mathematics)
Languages : en
Pages : 834
View: 6954

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Reviews In Global Analysis 1980 86 As Printed In Mathematical Reviews Book Description

by , Reviews In Global Analysis 1980 86 As Printed In Mathematical Reviews Books available in PDF, EPUB, Mobi Format. Download Reviews In Global Analysis 1980 86 As Printed In Mathematical Reviews books,


Modern Differential Geometric Techniques In The Theory Of Continuous Distributions Of Dislocations

Modern Differential Geometric Techniques in the Theory of Continuous Distributions of Dislocations PDF
Author: F. Bloom
Publisher: Springer Verlag
Size: 60.69 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 206
View: 6930

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Modern Differential Geometric Techniques In The Theory Of Continuous Distributions Of Dislocations Book Description

by F. Bloom, Modern Differential Geometric Techniques In The Theory Of Continuous Distributions Of Dislocations Books available in PDF, EPUB, Mobi Format. Download Modern Differential Geometric Techniques In The Theory Of Continuous Distributions Of Dislocations books,