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001482794 001__ 1482794
001482794 003__ OCoLC
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001482794 019__ $$a1407318129
001482794 020__ $$a9783031356551$$q(electronic bk.)
001482794 020__ $$a3031356551$$q(electronic bk.)
001482794 020__ $$z3031356543
001482794 020__ $$z9783031356544
001482794 0247_ $$a10.1007/978-3-031-35655-1$$2doi
001482794 035__ $$aSP(OCoLC)1407211442
001482794 040__ $$aYDX$$beng$$cYDX$$dOCLCO$$dGW5XE$$dEBLCP
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001482794 08204 $$a531/.7$$223/eng/20231113
001482794 1001_ $$aSegev, Reuven.
001482794 24510 $$aFoundations of geometric continuum mechanics :$$bgeometry and duality in continuum mechanics /$$cReuven Segev.
001482794 260__ $$aCham :$$bBirkhäuser,$$c2023.
001482794 300__ $$a1 online resource
001482794 4901_ $$aAdvances in mechanics and mathematics ;$$vv.49
001482794 504__ $$aIncludes bibliographical references and index.
001482794 5050_ $$aIntro -- Preface -- Contents -- 1 Introduction -- 2 Prelude: Finite-Dimensional Systems -- 2.1 The Framework for the Problem of Statics -- 2.2 On the Solutions of the Problem of Statics -- 2.2.1 Existence of Solutions -- 2.2.2 Static Indeterminacy and Optimal Solutions -- 2.2.3 Worst-Case Loading and Load Capacity -- Part I Algebraic Theory: Uniform Fluxes -- 3 Simplices in Affine Spaces and Their Boundaries -- 3.1 Affine Spaces: Notation -- 3.2 Simplices -- 3.3 Cubes, Prisms, and Simplices -- 3.4 Orientation -- 3.5 Simplices on the Boundaries and Their Orientations -- 3.6 Subdivisions
001482794 5058_ $$a4 Uniform Fluxes in Affine Spaces -- 4.1 Basic Assumptions -- 4.2 Balance and Linearity -- 4.3 Immediate Implications of Skew Symmetry and Multi-Linearity -- 4.4 The Algebraic Cauchy Theorem -- 5 From Uniform Fluxes to Exterior Algebra -- 5.1 Polyhedral Chains and Cochains -- 5.2 Component Representation of Fluxes -- 5.3 Multivectors -- 5.4 Component Representation of Multivectors -- 5.5 Alternation -- 5.6 Exterior Products -- 5.7 The Spaces of Multivectors and Multi-Covectors -- 5.8 Contraction -- 5.9 Pullback of Alternating Tensors -- 5.10 Abstract Algebraic Cauchy Formula
001482794 5058_ $$aPart II Smooth Theory -- 6 Smooth Analysis on Manifolds: A Short Review -- 6.1 Manifolds and Bundles -- 6.1.1 Manifolds -- 6.1.2 Tangent Vectors and the Tangent Bundle -- 6.1.3 Fiber Bundles -- 6.1.4 Vector Bundles -- 6.1.5 Tangent Mappings -- 6.1.6 The Tangent Bundle of a Fiber Bundle and Its Vertical Subbundle -- 6.1.7 Jet Bundles -- 6.1.8 The First Jet of a Vector Bundle -- 6.1.9 The Pullback of a Fiber Bundle -- 6.1.10 Dual Vector Bundles and the Cotangent Bundle -- 6.2 Tensor Bundles and Differential Forms -- 6.2.1 Tensor Bundles and Their Sections -- 6.2.2 Differential Forms
001482794 5058_ $$a6.2.3 Contraction and Related Mappings -- 6.2.4 Vector-Valued Forms -- 6.2.5 Density-Dual Spaces -- 6.3 Differentiation and Integration -- 6.3.1 Integral Curves and the Flow of a Vector Field -- 6.3.2 Exterior Derivatives -- 6.3.3 Partitions of Unity -- 6.3.4 Orientation on Manifolds -- 6.3.5 Integration on Oriented Manifolds -- 6.3.6 Stokes's Theorem -- 6.3.7 Integration Over Chains on Manifolds -- 6.4 Manifolds with Corners -- 7 Interlude: Smooth Distributions of Defects -- 7.1 Introduction -- 7.2 Forms and Hypersurfaces -- 7.3 Layering Forms, Defect Forms
001482794 5058_ $$a7.4 Smooth Distributions of Dislocations -- 7.5 Inclinations and Disclinations, the Smooth Case -- 7.6 Frank's Rules for Smooth Distributions of Defects -- 8 Smooth Fluxes -- 8.1 Balance Principles and Fluxes -- 8.1.1 Densities of Extensive Properties -- 8.1.2 Flux Forms and Cauchy's Formula -- 8.1.3 Extensive Properties and Cauchy Formula-Local Representation -- 8.1.4 The Cauchy Flux Theorem -- 8.1.4.1 Assumptions -- 8.1.4.2 Notation -- 8.1.4.3 Construction -- 8.1.5 The Differential Balance Law -- 8.2 Properties of Fluxes -- 8.2.1 Flux Densities and Orientation
001482794 506__ $$aAccess limited to authorized users.
001482794 520__ $$aThis monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the authors extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
001482794 588__ $$aDescription based on print version record.
001482794 650_0 $$aContinuum mechanics$$xMathematics.
001482794 655_0 $$aElectronic books.
001482794 77608 $$iPrint version: $$z3031356543$$z9783031356544$$w(OCoLC)1380386063
001482794 830_0 $$aAdvances in mechanics and mathematics ;$$vv.49.
001482794 852__ $$bebk
001482794 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-35655-1$$zOnline Access$$91397441.1
001482794 909CO $$ooai:library.usi.edu:1482794$$pGLOBAL_SET
001482794 980__ $$aBIB
001482794 980__ $$aEBOOK
001482794 982__ $$aEbook
001482794 983__ $$aOnline
001482794 994__ $$a92$$bISE