Geometry of Incompatible Deformations: Differential Geometry in Continuum MechanicsWalter de Gruyter GmbH & Co KG, 4 мар. 2019 г. - Всего страниц: 408 This monograph provides a systematic treatment of differential geometry in modeling of incompatible fiite deformations in solids. Included are discussions of generalized deformations and stress measures on smooth manifolds, geometrical formalizations for structurally inhomogeneous bodies, representations for configurational forces, and evolution equations. |
Содержание
| 1 | |
| 3 | |
3 Essentials of NonLinear Elasticity Theory | 59 |
4 Geometric Formalization of the Body and Its Representation in Physical Space | 119 |
5 Strain Measures | 141 |
6 Motion | 161 |
7 Stress Measures | 179 |
8 Material Uniformity and Inhomogeneity | 195 |
10 Balance Equations | 231 |
11 The Evolutionary Problem Examples | 249 |
12 Algebraic Structures | 297 |
13 Review of Smooth Manifolds and Vector Bundles | 315 |
14 Connections on Principal Bundles | 359 |
Bibliography | 381 |
| 387 | |
9 Material Connections | 209 |
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Geometry of Incompatible Deformations: Differential Geometry in Continuum ... Sergey Lychev,Konstantin Koifman Недоступно для просмотра - 2019 |
Часто встречающиеся слова и выражения
affine connection affine space atlas basis body boundary called Cauchy stress Cauchy-Green Chapter components configuration connection Consider continuum mechanics coordinate representation corresponding covector curvature curve defined definition deformation gradient denoted density derivative diffeomorphism differential dual dx¹ elastic elements embedding equations Euclidean space exterior fiber formula frame function geometric homomorphism isomorphism layers Lie derivative Lin(V linear mappings material points non-Euclidean notion obtains open set open subset operation physical space principal bundle pullback Ra)² reference shape relation represented Riemannian metric s-dimensional scalar Section smooth chart smooth manifold smooth mapping smooth vector spatial stress tensor submanifold Suppose tangent space tangent vector tensor field theorem theory tion topological transformation two-point tensor Vec(M vector bundle vector field vector space velocity Θα φα дх дхі