Titlebook: Geometrical Foundations of Continuum Mechanics; An Application to Fi Paul Steinmann Book 2015 Springer-Verlag Berlin Heidelberg 2015 Applie

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Representations in Four-, Three-, Two-Spaced detailed to the cases of four-, three- and two-dimensional manifolds. (The case of one-dimensional manifolds, i.e. curves is not of relevance here, since the curvature tensor, that measures solely the internal geometry of a manifold, degenerates to zero in one dimension.) The above manifolds will

種類

Continuum Kinematics curvilinear coordinates. Expressed in curvilinear coordinates the differential geometry of flat Euclidean space is captured by the Christoffel symbols that take the role of a symmetric and integrable metric connection with associated zero curvature tensor. The position of a physical point together

Dictation

Elasticityd-order (nonlinear) elasticity. Thereby it shall be noted that both the material and spatial configurations of first- and second-order elasticity ought to be compatible, see Fig. 7.1. Then, two cases may be considered: firstly the material configuration is assumed compatible and the conditions on th