Statics of One-Dimensional Media
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We shall now present two approaches to one-dimensional modelling of the continuum. The starting point for this theory of one-dimensional media must clearly be geometrical, based on the observation that many solids used as structural elements in constructions (civil or industrial engineering, ship building, aeronautics, etc.) have a slender shape (Fig. 1). This suggests that it should be possible to carry out mechanical studies on the one-dimensional geometry defined by a director curve.
Key WordsSlender solids One-dimensional media Director curve Transverse section Orthogonal section Statics of wires Tension Statics of beams External force wrench Field of internal force wrenches Normal force Shearing force Twisting moment Bending moment Navier-Bernoulli condition Endpoint boundary conditions Support boundary conditions Assembly boundary conditions Static determinacy Static indeterminacy Geometrical instability
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