Continuum Mechanics Via Problems and Exercises. Part I: by Eglit M.E., Hodges D.H. (eds.) PDF

By Eglit M.E., Hodges D.H. (eds.)

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Extra info for Continuum Mechanics Via Problems and Exercises. Part I: Theory and Problems

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Vorticity. Deformation. Strain tensors. Deformation of a continuum is variation of distances between its particles. Deforma­ tion causes a response of the continuum and, in particular, results in the appearance of internal forces in it. So it is necessary to introduce quantitative deformation mea­ sures. For example, longitudinal deformation of an extended rod can be characterized by the relative elongation (/ - l0)/l0 where I and l0 are respectively the lengths of the rod in the current state and in a state relative to which deformation is measured (called the reference state).

As Lagrangian coordinates of a particle, spatial coordinates of the point, at which the particle was situated at the initial instant (in the undeformed state), are taken. Unless otherwise stipulated, the spatial coordinate system is Cartesian. — PROBLEMS — Deformation. Strain tensors. 6) situated at the points with the coordinates 0I a continuum are zi = & + a£i , x2 = & i x3 = £3 (a = const) with reference to a spatial Cartesian coordinate system ii. ) What happened to the material line elements initially situated parallel to the coordinate axis xt and those orthogonal to this axis?

They result in differential equations satisfied at each point of a domain occupied by a medium for motions described by smooth functions. If the functions describing a motion are discontinuous on some surfaces the jumps of the functions across these surfaces are related by equalities called jump conditions also resulted from the general conservation laws written in integral form. Below, the summary of the general laws and equations is given. They are considered in detail in Sections 7-18. The mass conservation law states that the mass of a material volume is constant | / ^ = 0.

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Continuum Mechanics Via Problems and Exercises. Part I: Theory and Problems by Eglit M.E., Hodges D.H. (eds.)


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