Get Cosserat Theories: Shells, Rods and Points PDF

By M.B. Rubin

ISBN-10: 9048155312

ISBN-13: 9789048155316

ISBN-10: 9401593795

ISBN-13: 9789401593793

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Of the stress T "'". 32) of the balance momentum. 8) is properly invariant under SRBM. (v) The tensors f* and y* are both independent of the rate L*. 5), can be rewritten in the form (f* - g-112 y* y*). y*) 0 n* = 0 . 11) vanishes. 5) for arbitrary values of the other components of n*. 13) where y* remains an arbitrary function of (x *,t) that is determined by the equations of motion and the boundary conditions. 14) In general, the constraint response f* influences the equation of linear momentum but not the conservation of mass or angular momentum equations (since it is a symmetric tensor).

9) For clarity in some instances, the value of a function and its specific functional form are distinguished by using an additional symbol over the usual symbol used for the value of the function. Specifically, an overbar ( ) is used when the independent space variable is /\ 1\ -Y, a hat ( ) is used when the independent space variable is X *, and a tilde ( ) is used when the independent space variable is x *. Moreover, f(Y,t) is called the material representation, f(X*,t) is called the Lagrangian or referential representation, and f(x*,t) is called the Eulerian or spatial representation.

8) J* > 0 . ~*(X*,t) X*(Y) i*(y,t) Fig. 1 Material description and reference and present configurations Since the above mappings are invertible, a general scalar or tensor function f can be expressed in terms of three possible representations - 1\ * . , * f = f(Y,t) = f(X ,t) = f(x· f(x' ,t) . 9) For clarity in some instances, the value of a function and its specific functional form are distinguished by using an additional symbol over the usual symbol used for the value of the function. Specifically, an overbar ( ) is used when the independent space variable is /\ 1\ -Y, a hat ( ) is used when the independent space variable is X *, and a tilde ( ) is used when the independent space variable is x *.

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Cosserat Theories: Shells, Rods and Points by M.B. Rubin


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