Variational models and methods in solid and fluid mechanics - download pdf or read online

By Francesco Dell'Isola; Sergey Gavrilyuk (eds.)

ISBN-10: 3709109833

ISBN-13: 9783709109830

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Let x ∈ p πi ∩ S . , np ) . 14. Admissible domains and contact surfaces. We only consider domains the topological boundary of which S (contact admissible surface) is piecewise regular. In other words we assume that i) S Contact Actions in N-th Gradient Generalized Continua 55 is a finite union of two-dimensional suitably regular compact manifolds with border (called the faces of S) ii) the union of the borders of these faces is a finite union of one-dimensional suitably regular compact manifolds with boundary (called the edges of S), iii) the edges are concurring in wedges and iv) the set of wedges is finite.

8. (divM P(T )) α times the following equality holds if T is a symmetric tensor field K− times contravariant : K−1 T · ∇K V = M (−1) α α M α=0 + (−1) K ((divM P) T )⊥ · ∇K−α V K (divM P) T V + ⊥ + (49) (50) M K−1 + (−1) α=0 α α P((divM P) T ) · ∇K−1−α V ⊗ ν ∂M (51) 40 F. dell’Isola, P. Seppecher and A. ν · ∇L V (54) ∂M L=0 The previous corollary allows us to find the unique representation in terms of transversal derivatives of the distribution of the type specified by equation 17. 3. 8 Principle of Virtual Powers applied to N − th gradient continua.

Contact Actions in N-th Gradient Generalized Continua 51 We will use the previous corollaries later, when we will consider the consequence of the Cauchy tetrahedron argument on the structure of contact actions in N − th gradient continua. N − 3 F (∂∂∂B, J) = HJ (106) (107) (108) (109) The first of the listed equations is a system of PDE defined inside the reference configuration of the body B,while the others are appropriate boundary conditions to be verified on regular surfaces, edges and wedges of the topological boundary of B.

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Variational models and methods in solid and fluid mechanics by Francesco Dell'Isola; Sergey Gavrilyuk (eds.)


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