By Roger Chesneau
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Extra info for British Aerospace Sea Harrier FRS.Mk.1
10), and thus the derivative of u can be expressed in terms of curvilinear components. Similar patterns follow for derivatives of higher-order tensors. All vector differential operators of gradient, divergence, curl, and so forth can be expressed in any general curvilinear system by using these techniques. 12) 2 3 h1 vx1 h2 vx2 h3 vx3 hi vxi i and this leads to the construction of the other common forms X 1 vf 1 vf 1 vf 1 vf ^ei þ ^e2 þ ^e3 ¼ 1 2 3 h1 vx h2 vx h3 vx hi vxi i 1 X v h 1 h2 h3 u Divergence of a Vector V$u ¼ h1 h2 h3 i vxi hi !
However, for large deformation theory, sizeable differences exist between these configurations, and the undeformed configuration (commonly called the reference configuration) is often used in problem formulation. This gives rise to the definition of an additional stress called the Piola–Kirchhoff stress tensor that represents the force per unit area in the reference configuration (see Chandrasekharaiah and Debnath, 1994). In the more general scheme, the stress sij is referred to as the Cauchy stress tensor.
7) where eij ¼ The tensor eij is called the strain tensor, while uij is referred to as the rotation tensor. 6) thus imply that for small deformation theory, the change in the relative position vector between neighboring points can be expressed in terms of a sum of strain and rotation components. 8) 34 CHAPTER 2 Deformation: Displacements and Strains Because we are considering a general displacement field, these results include both strain deformation and rigid-body motion. 15 that a dual vector ui can be associated with the rotation tensor such that ui ¼ À1/2εijkujk.