By Francis K. Mason
London released WW II - Air
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6) establishes the relation between the two variables, thereby indicating that each traction component can be expressed as a linear combination of particular stress components. 2 when boundary condition development is presented. Following the principles of small deformation theory, the previous definitions for the stress tensor and traction vector do not make a distinction between the deformed and undeformed configurations of the body. As mentioned in the previous chapter, such a distinction only leads to small modifications that are considered higher-order effects and are normally neglected.
Using Cartesian coordinates, define the displacement vectors of points Po and P to be uo and u respectively. 1) where u, v, w are the Cartesian components of the displacement vector. 2 General Deformation Between Two Neighboring Points. 1 General deformations 33 Note that the higher-order terms of the expansion have been dropped since the components of r are small. 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.
7) must be the same for any curve C; that is, the integral must be independent of the path of integration. This implies that the integrand must be an exact differential, so that the value of the integral depends only on the end points. Invoking Stokes theorem, we can show that if the region is simply connected (definition of the term simply connected is postponed for the moment), a necessary and sufficient condition for the integral to be path independent is for Uik,l ¼ Uil,k. 2) are the necessary and sufficient conditions for continuous, singlevalued displacements in simply connected regions.
Avro Lancaster II by Francis K. Mason