Lecture Jan 22 2014

Ij ji or xy yx xz zx yz zy

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Unformatted text preview: at a stressed point produces the result that the 3 x 3 array of the 9 stress components must be symmetric. ij ji or xy yx , xz zx , yz zy So the Equilibrium Equations can then be written as follows. ij ij , j bi 0 or bi 0 x j 1.6 Coordinate Transformation Consistent with the statement at the end of Section 1.4 on the previous page, the stress 3 x 3 array (2nd rank tensor) can be transformed at a point from one orthogonal (x, y, z) coordinate system to a differently oriented (rotated) orthogonal coordinate system, using the 3 x 3 array of the 9 direction cosines that relate the two coordinate systems. Stress is a 2nd rank tensor. A vector is a 1st rank tensor. What makes a tens...
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