Chapter 10: Q11P (page 528)
:Do Problem 5 for the coordinate systems indicated in Problems 10 to 13.Eliptical cylinder.
Short Answer
The required values are mentioned below.
Chapter 10: Q11P (page 528)
:Do Problem 5 for the coordinate systems indicated in Problems 10 to 13.Eliptical cylinder.
The required values are mentioned below.
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If P and S are -rank tensors, show that coefficients are needed to write each component of P as a linear combination of the components of S. Show that is the number of components in a -rank tensor. If the components of the -rank tensor are , then equation gives the components of P in terms of the components of S. If P and S are both symmetric, show that we need only 36different non-zero components in . Hint: Consider the number of different components in P and S when they are symmetric. Comment: The stress and strain tensors can both be shown to be symmetric. Further symmetry reduces the 36components of C in (7.5)to 21or less.
Show that, in polar coordinates, thecontravariant component of dsis which is unitless, the physical component of ds is which has units of length, and thecovariant component of ds iswhich has units role="math" localid="1659265070715" .
Using (10.15) show thatis a-rank covariant tensor. Hint:Write the transformationequation for each, and set the scalarto find the transformationequation for.
Verify equations(2.6).
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