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Trouble with algebra at the end of an elasticity problem

  1. Oct 14, 2012 #1


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    I have a spherical shell with inner radius [itex]a_{1}[/itex] and outer radius [itex]a_{2}[/itex]

    I have worked out that the tension at [itex]r=a_{1}[/itex] is

    ([itex]P_{1}[/itex] is pressure from the inside of the shell, causing the tension.

    Now if the shell is not very thick. [itex]t=a_{2}-a_{1}[/itex] is small. [itex]\frac{t}{a_1}<<1[/itex]

    and I should be able to show


    But I am not sure about the first step to take in getting there. Any ideas? Please help.
  2. jcsd
  3. Oct 14, 2012 #2


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    You can factor a difference of cubes.
  4. Oct 15, 2012 #3


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    Thank you
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