Example : Rotating Rectangular Beam
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The body force potential is given by
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Hence,
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or,
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The compatibility condition (in terms of stress) is
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Plug in to get
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Since is even in and and BCs are homogeneous, assume
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Hence,
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The traction BCs are
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Apply BCs at .
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Therefore,
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We then have,
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Plug into compatibility equation
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to get
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or,
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Apply BCs at .
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Strong BCs imply that
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which cannot be true. So weak BCs on need to be applied at .
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Hence,
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or,
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Hence,
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The stress field is, therefore,
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or,
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The displacements can be found in the standard manner.
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