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Localized compliance with Castigliano's theorem

I'm attempting to compile a local compliance matrix using Castigliano's theorem as described here. I'm having trouble with it and attempted to do a simple example by hand and picked the double cantilever beam specimen and analyzed it with Euler-Bernoulli beam theory (attached). Despite my best efforts, I can't reproduce the correct answer using the theorem as is but only if I modify the limits of integration.

I'd really appreciate any help towards revealing where I go wrong or what I've misunderstood!

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