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MATLAB optimization toolbox for minimizing energy of a beam

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I am working with a modified Euler Bernoulli beam. The energy functional is a function of curvature (theta') and also the slope (tan(theta)). I want to obtain the theta profile which minimizes the energy. The problem is defined on the domain which spans the length of the beam (0 to L). The beam is inextensible so that can be included in the energy functional with a Lagrange multiplier. I have been looking up a lot of examples and documentation but I can't figure out if MATLAB optimization can handle this sort of problem, where the derivatives are also included. Any suggestions or additional information would be very appreciated. Thanks in advance!

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