Generalized shooting method for elastic stability analysis and optimization of structural members

Various methods are reviewed and the generalized shooting method for determining the elastic buckling loads of structural members is considered. Since the shooting method requires solving the equations representing the terminal boundary conditions as functions of the eigenvalue and other unknown parameters, the gradient expressions for the functions are presented for a more efficient iterative method. The shooting method has several advantages which will be highlighted through some buckling problems. Finally, as the gradient formulae are derived from optimal control theory, the generalized shooting method can be naturally embedded into a combined optimal control and optimal parameter selection approach for optimization purposes.

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