A direct minimization technique for finding minimum energy configurations for beam buckling and post-buckling problems with constraints

We present a novel technique to simulate the deformation of a cantilever elastic beam constrained in a curved solid channel subject to end forces. We pose this as the minimization of an energy functional and solve it by a variant of a dynamic programming approach called the Viterbi algorithm. The core idea of this approach is to discretize the variables describing the potential energy and to construct a set of admissible configurations of the beam. The Viterbi algorithm is then employed to search through the set of possible beam configurations and locate the one with the minimum potential energy in a very computationally efficient way. The new approach does not require any gradient computations and could be considered as a direct search method, and thus can be guaranteed to find the global minimum potential energy. Also the constraints can be automatically satisfied by constructing the proper set of all the possible configurations. The approach can also be used to find feasible starting configurations associated with conventional minimizing algorithms.