A new least-squares DQ-based method for the buckling of structures with elastic supports

This note introduces a new computational scheme based on a numerical Picard-like method, which combines successive approximations with differential quadrature rules in order to improve the computational efficiency. Despite of its recursive nature, this scheme can generate the approximate solution in terms of operational matrices and vectors of known quantities. This allows to define explicitly an error functional which can be minimized in order to easily compute the critical load. The performance of this new scheme is examined by means of two application examples. A comparison with the available solutions is carried out, by showing that the method behaves satisfactorily.