Un Método de Menor Degeneración para Problemas de Perturbación Singular

Abstract

In this work, we describe a direct procedure for obtaining the relationships between the critical loads, the critical coordinates, and the amplitude of the imperfection. For critical states characterized as bifurcations the zeros of the
first and second variations of the potencial energy of the perfect system are always repeated roots. Thus, the expansions of the critical loads and coordinates do not go in integrer powers of the imperfection parameter, and regular perturbation methods are not applicable. In the present approach we assume the expansions for the critical loads and corresponding coordinates in terms of arbitrary powers of the imperfections parameter. Then by the principle of least degeneracy, we determine the exponents and the coefficients of the expansions.