Sensibilidad de estados críticos en inestabilidad estructural vía perturbaciones singulares

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. 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. The technique developed in this work employs singular perturbations and includes a methodology to identify the set of exponents for general cases of critical states. The classification of critical states in the general theory of elastic stability is obtained from the critical and the initial post-critical states. We show that the some type of classification can be obtained from a detailed investigation of the sensitivity of the critical states, without making use of the post-critical path.

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