Continuité et différentiabilité d'Éléments propres: Application à l'optimisation de structures

The buckling load of a structure may usually be computed with an eigenvalue problem: it is the eigenvalue of smallest absolute value. In optimizing structures with a constraint on the buckling load, repeated eigenvalues are likely to occur. We prove continuity and differentiability results of eigenelements with respect to design variables using the variational characterization of eigenvalues. We illustrate these results with a classical problem: buckling of a beam. Application to arch buckling is presented in another article.