Buckling of unilaterally constrained columns by complementarity eigenvalue analyses

•Buckling of elastic columns in the presence of rigid obstacles is formulated in terms of an eigenvalue complementarity problem.•The resolution of the eigenvalue complementarity problem for the computation of bifurcation loads and instability modes by a semismooth Newton method is proposed.•The unilateral constraints materialized by the obstacles are rigorously satisfied without penalty-type techniques.•The algorithm is able to compute all the lower order modes with a relatively small grid of initial values. A numerical approach for the study of the elastic buckling of slender columns with unilateral supports is proposed. This new approach is based on the numerical solution of a special type of eigenvalue problems that takes into account the complementarity character of the pair (displacement, obstacle reaction) at each unilateral support. The implementation of the proposed approach is illustrated by the determination of bifurcation loads and corresponding modes for several finite element models of columns.