Solution methods for the growth of a repeating imperfection in the line of a strut on a nonlinear foundation

Using the Galerkin method, we then establish an exact formula for this maximum imperfection size and we show that it does not depend on the choice of the restoring force. We also show that this method provides a better estimate with respect to previous publications. The decrease in the maximum compressive force supported by the beam as a function of the imperfection magnitude is also determined. We show that the leading term of the development has a different exponent than in subcritical buckling of elastic systems, and that the exponent values depend on the choice of the restoring force.