Effects of surface deformation on the collective buckling of an array of rigid beams on an elastic substrate

We analyze the collective buckling of a row of rigid beams with their lower ends built into an elastic substrate.The beams interact among themselves through the deformation of the substrate.The present analysis is more sophisticated than previous ones in that the lower ends of the beams are allowed to move vertically and horizontally, in addition to rotation.From the linear theory of elasticity and rigid body statics, an eigenvalue problem is formulated and solved.Calculations showed that periodic deformations resulted atop the compliant substrate after restrictions on the beam base displacements were released.Consequently, the refined model found good match with the height measurements from Atomic Force Microscope (AFM).Our work suggests that both the compliant substrate and the interaction of neighboring beams through the deformation of the substrate dominate the collective buckling.Furthermore, these results contribute toward the understanding, design and application of soft nanostructures produced by soft lithography in a variety of fields.