Buckling of a clamped strip‐like beam with a linear pre‐stress distribution

Abstract

A thin linear elastic strip is clamped at both ends and subjected to a linear stress distribution across its width. We use Kirchhoff beam theory to study this problem. If displacements out of the strips own plane are prohibited, the straight configuration remains stable as long as the compression is not too high. With the three‐dimensional spatial description of the rod theory, we find possible buckling modes even in the case of average tensile stresses in the beam. Comparison with shell and beam finite elements shows excellent agreement with the analytical investigation, also with respect to the supercritical behavior.

Non‐material finite element rod model for the lateral run‐off in a two‐pulley belt drive

“…It can be shown [19][20][21] that its actual components Ω 𝑘 and those of the undeformed reference state Ω 0 𝑘 form the strain measures 𝜅 𝑘 = Ω 𝑘 − Ω 0 𝑘 (12) for bending (𝜅 1 and 𝜅 2 ) and twisting (𝜅 3 ); see [11,20,22,23] for the actual computation of these components. A brief explanation on the relation between the local frame 𝐞 𝑘 and other the field variables is provided in the Appendix.…”

“…Static solutions using beam finite elements with the MEL formulation were already presented in [5] and [11] for a belt drive and in [12] for buckling of a clamped strip. For the analysis of the plane problem of a moving shear-deformable belt without imperfections we refer to [7].…”