The eigenvalue problem associated with the nonlinear buckling of a shear bending column
2011
This paper discusses the eigenvalue problem of a nonlinear differential equation that governs the stability of a shear
bending column under extremely large deformation. What is taken into consideration is the geometrical nonlinearity
while the material is supposed to be linear. The reason of a superbly stable buckling behavior of a slender rubber bearing
is physically explained by pointing out the analogy that is similar to the nonlinear wave propagation expressed in KdV
equation. The nonlinear boundary condition and the nonlinear term of the differential equation cancel each other and
make the associated eigenvalue rather constant. In other words, as far as the material is supposed to be linear, the column
does not buckle no matter how large the deformation is. This theoretical prediction is experimentally verified and
successfully applied to a base isolation system of a lightweight structure.
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