DERIVATION OF EULER BUCKLING EQUATION FROM CONTINUUM AT FINITE DEFORMATION STATE

抄録

 In this paper, we study Euler’s theory of column buckling based on continuum mechanics. The key point is the use of a recursive-form function for displacement at a finite deformation state. It is shown that the governing equation of Euler’s theory can be derived from a functional of a linearly elastic continuum by using the recursive-form displacement, and analytical solutions are obtained by solving the resulting nonlinear differential equation. The load coincides with that predicted by the original theory, but the mode is slightly different due to the effect of finite deformation. Discussions are made on the results obtained for the column buckling equation considering finite deformation.