Post-buckling of compound cantilever Elastica based on Galerkin finite element formulation

Abstract

The large deflection buckling of a compound cantilever column (Elastica), subjected to a free end concentrated compressive load, which always acts in the initial Cartesian x-direction, is studied, with different free end angles. The compound column consists of two segments of different materials. The Young's modulus of the material of the segment at the clamped end is E₁ and the same at the free end is E₂. The advantage of using the compound cantilever column and its production techniques are presented. The solution of the problem in the Cartesian system is complex, and hence the S system is used to obtain the simpler nonlinear differential equation. The Galerkin finite element formulation is used to obtain the solution of the Elastica problem and the difficulty in the assembly is discussed. The numerical results for uniform/compound cantilever columns match excellently with the literature values.

Keywords:

• large deflections
• post-buckling
• Elastica
• Galerkin finite element
• eigenvalue problem
• iterative solution

Acknowledgements

The authors would like to sincerely acknowledge the managements of their institutions during the course of this work.

Disclosure statement

No potential conflict of interest was reported by the authors.