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Non-conservative problems of Leipholz’s composite beams considering shear deformation and rotary inertia effects

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Abstract

The non-conservative problems of the shear-flexible Leipholz’s type of laminated composite beams are studied based on the finite element method. A formal engineering approach of the mechanics of thin-walled laminated composite beams on the basis of kinematic assumptions consistent with Timoshenko beam theory is presented. The explicit expression for the shear stiffness of composite beam is derived from the energy equivalence. In the present finite element formulation, the shape functions which contain the shear stiffness are presented, and the effects of both transverse shear deformation and rotary inertia are included. The advantage of this formulation is that if a suitable value of the shear stiffness parameter is given, a specific composite beam model is then simulated without too much additional work to modify the original formulation. Then the evaluation procedure for the critical values of the divergence and flutter loads of the Leipholz’s type of composite beam is briefly introduced. In order to verify accuracy of the composite beam model and the numerical calculation applied, the critical loads of divergence and flutter, and the static deflection of beams are compared with those from available references. Especially, the important structural parameters such as shear deformation, rotary inertia, boundary condition, fiber angle change, and non-conservativeness factor on the divergence and flutter behavior of the Leipholz’s type of composite beams are parametrically investigated.

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Acknowledgments

This research was supported by a Grant (14CTAP-C077285-01-000000) from Infrastructure and transportation technology promotion research Program funded by MOLIT(Ministry Of Land, Infrastructure and Transport) of Korean government and a Grant (2013-R1A12058208) from NRF (National Research Foundation of Korea) funded by MEST (Ministry of Education and Science Technology) of Korean government.

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  1. Department of Architectural Engineering, Sejong University, 98 Kunja Dong, Kwangjin Ku, Seoul, 143-747, South Korea

    Nam-Il Kim & Jaehong Lee

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  1. Nam-Il Kim
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  2. Jaehong Lee
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Correspondence to Jaehong Lee.

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Kim, NI., Lee, J. Non-conservative problems of Leipholz’s composite beams considering shear deformation and rotary inertia effects. Meccanica 50, 2239–2256 (2015). https://doi.org/10.1007/s11012-015-0169-1

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  • DOI: https://doi.org/10.1007/s11012-015-0169-1

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