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A novel updated Lagrangian complementary energy-based formulation for the elastica problem: force-based finite element model

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Abstract

This paper addresses the development of a novel updated Lagrangian variational formulation and its associated finite element model for the geometrically nonlinear quasi-static analysis of cantilever beams. The formulation is based on an incremental complementary energy principle. The proposed finite element model only contains nodal bending moments as degrees of freedom. The model is used for the analysis of problems modeled by the so-called elastica theory. Numerical solutions satisfying all equilibrium equations in a strong sense can be obtained for arbitrarily large displacements and rotations. A Newton–Raphson method is adopted to trace the post-buckling response. Numerical results are presented and compared with those produced by the standard total Lagrangian two-node displacement-based finite element model.

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  1. Instituto Superior de Educação e Ciências, Alameda das Linhas de Torres 179, 1750-142, Lisboa, Portugal

    H. A. F. A. Santos

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Santos, H.A.F.A. A novel updated Lagrangian complementary energy-based formulation for the elastica problem: force-based finite element model. Acta Mech 226, 1133–1151 (2015). https://doi.org/10.1007/s00707-014-1237-7

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  • DOI: https://doi.org/10.1007/s00707-014-1237-7

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