Hierarchical Beam Finite Elements Based Upon a Variables Separation Method

Abstract : A family of hierarchical one-dimensional beam finite elements developed within a vari-ables separation framework is presented. A Proper Generalized Decomposition (PGD) is used to divide the global three-dimensional problem into two coupled ones: one defined on the cross-section space (beam modeling kinematic approximation) and one belonging to the axis space (finite element solution). The displacements over the cross-section are approximated via a Unified Formulation (UF). A Lagrangian approximation is used along the beam axis. The resulting problems size is smaller than that of the classical equiv-alent finite element solution. The approach is, then, particularly attractive for higher-order beam models and refined axial meshes. The numerical investigations show that the proposed method yields accurate yet computationally affordable three-dimensional displacement and stress fields solutions.
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G. Giunta, S. Belouettar, O. Polit, L. Gallimard, P. Vidal, et al.. Hierarchical Beam Finite Elements Based Upon a Variables Separation Method. International Journal of Applied Mechanics, 2016, 8 (2), pp.1650026. ⟨10.1142/S1758825116500265⟩. ⟨hal-01367029⟩

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