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A new assumed strain solid-shell formulation “SHB6” for the six-node prismatic finite element

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Abstract

This paper presents the development of a new prismatic solid-shell finite element, denoted SHB6, obtained using a purely three-dimensional approach. This element has six nodes with displacements as the only degrees of freedom, and only requires two integration points distributed along a preferential direction, designated as the “thickness”. Although geometrically three-dimensional, this element can be conveniently used to model thin structures while taking into account the various phenomena occurring across the thickness. A reduced integration scheme and specific projections of the strains are introduced, based on the assumed-strain method, in order to improve performance and to eliminate most locking effects. It is first shown that the adopted in-plane reduced integration does not generate “hourglass” modes, but the resulting SHB6 element exhibits some shear and thickness-type locking. This is common in linear triangular elements, in which the strain is constant. The paper details the formulation of this element and illustrates its capabilities through a set of various benchmark problems commonly used in the literature. In particular, it is shown that this new element plays a useful role as a complement to the SHB8PS hexahedral element, which enables one to mesh arbitrary geometries. Examples using both SHB6 and SHB8PS elements demonstrate the advantage of mixing these two solid-shell elements.

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Authors and Affiliations

  1. LEM3, UMR CNRS 7239, Arts et Métiers ParisTech, 4 rue A. Fresnel, 57078, Metz Cedex 03, France

    Vuong-Dieu Trinh & Farid Abed-Meraim

  2. LaMSID, UMR EDF/CNRS 2832, EDF R&D, 1 avenue du Général de Gaulle, 92141, Clamart Cedex, France

    Vuong-Dieu Trinh

  3. LaMCoS, UMR CNRS 5259, INSA de Lyon, 18-20 rue des Sciences, 69621, Villeurbanne Cedex, France

    Alain Combescure

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  1. Vuong-Dieu Trinh
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  2. Farid Abed-Meraim
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  3. Alain Combescure
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Correspondence to Farid Abed-Meraim.

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This paper was recommended for publication in revised form by Editor Maenghyo Cho

Vuong-Dieu Trinh graduated as a Civil Engineer from the National Civil Engineering School, Ha Noi, Vietnam in 2001. He received his M.S. in Structural Mechanics from École Nationale des Ponts et Chaussées, Paris in 2003 and his Ph.D in Structural and Applied Mechanics from Arts et Métiers ParisTech, Metz Campus in 2008. He is currently working as a Civil Engineer at Peikko Group Corporation, an international company.

Farid Abed-Meraim received his Ph.D in Theoretical and Applied Mechanics from École Polytechnique, Paris in 1999. He joined Arts et Métiers ParisTech, Metz Campus in 2000, where he is currently an Associate Professor at the LEM3 laboratory. His main research interests include structural stability (bifurcation) analysis of dissipative systems (elasto-plastic, visco-elastic and visco-plastic), material instability modeling in relation to the prediction of formability of metal sheets, as well as finite element technology (solid-shell formulations).

Alain Combescure graduated from École Polytechnique, Paris in 1973. After 20 years at the French Atomic Commission as a research engineer and team leader, working on the simulation of buckling under complex loads, he joined the LMT laboratory at ENS Cachan, where he has been working for six years as a Professor in the field of transient non-linear Mechanics. He was then appointed Professor at INSA Lyon and head of the LaMCoS laboratory. His main research interests concern fracture mechanics, phase transformation in metals, time space subdomain coupling, and X-FEM methods for transient crack propagation.

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Trinh, VD., Abed-Meraim, F. & Combescure, A. A new assumed strain solid-shell formulation “SHB6” for the six-node prismatic finite element. J Mech Sci Technol 25, 2345–2364 (2011). https://doi.org/10.1007/s12206-011-0710-7

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