A new shell formulation using complete 3D constitutive laws

This paper should not be only regarded as a presentation of new shell elements but rather as a methodology which can be applied to most classical shell elements and has two aims: Achieving the same results in bending cases while breaking from plane stress state hypothesis and adding a normal stress component for process simulations such as hydro‐forming, hemming, sheet metal forming with bottoming, flanging, incremental forming and so on. Owing to the non‐linear applications quoted before, only shell elements with one integration point on the mid‐plane are selected: Triangles that are naturally constant strain elements and reduced integration quadrilaterals. The method mainly consists of adding a central node at the center (of gravity for a triangle) with two degrees of freedom: Two translations normal to the mid‐surface for which one corresponds to the bottom surface (‘lower skin’ of the shell) and the other to the top surface (‘upper skin’ of the shell). Then a full 3D constitutive strain–stress behavior can be used. For triangles in bending state—either based on Kirchhoff's or on Mindlin's assumptions—, it is shown that the results are exactly the same as those given by the initial formulation of these elements using a plane stress hypothesis. For quadrilaterals, the results are slightly different but many numerical examples—including non‐linear computations—prove that those differences are not significant. Copyright © 2010 John Wiley & Sons, Ltd.

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