On the physical significance of higher order kinematic and static variables in a three-dimensional shell formulation

By Manfred Bischoff, Ekkehard Ramm. 2000

168 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/20567b0002c15e1b037f3a846a8eed31299aaf81

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In Biomedical Engineering

In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery (2014, background): “Bischoff and Ramm [21] discussed the physical significance of higher order kinematic and static variables in a three dimensional shell formulation.”
3D-SHELL ELEMENTS AND THEIR UNDERLYING MATHEMATICAL MODEL (2004, unknown): “(6) Using (3), we obtain(13) gα = (δ λ α − ξ(3)bα)aλ , g3 = a3 , (7) and the following components for the 3D metric tensor gαβ = gα · gβ = aαβ − 2ξ(3)bαβ + (ξ(3))(2)cαβ , (8) gα3 = gα · g3 = 0 , (9) g33 = g3 · g3 = 1 .”
Unilateral non‐linear dynamic contact of thin‐walled structures using a primal‐dual active set strategy (2007, unknown): “Also, the normal strain enhancement in thickness direction, the so-called seventh parameter, is needed for a consistent solid shell formulation; locking phenomena are treated in the same manner as in the original formulation [27].”
An Alternative Positional FEM Formulation for Geometrically Non-linear Analysis of Shells: Curved Triangular Isoparametric Elements (2007, methodology): “[2] or Sansour and Kollman [6] for example, but to offer an alternative way to achieve the numerical procedure for geometrical non-linear analysis of shell using curved triangular (or any geometry) elements without the use of ‘cumbersome notations’, Bischoff and Ramm [7].”
Fully C1‐conforming subdivision elements for finite deformation thin‐shell analysis (2001, background): “For thick shells, the thickness stretching can be embedded simply into the kinematics and inserted directly into three-dimensional constitutive models ( [55, 15, 51, 10, 6, 50, 13] among others).”
A mixed shell formulation accounting for thickness strains and finite strain 3d material models (2008, methodology): “[9, 10, 11] applying the enhanced assumed strain method (EAS–method) [12].”
3D capability of refined GDQ models for the bending analysis of composite and sandwich plates, spherical and doubly-curved shells (2018, methodology): “The most popular numerical methods available in the literature are based on the weak formulation of the governing equations, a typical example is the Finite Element Method (FEM).”
Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics (2003, background): “in the localized effects due to the concentrated surface loading and the delamination of composite shells), (iv) Combination with regular solid-shell elements: transition elements are needed to connect rotational dofs and displacement dofs (e.g., [13] and the contact problem), (v) Through-the-thickn”