Detailed formulation of the rotation‐free triangular element “S3” for general purpose shell analysis

Abstract

Purpose

The aim of this paper is to present an enriched formulation of a rotation‐free (RF) triangular shell element in order to use it for shells of general shapes while, up to now, it is limited to shells without branching surfaces and progressive variations in terms of material behavior and thickness.

Design/methodology/approach

The formulation keeps the main characteristic of Morley's element: bending effects can be expressed with three “bending angles” only. But, for a RF element, these angles are defined with the rigid body rotations of the element itself and those of its neighbours. This usual formulation of a RF shell element can be extended provided that curvatures‐displacements relation involves the material characteristics of the element itself and of its neighbours and the same goes for thickness.

Findings

Numerous examples with regular and irregular meshes of structures involving branching surfaces point out convergence and accuracy. Large displacement analyses – including crash simulations – show the effectiveness, too. A deep‐drawing of a “U” shape and the following springback prediction highlight the fact that the curvatures are captured more exactly (when nodes slide on die radius) since they are imposed in terms of translations whereas they are traditionally computed with nodal rotations not managed by contact conditions on the tooling.

Practical implications

The “S3” element detailed here is implemented in RADIOSS^® software. The general conclusions are that this triangle often gives almost the same result as “DKT18” but is two times less cheaper and it is found interesting for sheet forming simulations.

Originality/value

Specificity of such an element clearly appears while lifting the initial restrictions quoted before.

Citation

Sabourin, F. and Brunet, M. (2006), "Detailed formulation of the rotation‐free triangular element “S3” for general purpose shell analysis", Engineering Computations, Vol. 23 No. 5, pp. 469-502. https://doi.org/10.1108/02644400610671090