An efficient three-node triangular Mindlin–Reissner flat shell element

Abstract

Shell elements are extensively used by engineers for modeling the behavior of shell structures. Among common shell elements, triangular shell elements are not influenced by element warping. This paper proposes a new three-node triangular flat shell element with six degrees of freedom per each node, named TMRFS. The element is formed by assemblage of new bending and membrane elements. The bending element is formulated based on the hybrid displacement function element method and Mindlin-Reissner plate theory. In this element, an assumed displacement function is employed as the trial function. The membrane component is an unsymmetric triangular membrane element with drilling vertex rotations. The membrane element employs two different types of displacement fields as the test and trial functions. The test function is a displacement field which is the same as one used in well-known Allman triangular element. Meanwhile, instead of displacement field, the analytical stress field is considered as the trial function. Numerical tests show that the accuracy of the proposed flat shell element is reasonable in comparison with some popular triangular elements and its performance is insensitive to geometry, load and boundary conditions. Moreover, the proposed element preserves the advantages of its formulation including free of membrane locking, shear locking and stiffness matrix singularity problems.

Robust flat‐facet triangular shell finite element

“…Regular mesh, with equal number of element edges per side of the modeled quarter of the shell in both directions. Comparison with other triangular elements: 23 Allman, 10 ProvKat, 22 Cook, 11 SL, 42 MITC3+. 37 Results scaled with (−100∕0.300592437) communication 40 has provided a more precise number of −0.300592437, which is used in Figure 13 to (re)normalize results from the literature in comparison with our own results.…”

“…In either method, there may be user‐tunable parameters upon which the accuracy or stability would depend. That is a problem: If the drilling rotation was coupled to the bending action, an excessive stiffness in the membrane drilling rotation would deleteriously affect inextensible bending 23 . On the other hand, too small of a drilling stiffness would destroy the condition number of the stiffness matrix.…”

“…That is a problem: If the drilling rotation was coupled to the bending action, an excessive stiffness in the membrane drilling rotation would deleteriously affect inextensible bending. 23 On the other hand, too small of a drilling stiffness would destroy the condition number of the stiffness matrix. Recently, some advances have been reported that reduced or eliminated the dependence of the solution on the drilling stiffness parameters.…”

“…Regular mesh, with equal number of element edges per side of the modeled quarter of the shell in both directions. Comparison with other triangular elements: 23 Allman, 10 ProvKat, 22 Cook, 11 SL, 42 MITC3+ 37 . Results scaled with ()…”

A higher order triangular plate finite element using Airy functions

“…To solve this problem, many methods was been introduced. We illustrated them without limitation: the hybrid mixed variational method 8 using shear strain interpolation obtained by Timoshenko's beam functions, 9 the smoothed finite element method, 10 -the combined hybrid method, 11 the discrete shear gap method, 12 -the enhanced assumed strain method, 13 polygonal finite element method, 14 hybrid displacement function element method and Mindlin-Reissner plate theory, 15 and the hybrid-Trefftez method used by Rezaiee-Pajand and Karkon 16 developing finite elements based on two independent displacement fields (internal and at the limits). Furthermore, other methods was been used by a multitude of researchers based, particularly, on selective integration, Hourglass mode, substitution strain method and the strain approach used in finite element formulations.…”