Orthotropic rotation-free basic thin shell triangle

SUMMARYIn this paper, a rotation-free triangle is formulated. Unlike the thin and degenerated shell finite element models, rotation-free triangles employ translational displacements as the only nodal DOFs. Compared with the existing rotation-free triangles, the present triangle is simple and physical yet its accuracy remains competitive. Using a corotational approach and the small strain assumption, the tangential bending stiffness matrix of the present triangle can be approximated by a constant matrix that does not have to be updated regardless of the displacement magnitude. This unique feature suggests that the triangle is a good candidate for fabric drape simulation in which fabric sheets are often flat initially and the displacement is much larger than those in conventional shell problems. Nonlinear shell and fabric drape examples are examined to demonstrate the efficacy of the formulation.

Section: Hemispherical Shell Subjected To Alternating Radial Forcessupporting

confidence: 88%

A geometric nonlinear rotation‐free triangle and its application to drape simulation

Zhou

Sze

2011

“…Such an approach, while circumventing some difficulties with other versions of the rotation‐free shell formulations by the same group (e.g. ) introduces new ones. In particular, as is well known, the curved isoparametric elements are prone to membrane locking .…”

Section: Finite Element Approximationmentioning

confidence: 99%

“…In Figure 3, the 'load-displacement' curves are shown for two irregular meshes with 222 (dashed line) and 894 (solid line) elements. The results of [23] and [9] are also shown in that figure and are marked with triangles and solid circles, correspondingly. One can see that the results obtained using the formulation presented herein are in good agreement with those available in the literature.…”

Section: Plate Under Uniformly Distributed Load Static Problemmentioning

confidence: 99%

“…Comparisons between the predictions of the new model and these solutions show that the new model accurately reproduces complex nonlinear analytical solutions as well as solutions obtained using existing, more complex finite element formulations.At approximately the same time with the contributions of Phaal and Calladine [3], Oñate and Cervera [5] presented their rotation-free formulation for plates. This was followed by a series of articles dealing with rotation-free formulations for large deformations of shells [6][7][8][9]. As in the approach of Phaal and Calladine [3], the basic idea in the work of Oñate et al was to define the curvature within a given triangle in terms of displacements at the nodes of a patch of elements, consisting of that triangle and its three neighbors.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear rotation‐free three‐node shell finite element formulation

Stolarski

Gilmanov

Sotiropoulos

2013

SUMMARYA new triangular thin‐shell finite element formulation is presented, which employs only translational degrees of freedom. The formulation allows for large deformations, and it is based on the nonlinear Kirchhoff thin‐shell theory. A number of static and dynamic test problems are considered for which analytical or benchmark solutions exist. Comparisons between the predictions of the new model and these solutions show that the new model accurately reproduces complex nonlinear analytical solutions as well as solutions obtained using existing, more complex finite element formulations. Copyright © 2013 John Wiley & Sons, Ltd.

“…As an extension of the original BST element, the basic shell quadrilateral element and the enhanced basic shell triangle element are further derived by the authors in the following years. Because the BST element exhibits good performance in thin shell problems, researchers then applied it to geometrically nonlinear analysis of orthotropic shells and obtained very accurate results. On an other front of development of rotation‐free methodology, Sabourin and Brunet proposed the so‐called triangular S3 and quadrilateral S4 shell elements by expressing the ‘side rotation’ with the displacements of the surrounding nodes when constructing the bending curvature.…”

Section: Introductionmentioning

confidence: 99%

A rotation‐free shell formulation using nodal integration for static and dynamic analyses of structures

Wang

Cui

2015

SUMMARYThis paper proposed a rotation-free thin shell formulation with nodal integration for elastic-static, free vibration, and explicit dynamic analyses of structures using three-node triangular cells and linear interpolation functions. The formulation is based on the classic Kirchhoff plate theory, in which only three translational displacements are treated as the filed variables. Based on each node, the integration domains are further formed, where the generalized gradient smoothing technique and Green divergence theorem that can relax the continuity requirement for trial function are used to construct the curvature filed. With the aid of strain smoothing operation and tensor transformation rule, the smoothed strains in the integration domain can be finally expressed by constants. The principle of virtual work is then used to establish the discretized system equations. The translational boundary conditions are imposed same as the practice of standard finite element method, while the rotational boundary conditions are constrained in the process of constructing the smoothed curvature filed. To test the performance of the present formulation, several numerical examples, including both benchmark problems and practical engineering cases, are studied. The results demonstrate that the present method possesses better accuracy and higher efficiency for both static and dynamic problems.