A refined non‐linear non‐conforming triangular plate/shell element

Abstract

SUMMARYA reÿned non-conforming triangular plate=shell element for geometric non-linear analysis of plates=shells using the total Lagrangian=updated Lagrangian approach is constructed in this paper based on the reÿned non-conforming element method for geometric non-linear analysis. The Allman's triangular plane element with vertex degrees of freedom and the reÿned triangular plate-bending element RT9 are used to construct the present element. Numerical examples demonstrate that the accuracy of the new element is quite high in the geometric non-linear analysis of plates=shells.

A 3-Node Co-Rotational Triangular Elasto-Plastic Shell Element Using Vectorial Rotational Variables

“…A flat shell element with 5 degrees-of-freedom per corner node can be obtained by combining a conventional triangular membrane element with a standard 9-dof triangular bending element. On the other hand, if several elements of this type sharing the same node are coplanar, it is difficult to achieve inter-element compatibility between membrane and transverse displacements, and the assembled global stiffness matrix is singular in shell analysis due to the absence of in-plane rotation degrees-of-freedom [9][10][11][12]34]. In addition, flat shell elements with 5 degrees-of-freedom per node lack proper nodal degrees of freedom to model folded plate/shell structures, making the assembly of elements troublesome [35].…”

Unsymmetric finite elements for mesh-distortion tolerance performance

“…Circular cylindrical shell subjected to a central point load, R = 2540mm, L = 254mm, t = 6.35mm, θ = 0.1rad, Young's modulus, E = 3.10275kN/mm 2 and Poisson's ratio, ν = 0.3 The converged solution of a 20 × 20 mesh of the 20-node hexahedron element of ANSYS is used as a reference solution for this problem. The performance of the present elementis comparable with the solutions yielded by ANSYS and the elements of Hsiao[138], and Zhang and Cheung[136]. As with the previous test problem, the distortions experienced by the element in the mesh are not distinct and hence, the advantage of US-HEXA20 element is not obvious.…”

“…A 27-element mesh of one quarter of a clamped circular plateTable 4.4 shows the dimensionless central deflection of the circular plate, w/t, of US-HEXA20 in comparison with the analytical solution of Chia[135]. The results obtained with the 20-node hexahedron element of ANSYS, the triangular plate/shell element of Zhang and Cheung[136] and the QS plate element of Pica et al[137] are also shown.The triangular plate-bending element of Zhang and Cheung[136] is a combination of Allman's triangular plate element with vertex degrees of freedom[71] and the refined non-conforming triangular plate-bending element RT9[185]. The 8-node serendipity plate element of Pica et al[137] is based on the Mindlin plate theory and is integrated using 2 × 2 quadrature rule for all bending, membrane and shear terms in the stiffness matrix.…”

“…18 shows the results ofTable 4.3 graphically. The linear solution obtained from the triangular plate/shell element of Zhang and Cheung[136] is also included inFigure 4.21 for reference. As observed fromTable 4.4 andFigure 4.21, the performance of US-HEXA20 is comparable with the other elements in consideration.…”

Linear and Geometrically nonlinear analysis of plates and shells by a new refined non-conforming triangular plate/shell element

“…In their work, the interelement displacement continuity was enforced in an average sense, which resulted in not only better convergence of the solution but also improvement of its accuracy. The efficiency of the RNEM has been manifested in analyses of static, dynamic, stability and geometrically nonlinear problems [23,[25][26][27][28][29][30][31].…”