Formulation and evaluation of new triangular, quadrilateral, pentagonal and hexagonal discrete Kirchhoff plate/shell elements

Abstract

SUMMARYThe paper deals with the formulation of plate and shell elements based on the discrete Kirchho technique. In the ÿrst part we review the at facet shell elements which have been formulated during the last 30 years. In the second part, we present the formulation of a new family of discrete Kirchho plate=shell elements based on the free formulation. The triangular, quadrilateral, pentagonal and hexagonal elements belong also to the family of semi-Loof elements having only displacements at the corner nodes and one tangential rotation along each side.

Rotation shape functions for a low‐order quadrilateral plate element with mid‐side rotations

“…Instead they are designed to ensure that the nodal rotations are the average of the rotations along the side so that, having also preserved a linear rotation ÿeld, the element passes the patch test. To illustrate the former, we will consider side 3 where Á = 1 and using Equation (2) can easily obtain…”

“…It can be considered to be part of a family of 'discrete Kirchho ' elements [2]. It is non-conforming but passes the patch test and has a nodal conÿguration with a translation at each corner node and a rotation about the side at each mid-side node.…”

A posteriori error analysis for the Morley plate element with general boundary conditions

“…The corner points of the domain Ω are now (0, 0), (1, 0), (1, 2.5), (2, 1), (3, 2.5), (3, 0), (4, 0), (4,4), (3,4), (2, 2.5), (1,4) and (0, 4).…”

“…Regarding the finite element methods for the Kirchhoff-Love plate model, there exists various classical [2,23,12] and more recent [15,14,3,17,5,7] non-standard finite elements which avoid using high-order polynomial spaces of conforming, globally C 1 -continuous elements [12,10]. The variety of a posteriori error analysis for Kirchhoff plate elements, instead, is still quite limited [11,24,5,7,6].…”

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

“…However, in the strict sense of the word those models cannot be shown to be displacement models because the additive shear strain does not relate to the displacements of a single element. Batoz et al [40] reviewed the discrete Kirchhoff flat shell elements for the linear analysis of plates and shells.…”