Assumed natural strain and stabilized quadrilateral Lobatto spectral elements for C0 plate/shell analysis

Abstract

SummaryLobatto elements are high order or spectral elements featured by non‐equispaced Lobatto nodes and the Lobatto nodal quadrature. The tensor product nature of the element interpolation allows the derivatives at the node be computed through the derivatives along the nodal line which involve only 1D interpolations. In this paper, generic schemes for formulating assumed natural strain and stabilized Lobatto Lagrange C0 plate/shell elements of order 2 are presented. Two assumed natural strain schemes are devised. Both schemes sample the normal membrane and transverse shear natural strain components at the 1D reduced‐order Gaussian quadrature points along the nodal lines. The difference is that the first and second schemes sample the membrane shear natural strain component at the Lobatto nodes and the 2D reduced‐order Gaussian quadrature points, respectively. Meanwhile, all the other natural strain components in both schemes can be obtained by 1D interpolation along the nodal lines. In the stabilization scheme for reduced‐integrated elements, only five stabilization vectors are required regardless of the element order. The new elements outperform the standard Lobatto element except when membrane‐dominated curved thin‐shell problems with strong boundary layer effect are considered by coarse meshes. Copyright © 2016 John Wiley & Sons, Ltd.