The present paper is made up of two parts. In the first part, we study the mathematical stability and convergence of the quadrilateral MITC elements for the Reissner-Mindlin plate problem in an abstract setting. We generalize the Brezzi-Bathe-Fortin conditions to the quadrilateral MITC elements by weakening the second and fourth conditions. Under these conditions, we show the well-posedness of ...

We will prove two conditions for a tangential quadrilateral to be cyclic. According to one of these, a tangential quadrilateral is cyclic if and only if its Newton line is perpendicular to the Newton line of its contact quadrilateral.

In the present paper, a comparison between five different shell finite elements, including the Linear Triangular Element, Linear Quadrilateral Element, Linear Quadrilateral Element based on deformation modes, 8-node Quadrilateral Element, and 9-Node Quadrilateral Element was presented. The shape functions and the element equations related to each element were presented through a detailed mathem...

Subelement patterns using bisection of edges and schemes for selecting edges to be split are described for the local refinement of elements in all-quadrilateral and quadrilateral-dominant planar meshes. Subelement patterns using trisection of edges are also described for the local refinement of elements in all-quadrilateral planar meshes. These patterns and schemes are easily extendible to quad...

Abstract A polygon P is called a reptile, if it can be decomposed into $$k\ge 2$$ k ≥ 2 nonoverlapping and congruent polygons similar to . We prove that cyclic quadrilateral then trapezoid. Comparing with results of Betke Osburg we find every convex rep...

We present a new and efficient method to compute the intersection point between a convex planar quadrilateral and a ray. Contrary to other methods, the bilinear coordinates of the intersection point are computed only for rays that hit the quadrilateral. Rays that do not hit the quadrilateral are rejected early. Our method is up to 40% faster compared to previous approaches.

We present a new definition of distortion and quality measures for high-order hexahedral (quadrilateral) elements. This definition leads to two direct applications. First, it can be used to check the validity and quality [1] of a high-order hexahedral (quadrilateral) mesh. Second, it allows the generation of high-order curved meshes [2, 3, 4, 5] composed of valid and high-quality hexahedral (qu...

A multilevel adaptive refinement technique is presented for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are re...

A P1-nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements, which contain quadratic polynomials or polynomials of degree greater than 2, our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges. One of the benefits of using our elem...

Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the mot...