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...

This work aims at presenting a novel four-node quadrilateral element, which is enhanced by integrating with discrete shear gap (DSG), for analysis of Reissner-Mindlin plates. In contrast to previous studies that are mainly based on three-node triangular elements, here we, the first time, extend DSG elements. We further integrate fictitious point located center element into present formulation e...

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...

This article presents the characteristics of changes in hearing and cerebral hemadynamics patients with deviation nasal septum. The septum occurs cartilaginous bone regions, both separately at same time. Deformations can be a different nature (bend, crest, spike) localization. They are one two-sided. Spines ridges more often localized junction quadrangular cartilage perpendicular plate, ploughs...

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...

Abstract The virtual element method allows to revisit the construction of Kirchhoff-Love elements because $$C^1$$ C 1 -continuity condition is much easier handle in VEM framework than traditional Finite Elements methodology. Here we study two most simple suitable for pl...

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...

This paper presents global and point-wise comparisons of experimental measurements and numerical simulation results of electro-osmotically driven flows in two elementary micro-channel configurations, a straight channel with a groove and a T-junction channel. The microchannels are made by photolithography using poly-dimethylsiloxane (PDMS), a type of silicon product, which is transparent, and el...