A methodology for quadrilateral finite element mesh coarsening

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedral meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. In addition, this method appears to be extensible to hexahedral meshes in three dimensions. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under Contract DE-AC04-94AL85000.     

Development of panel generation system for seakeeping analysis

In this paper, a panel generation system for analyzing seakeeping performance of a ship is developed. Given a set of offset data representing the ship hull, the system first creates a surface model of the ship. From the surface model, the wetted part of the ship is obtained by computing the intersection between the water surface and the hull, which is then processed to generate quadrilateral panels for the hull and the water surface. The system is designed to handle various kinds of ships such as ships with a mono-skeg, a twin-skeg and/or a bulbous bow in either an automatic or an interactive manner. Moreover, it can generate input panels for three different seakeeping analysis methods. Examples are provided to demonstrate the capabilities of the system.     

Template-based quadrilateral meshing

Generating quadrilateral meshes is a highly non-trivial task, as design decisions are frequently driven by specific application demands. Automatic techniques can optimize objective quality metrics, such as mesh regularity, orthogonality, alignment and adaptivity; however, they cannot make subjective design decisions. There are a few quad meshing approaches that offer some mechanisms to include the user in the mesh generation process; however, these techniques either require a large amount of user interaction or do not provide necessary or easy to use inputs. Here, we propose a template-based approach for generating quad-only meshes from triangle surfaces. Our approach offers a flexible mechanism to allow external input, through the definition of alignment features that are respected during the mesh generation process. While allowing user inputs to support subjective design decisions, our approach also takes into account objective quality metrics to produce semi-regular, quad-only meshes that align well to desired surface features.     

Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes

We propose a discrete approximation of Gaussian curvature over quadrilateral meshes using a linear combination of two angle deficits. Let g_ij and b_ij be the coefficients of the first and second fundamental forms of a smooth parametric surface F. Suppose F is sampled so that a surface mesh is obtained. Theoretically we show that for vertices of valence four, the considered two angle deficits are asymptotically equivalent to rational functions in g_ij and b_ij under some special conditions called the parallelogram criterion. Specifically, the numerators of the rational functions are homogenous polynomials of degree two in b_ij with closed form coefficients, and the denominators are . Our discrete approximation of the Gaussian curvature derived from the combination of the angle deficits has quadratic convergence rate under the parallelogram criterion. Numerical results which justify the theoretical analysis are also presented.     

Fabrication and mechanical properties of Al2O3–TiC ceramic composites synergistically reinforced with multi-walled carbon nanotubes and graphene nanoplates

In this study, Al₂O₃–TiC composites synergistically reinforced with multi-walled carbon nanotubes (MWCNTs) and graphene nanoplates (GNPs) were prepared via spark plasma sintering (SPS). The effects of the MWCNT and GNP contents on the phase composition, mechanical properties, fracture mode, and toughening mechanism of the composites were systematically investigated. The experimental results indicated that the composite grains became more refined with the addition of MWCNTs and GNPs. The nanocomposites presented high compactness and excellent mechanical properties. The composite with 0.8 wt% MWCNTs and 0.2 wt% GNPs presented the best properties of all analysed specimens, and its relative density, hardness, and fracture toughness were 97.3%, 18.38 ± 0.6 GPa, and 9.40 ± 1.6 MPa m^1/2, respectively. The crack deflection, bridging, branching, and drawing effects of MWCNTs and GNPs were the main toughening mechanisms of Al₂O₃–TiC composites synergistically reinforced with MWCNTs and GNPs.     

Polarized Optoelectronics of CsPbX3 (X = Cl,Br, I) Perovskite Nanoplates with Tunable Size and Thickness

Low dimensional semiconductor nanomaterials have shown their tailorable properties for a variety of promising applications in decades. Here a general strategy to synthesize all‐inorganic CsPbX₃ (X = Cl, Br, I or their mixture) perovskite 2D nanoplates by introducing additional metal halides MX'₂ or MX'₃ (M = Cu, Zn, Al or Pb, etc.; X' = Cl, Br or I) is reported. These CsPbX₃ perovskite nanoplates have uniform thickness and tunable size, which can be feasibly controlled by the component and ratio of the metal halides, temperature, time, and ligands. The well‐defined morphology of the nanoplates makes them ideal building blocks for the self‐assembly in the face‐to‐face and column‐by‐column arrangement. Compared to the optically isotropic CsPbX₃ nanocubes, the 2D CsPbX₃ nanoplates exhibit remarkable polarized UV–vis absorption and photoluminescence not only in liquid solvent and solid resin matrix, but also in self‐assembled films. An optoelectronic photodetector sensitive for linear polarized light is fabricated to demonstrate the proof‐of‐concept.     

Automatic generation of quadrilateral finite element meshes

This paper describes an efficient, accurate and simple implementation of an algorithm for generation of quadrilateral finite element meshes. An original algorithm by Talbert and Parkinson [J.A. Talbert, A. Parkinson, Development of an automatic two-dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition, Int. J. Numer. Meth. Eng., 29 (1990) 1551–1567], has been substantially redeveloped and modified and presented in greater detail. We cover several important issues omitted in publication mentioned and we will provide interested readers with fully documented source code of the program.     

Planar quadrilateral quality measures

This article examines the quality assessment of planar quadrilateral mesh elements in a comprehensive way. First, an analytic characterization of quadrangular shape is provided, and existing concepts of stretching and skewness, earlier proposed for specific geometries, are generalized. Then, two triangle quality measures are extended to quadrilaterals and their respective extremal and asymptotic behaviors examined, showing in particular that even if needed they cannot detect the triangular degeneracy of a quadrilateral. An existing quality measure is then discussed, which is able to handle this case. In particular, an unbalanced asymptotic behavior is demonstrated, justifying the need for a new approach. Toward this goal, the triangle quality measure based on Frobenius norm is modified in order to replace equilateral reference element by right isosceles triangles, with control on the specific right angle. Finally, two new quadrilateral quality measures are designed and examined using these results. Numerical results illustrate the matter.