All‐hexahedral mesh smoothing with a node‐based measure of quality

This research work deals with the analysis and test of a normalized‐Jacobian metric used as a measure of the quality of all‐hexahedral meshes. Instead of element qualities, a measure of node quality was chosen. The chosen metric is a bound for deviation from orthogonality of faces and dihedral angles. We outline the main steps and algorithms of a program that is successful in improving the quality of initially invalid meshes to acceptable levels. For node movements, the program relies on a combination of gradient‐driven and simulated annealing techniques. Some examples of the results and speed are also shown. Copyright © 2001 John Wiley & Sons, Ltd.     

Octree‐based reasonable‐quality hexahedral mesh generation using a new set of refinement templates

An octree‐based mesh generation method is proposed to create reasonable‐quality, geometry‐adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy‐to‐implement, easy‐to‐understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes. A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly. Laplacian‐like smoothing, angle‐based smoothing and local optimization‐based untangling methods are used with certain restrictions to further improve the mesh quality. Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries. Copyright © 2008 John Wiley & Sons, Ltd.     

Remeshing for metal forming simulations—Part II: Three‐dimensional hexahedral mesh generation

In the present study, a hexahedral mesh generator was developed for remeshing in three‐dimensional metal forming simulations. It is based on the master grid approach and octree‐based refinement scheme to generate uniformly sized or locally refined hexahedral mesh system. In particular, for refined hexahedral mesh generation, the modified Laplacian mesh smoothing scheme mentioned in the two‐dimensional study (Part I) was used to improve the mesh quality while also minimizing the loss of element size conditions. In order to investigate the applicability and effectiveness of the developed hexahedral mesh generator, several three‐dimensional metal forming simulations were carried out using uniformly sized hexahedral mesh systems. Also, a comparative study of indentation analyses was conducted to check the computational efficiency of locally refined hexahedral mesh systems. In particular, for specification of refinement conditions, distributions of effective strain‐rate gradient and posteriori error values based on a Z² error estimator were used. From this study, it is construed that the developed hexahedral mesh generator can be effectively used for three‐dimensional metal forming simulations. Copyright © 2002 John Wiley & Sons, Ltd.     

An unsymmetric 8‐node hexahedral element with high distortion tolerance

Among all 3D 8‐node hexahedral solid elements in current finite element library, the ‘best’ one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8‐node, 24‐DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8‐node trilinear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US‐ATFH8, contains no adjustable factor and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first‐order (constant stress/strain) patch test and the second‐order patch test for pure bending, remove the volume locking, and provide the invariance for coordinate rotation. Especially, it is insensitive to various severe mesh distortions. Copyright © 2016 John Wiley & Sons, Ltd.     

Applications of mesh smoothing: copy,morph, and sweep on unstructured quadrilateral meshes

Mesh smoothing is demonstrated to be an effective means of copying, morphing, and sweeping unstructured quadrilateral surface meshes from a source surface to a target surface. Construction of the smoother in a particular way guarantees that the target mesh will be a ‘copy’ of the source mesh, provided the boundary data of the target surface is a rigid body rotation, translation, and/or uniform scaling of the original source boundary data and provided the proper boundary node correspondence between source and target has been selected. Copying is not restricted to any particular smoother, but can be based on any locally elliptic second‐order operator. When the bounding loops are more general than rigid body transformations the method generates high‐quality, ‘morphed’ meshes. Mesh sweeping, if viewed as a morphing of the source surface to a set of target surfaces, can be effectively performed via this smoothing algorithm. Published in 1999 by John Wiley & Sons, Ltd. This article is a U.S. government work and is in the public domain in the United States.     

Quality improvement methods for hexahedral element meshes adaptively generated using grid‐based algorithm

The quality of finite element meshes is one of the key factors that affects the accuracy and reliability of numerical simulation results of many science and engineering problems. In order to solve the problem wherein the surface elements of the mesh generated by the grid‐based method have poor quality, this paper studied mesh quality improvement methods, including node position smoothing and topological optimization. A curvature‐based Laplacian scheme was used for smoothing of nodes on the C‐edges, which combined the normal component with the tangential component of the Laplacian operator at the curved boundary. A projection‐based Laplacian algorithm for smoothing the remaining boundary nodes was established. The deviation of the newly smoothed node from the practical surface of the solid model was solved. A node‐ and area‐weighted combination method was proposed for smoothing of interior nodes. Five element‐inserting modes, three element‐collapsing modes and three mixed modes for topological optimization were newly established. The rules for harmonious application and conformity problem of each mode, especially the mixed mode, were provided. Finally, several examples were given to demonstrate the practicability and validity of the mesh quality improvement methods presented in this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

六面体网格体积成形有限元分析关键技术

为提高三维体积成形有限元分析软件的计算精度、减少网格数量,基于六面体网格特性研究了六面体网格体积成形有限元分析系统的关键技术,通过对STL文件的索引重构建立了模具实体模型顶点和三角形面片拓扑连接关系,提出了一种局部坐标系建立方法保证触模和对称约束条件的正确施加,给出了相对速度和相对位置两种节点触模判断方法,并提出了调整触模节点位置的最短距离法,与初矢修正法和原长修正法比较,其调整距离短,体积损失小.基于以上技术,开发了基于三维六面体网格的体积成形有限元分析系统,对典型体积成形工艺进行了有限元模拟,并与Deform模拟结果进行对比,二者吻合较好,验证了所建立模型与相应处理技术的可行性.     

Q‐Morph: an indirect approach to advancing front quad meshing

Q‐Morph is a new algorithm for generating all‐quadrilateral meshes on bounded three‐dimensional surfaces. After first triangulating the surface, the triangles are systematically transformed to create an all‐quadrilateral mesh. An advancing front algorithm determines the sequence of triangle transformations. Quadrilaterals are formed by using existing edges in the triangulation, by inserting additional nodes, or by performing local transformations to the triangles. A method typically used for recovering the boundary of a Delaunay mesh is used on interior triangles to recover quadrilateral edges. Any number of triangles may be merged to form a single quadrilateral. Topological clean‐up and smoothing are used to improve final element quality. Q‐Morph generates well‐aligned rows of quadrilaterals parallel to the boundary of the domain while maintaining a limited number of irregular internal nodes. The proposed method also offers the advantage of avoiding expensive intersection calculations commonly associated with advancing front procedures. A series of examples of Q‐Morph meshes are also presented to demonstrate the versatility of the proposed method. Copyright © 1999 John Wiley & Sons, Ltd.     

Voxel‐based meshing and unit‐cell analysis of textile composites

Unit‐cell homogenization techniques are frequently used together with the finite element method to compute effective mechanical properties for a wide range of different composites and heterogeneous materials systems. For systems with very complicated material arrangements, mesh generation can be a considerable obstacle to usage of these techniques. In this work, pixel‐based (2D) and voxel‐based (3D) meshing concepts borrowed from image processing are thus developed and employed to construct the finite element models used in computing the micro‐scale stress and strain fields in the composite. The potential advantage of these techniques is that generation of unit‐cell models can be automated, thus requiring far less human time than traditional finite element models. Essential ideas and algorithms for implementation of proposed techniques are presented. In addition, a new error estimator based on sensitivity of virtual strain energy to mesh refinement is presented and applied. The computational costs and rate of convergence for the proposed methods are presented for three different mesh‐refinement algorithms: uniform refinement; selective refinement based on material boundary resolution; and adaptive refinement based on error estimation. Copyright © 2003 John Wiley & Sons, Ltd.     

Quality improvement of non‐manifold hexahedral meshes for critical feature determination of microstructure materials

This paper describes a novel approach to improve the quality of non‐manifold hexahedral meshes with feature preservation for microstructure materials. In earlier works, we developed an octree‐based isocontouring method to construct unstructured hexahedral meshes for domains with multiple materials by introducing the notion of material change edge to identify the interface between two or more materials. However, quality improvement of non‐manifold hexahedral meshes is still a challenge. In the present algorithm, all the vertices are categorized into seven groups, and then a comprehensive method based on pillowing, geometric flow and optimization techniques is developed for mesh quality improvement. The shrink set in the modified pillowing technique is defined automatically as the boundary of each material region with the exception of local non‐manifolds. In the relaxation‐based smoothing process, non‐manifold points are identified and fixed. Planar boundary curves and interior spatial curves are distinguished, and then regularized using B‐spline interpolation and resampling. Grain boundary surface patches and interior vertices are improved as well. Finally, the optimization method eliminates negative Jacobians of all the vertices. We have applied our algorithms to two beta titanium data sets, and the constructed meshes are validated via a statistics study. Finite element analysis of the 92‐grain titanium is carried out based on the improved mesh, and compared with the direct voxel‐to‐element technique. Copyright © 2009 John Wiley & Sons, Ltd.     

An imprint and merge algorithm incorporating geometric tolerances for conformal meshing of misaligned assemblies

A size tolerant algorithm for imprinting and merging adjacent part geometries is presented in this paper. This approach cleans up misaligned and dirty assembly geometry that is intended for conformal mesh generation. The algorithm first discretizes the boundary edges of adjacent faces into linear segments. The segments are then intersected and a partial intersection graph is calculated from the intersection results. The intersections are calculated by accounting for size tolerances to minimize the effect of misaligned parts on the meshing process. The partial intersection graph is next used to imprint the adjacent faces as appropriate. The imprints are generated using virtual geometry so that the tolerant topology created therein can be employed. Several examples are given to demonstrate the resulting improvement in the mesh quality of conformal meshes. The approach is shown to work robustly with misaligned and poorly defined parts. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimization of a regularized distortion measure to generate curved high‐order unstructured tetrahedral meshes

We present a robust method for generating high‐order nodal tetrahedral curved meshes. The approach consists of modifying an initial linear mesh by first, introducing high‐order nodes, second, displacing the boundary nodes to ensure that they are on the computer‐aided design surface, and third, smoothing and untangling the mesh obtained after the displacement of the boundary nodes to produce a valid curved high‐order mesh. The smoothing algorithm is based on the optimization of a regularized measure of the mesh distortion relative to the original linear mesh. This means that whenever possible, the resulting mesh preserves the geometrical features of the initial linear mesh such as shape, stretching, and size. We present several examples to illustrate the performance of the proposed algorithm. Furthermore, the examples show that the implementation of the optimization problem is robust and capable of handling situations in which the mesh before optimization contains a large number of invalid elements. We consider cases with polynomial approximations up to degree ten, large deformations of the curved boundaries, concave boundaries, and highly stretched boundary layer elements. The meshes obtained are suitable for high‐order finite element analyses. Copyright © 2015 John Wiley & Sons, Ltd.     

A Flexible Stretchable Hydrogel Electrolyte for Healable All‐in‐One Configured Supercapacitors

The development of integrated high‐performance supercapacitors with all‐in‐one configuration, excellent flexibility and autonomously intrinsic self‐healability, and without the extra healable film layers, is still tremendously challenging. Compared to the sandwich‐like laminated structures of supercapacitors with augmented interfacial contact resistance, the flexible healable integrated supercapacitor with all‐in‐one structure could theoretically improve their interfacial contact resistance and energy densities, simplify the tedious device assembly process, prolong the lifetime, and avoid the displacement and delamination of multilayered configurations under deformations. Herein, a flexible healable all‐in‐one configured supercapacitor with excellent flexibility and reliable self‐healing ability by avoiding the extra healable film substrates and the postassembled sandwich‐like laminated structures is developed. The healable all‐in‐one configured supercapacitor is prepared from in situ polymerization and deposition of nanocomposites electrode materials onto the two‐sided faces of the self‐healing hydrogel electrolyte separator. The self‐healing hydrogel film is obtained from the physically crosslinked hydrogel with enormous hydrogen bonds, which can endow the healable capability through dynamic hydrogen bonding. The assembled all‐in‐one configured supercapacitor exhibits enhanced capacitive performance, good cycling stability, reliable self‐healing capability, and excellent flexibility. It holds broad prospects for obtaining various flexible healable all‐in‐one configured supercapacitors for working as portable energy storage devices in wearable electronics.     

Flexible and High‐Performance All‐2D Photodetector for Wearable Devices

Emerging novel applications at the forefront of innovation horizon raise new requirements including good flexibility and unprecedented properties for the photoelectronic industry. On account of diversity in transport and photoelectric properties, 2D layered materials have proven as competent building blocks toward next‐generation photodetectors. Herein, an all‐2D Bi₂Te₃‐SnS‐Bi₂Te₃ photodetector is fabricated with pulsed‐laser deposition. It is sensitive to broadband wavelength from ultraviolet (370 nm) to near‐infrared (808 nm). In addition, it exhibits great durability to bend, with intact photoresponse after 100 bend cycles. Upon 370 nm illumination, it achieves a high responsivity of 115 A W^?1, a large external quantum efficiency of 3.9 × 10⁴%, and a superior detectivity of 4.1 × 10¹¹ Jones. They are among the best figures‐of‐merit of state‐of‐the‐art 2D photodetectors. The synergistic effect of SnS's strong light–matter interaction, efficient carrier separation of Bi₂Te₃–SnS interface, expedite carrier injection across Bi₂Te₃–SnS interface, and excellent carrier collection of Bi₂Te₃ topological insulator electrodes accounts for the superior photodetection properties. In summary, this work depicts a facile all‐in‐one fabrication strategy toward a Bi₂Te₃‐SnS‐Bi₂Te₃ photodetector. More importantly, it reveals a novel all‐2D concept for construction of flexible, broadband, and high‐performance photoelectronic devices by integrating 2D layered metallic electrodes and 2D layered semiconducting channels.     

Sparse self‐stress matrices for the finite element force method

A basic problem in the finite element force method is that of obtaining a sparse and banded self‐stress matrix and a sparse and banded structure flexibility matrix.Traditionally the self‐stress matrix is obtained through the application of algebraic procedures to the equilibrium matrix. The self‐stress matrix for an indeterminate structure is not unique, and it is possible to obtain another self‐stress matrix from an existing one through algebraic operations and grouping of redundants. The purpose of this paper is to describe and test an algorithm, called REDUC, which combines the vectors of the self‐stress matrix obtained from the LU procedure of the force method. The rows of the transpose of this matrix are combined by using a special form of the Gaussian elimination technique. A plane frame example is presented to demonstrate the algorithm at work. The algorithm REDUC is applied to a plane truss and physical interpretation of the resulting self‐stress matrix highlights the grouping of redundants, improved sparsity and bandwidth. Improvements in the conditioning and bandwidth of the structure flexibility matrix are also observed. The algorithm yields results similar to those of the turn‐back LU procedure, but requires less computation time and programming effort. Copyright © 2001 John Wiley & Sons, Ltd.     

All‐Organic Dual Spin Valves with Well‐Resolved Four Resistive‐States

The formation of all‐organic dual spin valves (DSVs) with three organic spin‐selective layers, that is, spin‐injection, spin‐detection, and an additional spin‐filtering layer at the intermediate, is reported. As spin‐selective layers, manganese‐ and cobalt phthalocyanines, which are well‐known single‐molecule magnets, are used in their immobilized forms, so that all‐organic DSVs can be prefabricated for characterization. The three spin‐selective layers have provided four configurations with at most two spin‐flip interfaces enforcing spin‐flipping at the two nonmagnetic organic spacer layers, for which copper phthalocyanine is used. Since a couple of the four configurations have exhibited similar resistivities, the degeneracy in the resistive‐states is broken through asymmetric spin‐injection and spin‐detection layers and also through asymmetric thickness of the nonmagnetic spacer layers. When both the spin‐flip interfaces are made operative independently, a 2‐bit logic with four distinct resistive states can be achieved.     

Defect‐Engineering‐Enabled High‐Efficiency All‐Inorganic Perovskite Solar Cells

The emergence of cesium lead iodide (CsPbI₃) perovskite solar cells (PSCs) has generated enormous interest in the photovoltaic research community. However, in general they exhibit low power conversion efficiencies (PCEs) because of the existence of defects. A new all‐inorganic perovskite material, CsPbI₃:Br:InI₃, is prepared by defect engineering of CsPbI₃. This new perovskite retains the same bandgap as CsPbI₃, while the intrinsic defect concentration is largely suppressed. Moreover, it can be prepared in an extremely high humidity atmosphere and thus a glovebox is not required. By completely eliminating the labile and expensive components in traditional PSCs, the all‐inorganic PSCs based on CsPbI₃:Br:InI₃ and carbon electrode exhibit PCE and open‐circuit voltage as high as 12.04% and 1.20 V, respectively. More importantly, they demonstrate excellent stability in air for more than two months, while those based on CsPbI₃ can survive only a few days in air. The progress reported represents a major leap for all‐inorganic PSCs and paves the way for their further exploration in order to achieve higher performance.     

A new automatic adaptive 3D solid mesh generation scheme for thin‐walled structures

A new algorithm to generate three‐dimensional (3D) mesh for thin‐walled structures is proposed. In the proposed algorithm, the mesh generation procedure is divided into two distinct phases. In the first phase, a surface mesh generator is employed to generate a surface mesh for the mid‐surface of the thin‐walled structure. The surface mesh generator used will control the element size properties of the final mesh along the surface direction. In the second phase, specially designed algorithms are used to convert the surface mesh to a 3D solid mesh by extrusion in the surface normal direction of the surface. The extrusion procedure will control the refinement levels of the final mesh along the surface normal direction. If the input surface mesh is a pure quadrilateral mesh and refinement level in the surface normal direction is uniform along the whole surface, all hex‐meshes will be produced. Otherwise, the final 3D meshes generated will eventually consist of four types of solid elements, namely, tetrahedron, prism, pyramid and hexahedron. The presented algorithm is highly flexible in the sense that, in the first phase, any existing surface mesh generator can be employed while in the second phase, the extrusion procedure can accept either a triangular or a quadrilateral or even a mixed mesh as input and there is virtually no constraint on the grading of the input mesh. In addition, the extrusion procedure development is able to handle structural joints formed by the intersections of different surfaces. Numerical experiments indicate that the present algorithm is applicable to most practical situations and well‐shaped elements are generated. Copyright © 2004 John Wiley & Sons, Ltd.