高精度自适应的四边形网格重建

提出了海量数据点集的四边形网格重建算法。首先根据精度要求简化数据点,按一定规则连接相邻的简化数据点生成多边形网格,对网格中高斯曲率较大的顶点进行局部细分提高其精度,然后对多边形网格进行整体细分使其全部转化为四边形网格,最后分裂度较大的顶点对其进行优化。实验结果表明,算法对拓扑结构较为复杂的海量数据点集的四边形网格重建是行之有效的。     

Adaptive triangular–quadrilateral mesh generation

In this paper, we begin by recalling an adaptive mesh generation method governed by isotropic and anisotropic discrete metric maps, by means of the generation of a unit mesh with respect to a Riemannian structure. We propose then an automatic triangular to quadrilateral mesh conversion scheme, which generalizes the standard case to the anisotropic context. In addition, we introduce an optimal vertex smoothing procedure. Application test examples, in particular a CFD test, are given to demonstrate the efficiency of the proposed method. © 1998 John Wiley & Sons, Ltd.     

On the discrete core of quadrilateral mesh refinement

We present a new approach to quadrilateral mesh refinement, which reduces the problem to its structural core. The resulting problem formulation belongs to a class of discrete problems, network‐flow problems, which has been thoroughly investigated and is well understood. The network‐flow model is flexible enough to allow the simultaneous incorporation of various aspects such as the control of angles and aspect ratios, local density control, and templates (meshing primitives) for the internal refinement of mesh elements. We show that many different variants of the general quadrilateral mesh‐refinement problem are covered. In particular, we present a novel strategy, which provably finds a conformal refinement unless there is none. Copyright © 1999 John Wiley & Sons, Ltd.     

Bending of bilinear quadrilateral shell elements

Formulae are derived for exact inextensional bending solutions for arbitrary quadrilateral shell finite elements of bilinear parametric representation. It is found that the polynomial degree of parametric representation of the rectangular components of displacement requires to be at least cubic in order to describe any inextensional bending modes.     

Feature based quadrilateral mesh generation for sculptured surface products

A successful approach to the generation of quadrilateral surface meshes for finite element analysis of sculptured surface products is presented. The free-form sculpted surface is divided into a feature based product anatomy which is used as the basis for defining regions of simpler shape that are related by the requirement for mesh continuity across their boundaries. Each surface region is meshed using a paving algorithm. Large surface areas are further subdivided to introduce new boundaries which improve contiol over mesh transitions and element distortion. A procedure, based on this approach, which generates well formed meshes on sculptured surface products is described using a hollow golf club head as an example. The approach is product specific and relies on initial user interaction to populate a feature based product data model. Thus, the data model contains, the attributes of a finite element mesh tailored to the product, which can be used to generate meshes on subsequent design iterations or other members of the product family with a high degree of automation, leading to reduced analysis cost.     

Asymmetric quadrilateral shell elements for finite strains

Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov–Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton–Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step independent and can replace the multiplicative plasticity approach if only moderate elastic strains are present, as is the case of most metals.     

Converting an unstructured quadrilateral mesh to a standard T-spline surface

This paper presents a novel method for converting any unstructured quadrilateral mesh to a standard T-spline surface, which is C ²-continuous except for the local region around each extraordinary node. There are two stages in the algorithm: the topology stage and the geometry stage. In the topology stage, we take the input quadrilateral mesh as the initial T-mesh, design templates for each quadrilateral element type, and then standardize the T-mesh by inserting nodes. One of two sufficient conditions is derived to guarantee the generated T-mesh is gap-free around extraordinary nodes. To obtain a standard T-mesh, a second sufficient condition is provided to decide what T-mesh configuration yields a standard T-spline. These two sufficient conditions serve as a theoretical basis for our template development and T-mesh standardization. In the geometry stage, an efficient surface fitting technique is developed to improve the geometric accuracy. In addition, the surface continuity around extraordinary nodes can be improved by adjusting surrounding control nodes. The algorithm can also preserve sharp features in the input mesh, which are common in CAD (Computer Aided Design) models. Finally, a Bézier extraction technique is used to facilitate T-spline based isogeometric analysis. Several examples are tested to show the robustness of the algorithm.     

Automatic quadrilateral/triangular free-form mesh generation for planar regions

Automation of finite element mesh generation holds great benefits for mechanical product development and analysis. In addition to freeing engineers from mundane tasks, automation of mesh generation reduces product cycle design and eliminates human-related errors. Most of the existing mesh generation methods are either semi-automatic or require specific topological information. A fully automatic free-form mesh generation method is described in this paper to alleviate some of these problems. The method is capable of meshing singly or multiply connected convex/concave planar regions. These regions can be viewed as crosssectional areas of 2 1/2 D objects analysed as plane stress, plane strain or axisymmetric stress problems. In addition to being fully automatic, the method produces quadrilateral or triangular elements with aspect rations near one. Moreover, it does not require any topological constraints on the regions to be meshed; i.e. it provides free-form mesh generation. The input to the method includes the region's boundary curves, the element size and the mesh grading information. The method begins by decomposing the planar region to be meshed into convex subregions. Each subregion is meshed by first generating nodes on its boundaries using the input element size. The boundary nodes are then offset to mesh the subregion. The resulting meshes are merged together to form the final mesh. The paper describes the method in detail, algorithms developed to implement it and sample numerical examples. Results on parametric studies of the method performance are also discussed.     

Mesh adaptation using a four-noded quadrilateral plate bending element

This paper uses a four-noded quadrilateral Reissner-Mindlin plate bending element for mesh adaptation. To overcome the problems of “locking” in the thin plate limit and zero energy modes the transverse shear strains are not evaluated from the displacements and rotations but are separately interpolated. The element is used in a hierarchical mesh adaptation which uses a node-averaging-based energy norm error estimator. Several examples illustrate the use of the adaptive algorithm.     

Axisymmetric quadrilateral elements for large deformation hyperelastic analysis

In this paper, axisymmetric 8-node and 9-node quadrilateral elements for large deformation hyperelastic analysis are devised. To alleviate the volumetric locking which may be encountered in nearly incompressible materials, a volumetric enhanced assumed strain (EAS) mode is incorporated in the eight-node and nine-node uniformly reduced-integrated (URI) elements. To control the compatible spurious zero energy mode in the 9-node element, a stabilization matrix is attained by using a hybrid-strain formulation and, after some simplification, the matrix can be programmed in the element subroutine without resorting to numerical integration. Numerical examples show the relative efficacy of the proposed elements and other popular eight-node elements. In view of the constraint index count, the two elements are analogous to the Q8/3P and Q9/3P elements based on the u–p hybrid/mixed formulation. However, the former elements are more straight forward than the latter elements in both formulation and programming implementation.     

Hierarchical p-version C1 finite elements on quadrilateral and triangular domains with curved boundaries and their applications to Kirchhoff plates

This work focuses on the construction of p-version finite elements that have curve boundaries for C¹ problems. Both triangular and quadrilateral elements are constructed based on the C¹-version blending function interpolation methods that are developed in this work and in the literature. Orthogonal hierarchical bases are constructed and subsequently transformed into interpolative nodal bases to facilitate the imposition of boundary conditions and the implementation of C¹ conformity on curvilinear domains. Nodal collocation strategies are also studied for improving the numerical performance, and novel nonuniformly distributed nodes, namely, Gauss-Jacobi (GJ) points, are proposed. For parallelograms and straight-sided triangular elements, C¹ continuity is exactly satisfied between neighboring elements. The difficulty of C¹ conformity for elements that have curved boundaries is circumvented by interpolating the normal derivatives at Gauss-Lobatto nodes. Moreover, with the help of the blending function interpolation method, the bases on edges and the internal modes can differ in terms of approximation order. Therefore, local p-refinements can be easily performed by these elements. Numerical results demonstrated that these elements are computationally inexpensive and converge fast for problems with regular and irregular domains.     

Converting an unstructured quadrilateral/hexahedral mesh to a rational T-spline

This paper presents a novel method for converting any unstructured quadrilateral or hexahedral mesh to a generalized T-spline surface or solid T-spline, based on the rational T-spline basis functions. Our conversion algorithm consists of two stages: the topology stage and the geometry stage. In the topology stage, the input quadrilateral or hexahedral mesh is taken as the initial T-mesh. To construct a gap-free T-spline, templates are designed for each type of node and applied to elements in the input mesh. In the geometry stage, an efficient surface fitting technique is developed to improve the surface accuracy with sharp feature preservation. The constructed T-spline surface and solid T-spline interpolate every boundary node in the input mesh, with C ²-continuity everywhere except the local region around irregular nodes. Finally, a Bézier extraction technique is developed and linear independence of the constructed T-splines is studied to facilitate T-spline based isogeometric analysis.     

Behaviour of isoparametric quadrilateral family of Lagrangian fluid finite elements

This paper presents the formulation of both the consistent and inconsistent four‐, eight‐ and nine‐noded isoparametric quadrilateral fluid finite elements that are based on Lagrangian frame of reference. The mesh locking phenomenon due to simultaneous enforcement of twin constraints, namely the incompressibility and irrotationality constraints, is studied in detail. The study shows that the characteristic of the locked fluid elements is that it always generates numerous spurious acoustic (volume change) modes upon the enforcement of rotational constraints. That is, the rotational constraints change the character of certain volume change modes. The study further reinforces the necessity of rotational constraints in not only identifying the spurious pressure modes, but also in reducing the computational effort for determining the eigenvalues and eigenvectors. It is found that all fully integrated inconsistent models exhibit locking behaviour. However, the inconsistent eight‐ and nine‐noded elements, integrated with full integration of volumetric stiffness and one point integration of the rotational stiffness matrices, gives excellent performance, although they do not pass the inf–sup test. The four‐ and nine‐noded consistent models are found to give locking free performance while their eight‐noded counterpart exhibited locking behaviour. The study shows that only consistent nine‐noded element models pass the inf–sup test. The utility of these elements in the coupled fluid–structure interaction problem is also demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Eigenvalue analysis of compatible and incompatible rectangular four-node quadrilateral elements

Exact analytical expressions for the eigenvalues of the elastic stiffness matrix are obtained for the four-node, rectangular, quadrilateral element. A procedure is given for identifying alternative hourglass modes and eigenvalues which render the element incompatible but with non-monotonic convergence assured. A convergence study confirms that for the special case of when the hourglass modes coincide with beam bending the element can serve as a beam element. Analytical expressions are given for the resulting element stiffness matrix.     

Derivation of Lagrangian and Hermitian shape functions for quadrilateral elements

This paper introduces a general theory for the derivation of the shape functions for the quadrilateral family of finite elements. The first section deals with the Lagrangian shape functions for the cases of uniform and boundary-described elements. Two basic procedures are introduced; the first by linear combinations of side-interpolations and the second by superposition. The remainder of the paper introduces a theory for the general uniform Hermitian element of any order. Details for quadrilateral elements, with first order derivatives are explained. All of the shape functions presented here were derived in the interval [0,1]. The shape functions, developed by such an engineering approach, have been used successfully in the ABSEA Finite Element System of Cranfield Institute of Technology.     

Automatic conversion of triangular finite element meshes to quadrilateral elements

A method is presented for the fully automatic conversion of a general finite element mesh containing triangular elements into a mesh composed of exclusively quadrilateral elements. The initial mesh may be constructed of entirely triangular elements or may consist of a mixture of triangular and quadrilateral elements. The technique used employs heuristic procedures and criteria to selectively combine adjacent triangular elements into quadrilaterals based on preestablished criteria for element quality. Additional procedures are included to eliminate isolated triangles. The methods operates completely without user intervention once the nodal co-ordinates and element connectivity of the original mesh are supplied.     

Impact-Resistant Hydrogels by Harnessing 2D Hierarchical Structures

With the strengthening capacity through harnessing multi-length-scale structural hierarchy, synthetic hydrogels hold tremendous promise as a low-cost and abundant material for applications demanding unprecedented mechanical robustness. However, integrating high impact resistance and high water content, yet superior softness, in a single hydrogel material still remains a grand challenge. Here, a simple, yet effective, strategy involving bidirectional freeze-casting and compression-annealing is reported, leading to a hierarchically structured hydrogel material. Rational engineering of the distinct 2D lamellar structures, well-defined nanocrystalline domains and robust interfacial interaction among the lamellae, synergistically contributes to a record-high ballistic energy absorption capability (i.e., 2.1 kJ m⁻¹), without sacrificing their high water content (i.e., 85 wt%) and superior softness. Together with its low-cost and extraordinary energy dissipation capacity, the hydrogel materials present a durable alternative to conventional hydrogel materials for armor-like protection circumstances.     

Two refined non‐conforming quadrilateral flat shell elements

Two refined quadrilateral flat shell elements named RSQ20 and RSQ24 are constructed in this paper based on the refined non‐conforming element method, and the elements can satisfy the displacement compatibility requirement at the interelement of the non‐planar elements by introducing the common displacements suggested by Chen and Cheung. A refined quadrilateral plate element RPQ4 and a plane quadrilateral isoparametric element are combined to obtain the refined quadrilateral flat shell element RSQ20, and a refined quadrilateral flat shell element RSQ24 is constructed on the basis of a RPQ4 element and a quadrilateral isoparametric element with drilling degrees of freedom. The numerical examples show that the present method can improve the accuracy of shell analysis and that the two new refined quadrilateral flat shell elements are efficient and accurate in the linear analysis of some shell structures. Copyright © 2000 John Wiley & Sons, Ltd.     

Modified crack closure integral using six-noded isoparametric quadrilateral singular elements

Six-noded, isoparametric serendipity type quadrilateral regular/singular elements are used for the estimation of stress intensity factors (SIF) in linear elastic fracture mechanics (LEFM) problems involving cracks in two-dimensional structural components. The square root singularity is achieved in the six-noded elements by moving the in-side nodes to the quarter point position. The modified crack closure integral (MCCI) method is adopted which could generate accurate estimates of SIF for a relatively coarse mesh. The equations for strain energy release rate and SIF are derived for mixed mode situations using six-noded quadrilateral elements at the crack tip. The model is validated by numerical studies for a centre crack in a finite plate under uniaxial tension, a single edge notched specimen under uniaxial tension, an inclined crack in a finite rectangular plate and cracks emanating from a pin-loaded lug (or lug attachment). The results compare very well with reference solutions available in the literature.