Chi King Lee

A new scheme for the generation of a graded quadrilateral mesh

Abstract A new scheme for the generation of a quadrilateral element mesh is presented. The algorithm makes use of the fact that a triangular element mesh bounded by an even number of line segments can always be converted into quadrilaterals. By using the advancing front technique for schematically merging of triangular elements, high-quality well-graded quadrilateral meshes can be formed without any tedious treatment for isolated triangles. Unlike many other methods, no cut-lines or manual division of the problem domain into simpler subregions is required before conversion. As the number and the position of the boundary nodes are not altered during the mesh generation process, different material regions sharing common boundary lines can be treated individually. Since a background triangular mesh is all that is needed, the process can be applied to any arbitrary 2D domain with or without internal openings. In fact, the method has an equal area of application as a general triangulator. This also implies that the proposed scheme can be used to generate strongly graded quadrilateral meshes of the same gradation effect as the background triangular meshes for adaptive finite element analysis.

Generation of quadrilateral mesh over analytical curved surfaces

Abstract An automatic adaptive quadrilateral mesh conversion scheme for the generation of adaptive refinement meshes over analytical curved surfaces is proposed. The starting point of the quadrilateral mesh generator is a background triangular mesh of the curved surface. By a carefully controlled process to merge two triangles at a time the triangular mesh can be completely converted to quadrilaterals. A rapidly graded quadrilateral mesh with node spacing compatible with the desired element size distribution can be obtained from a well-graded triangular mesh. The quality of the quadrilateral mesh can be subsequently enhanced by a series of mesh modifications and element shape improvement procedures. The present scheme can be used in conjunction with an adaptive surface triangular mesh generator to generate quadrilaterial meshes suitable for adaptive shell refinement analysis.

On using meshes of mixed element types in adaptive finite element analysis

Abstract Four different automatic mesh generators capable of generating either triangular meshes or hybrid meshes of mixed element types have been used in the mesh generation process. The performance of these mesh generators were tested by applying them to the adaptive finite element refinement procedure. It is found that by carefully controlling the quality and grading of the quadrilateral elements, an increase in efficiency over pure triangular meshes can be achieved. Furthermore, if linear elements are employed, an optimal hybrid mesh can be obtained most economically by a combined use of the mesh coring technique suggested by Lo and Lau and a selective removal of diagonals from the triangular element mesh. On the other hand, if quadratic elements are used, it is preferable to generate a pure triangular mesh first, and then obtain a hybrid mesh by merging of triangles.

Automatic metric advancing front triangulation over curved surfaces

A 3D surface mesh generation scheme is suggested for the triangulation of general bi‐variate surfaces. The target surface to be meshed is represented as a union of bi‐variate sub‐surfaces and hence a wide range of surfaces can be modelled. Different useful features such as repeated curves, crack lines and surface branches are included in the geometrical and topological models to increase the flexibility of the mesh generation scheme. The surface metric tensor specification is employed to define and control the element characteristics in the mesh generation procedure. A robust metric triangulation kernel is used for parametric space mesh generation. The shape qualities of the sub‐surface meshes generated are then improved by using some ad hoc mesh quality enhancement schemes before they are combined together to form the final mesh. Numerical examples indicate that high quality surface meshes with rapid varying element size and stretching characteristics can be generated within a reasonable time limit in a few mesh adaptive iterations.

Automatic adaptive mesh generation using metric advancing front approach

A new mesh generation procedure is suggested for the generation of 2D adaptive finite element meshes with strong element gradation and stretching effects. Metric tensors are employed to define and control the element characteristics during the mesh generation process. By using the metric tensor specification and a new, robust and refined advancing front triangulation kernel, triangles with nearly unit edge length with respect to the normalized space are generated. Highly graded and stretched elements can be generated without much difficulty and the operation complexity of the mesh generation process is exactly the same as the usual 2D advancing front mesh generator. A set of mesh quality enhancement procedures has also been suggested for the further improvement of the quality of the finite element meshes. A simple and effective mesh conversion scheme is used to convert the output triangular mesh to a pure quadrilateral mesh while all the essential element characteristics are preserved. Mesh generation examples show that high quality finite element meshes with element characteristics compatible with the specified metric tensors are generated within a reasonable time limit in a common small computing environment.

Model and mesh generation of cracked tubular Y-joints

Abstract In this study, the methods for constructing accurate and consistent geometrical and finite element (FE) models for general cracked tubular Y-joints are described. Firstly, geometrical analysis of welded tubular joint is given and it is then extended to the modelling of general cracked Y-joints. The concept of crack surface and a simple mapping approach are suggested to model either through-thickness or surface cracks which can be of any length and located at any position along the brace–chord intersection. Secondly, the geometrical model developed will be used in the generation of consistent FE meshes. The basic concepts used for the design and generation of three-dimensional FE meshes will be described. This will include the meshing procedures for discretization of tubular joints with through-thickness and surface cracks which are frequently regarded as one of the most difficult steps in the construction of tubular joint models. Finally, some mesh generation examples for uncracked and cracked Y-joints will be presented to demonstrate the use of the purposed geometrical model and mesh generation scheme developed.

Modelling and mesh generation of weld profile in tubular Y-joint

Abstract This paper describes a systematic method of modelling the weld thickness of a tubular Y-joint. The intersection between the chord and the brace members is defined precisely. This intersection curve will then be used to evaluate the dihedral angle γ , which is the angle between the chord and the brace surfaces along the intersecting line. As the dihedral angle γ is an important parameter used to determine the weld thickness, its variation along the intersection curve and its relationship with the weld thickness is investigated first. It is shown that the smoothness of the weld path may not always be maintained if the minimum weld thickness, as specified in the American Welding Society (AWS) Codes D1.1-96, is to be followed strictly. Thus in some cases, modification of the intersection curve is necessary in order to model the weld path along the joint. Two scale factors F os outer and F os inner for the outer and inner intersection curves, and two constants m and n are introduced and proposed in this study. They are used to control the parameter k TW , which in turn controls the minimum weld thickness T W . Based on this model, an automatic mesh generator is developed to produce a well-graded finite element mesh. The stress concentration factors (SCFs) are shown to converge when the mesh is doubled and then tripled. Finally, some tubular welded specimens are fabricated, and the outer weld profiles are measured physically. It is shown that scale factors F os outer =0.3, F os inner =0.25 and constants m =2.0, n =0.4, are adequate to satisfy the required minimum outer weld profile. Therefore, the proposed method to model the weld size is both consistent and accurate for any tubular Y-joints.

Automatic adaptive finite element mesh generation over arbitrary two-dimensional domain using advancing front technique

Abstract The basic principles for the generation of adaptive finite element meshes over arbitrary two-dimensional domains using the advancing front technique are described. Methods to generate triangular and quadrilateral meshes are also presented. In addition to the description of the mesh generation algorithms, implementation details concerning both the speed and memory requirement are given. Mesh generation examples demonstrate that the proposed mesh generator is capable of discretizing the problem domain into a well-graded, high quality adaptive finite element mesh with element sizes compatible with the user specification. The whole automatic mesh generation program can be run on an IBM PC compatible machine and meshes with up to 9000 elements can be generated within a practical time limit.

Solving crack problems by an adaptive refinement procedure

Abstract The effect of using collapsed quarter-point elements (CQPE) in conjunction with the adaptive refinement procedure in solving crack problems is investigated. It is found that by using the collapsed quarter-point elements around the tip of the crack, the efficiency of the adaptive procedure can be increased considerably. The number of times of remeshing, and hence the computation time, required for achieving a solution with the same prescribed accuracy is much reduced. In addition, it is demonstrated that by using a simple swapping procedure to control the mesh layout surrounding the crack tip, it is possible to obtain highly accurate estimates of stress intensity factors by the adaptive refinement procedure. From the results of the uniform and adaptive finite element analysis on a set of problems, we conclude that in general there is no strong correlation between the relative error in energy norm of the solution and the relative percentage error of the stress intensity factors. The latter is much more dependent on the mesh geometry around the crack tip.

Automatic Adaptive Finite Element Mesh Generation Over Rational B-spline Surfaces

Abstract A new approach is suggested for the generation of adaptive finite element meshes over three-dimensional surfaces. The surfaces to be meshed are represented as the unions of rational B-spline surface (RBSS) patches such that the mesh generation process is reduced to the formation of nodes and elements in a parametric space. A robust and refined triangular element formation procedure is employed for the generation of highly skewed meshes in the parametric space such that well-shaped finite elements are obtained after mapping back to the three-dimensional (3D) space. By carefully monitoring the geometrical distortion effect due to the parametric mapping, the suggested element formation procedure can be used on convoluted and rough surfaces without impairing the quality of the meshes generated. In fact, the proposed generation scheme can easily be extended to many other bivariate surfaces without major modification. A simple and effective conversion scheme is also developed for the generation of pure quadrilateral meshes. Numerical experiments show that the operational complexity of the surface mesh generator is exactly the same as in two-dimensional (2D) planar mesh generation. High quality finite element meshes with element size grading compatible with the specified node spacing requirement are generated within a reasonable time limit in a common small computing environment.