PurposeThe purpose of this paper is to present an adaptive binary-tree element subdivision method (BTSM) for the evaluation of nearly singular integrals in three-dimensional boundary element method, ...which can facilitate automatic and high-quality patch generation.Design/methodology/approachIn this method, the nearly singular element is split into two sub-elements. Each sub-element is then examined to determine if it is to be subdivided based on a specific subdivision criterion. The specific subdivision ensures that those sub-elements far from the source point are sparse. And then those sub-elements in close proximity to the source point are replaced by regular triangular elements.FindingsWith the proposed method, the sub-elements obtained are automatically refined as they approach the projection point, and they are “good” in shape and size for standard Gaussian quadrature. Thus, the proposed method can be used to evaluate nearly singular integrals accurately for cases of different element shapes and various locations of the source point.Originality/valueNumerical examples for surface elements with various relative locations of the source point are presented. The results demonstrate that the proposed method has much better accuracy and robustness than some other methods.
Purpose
The purpose of this paper is to present a fast algorithm for the adaptive discretization of three-dimensional parametric curves.
Design/methodology/approach
The proposed algorithm computes ...the parametric increments of all segments to obtain the parametric coordinates of all discrete nodes. This process is recursively applied until the optimal discretization of curves is obtained. The parametric increment of a segment is inversely proportional to the number of sub-segments, which can be subdivided, and the sum of parametric increments of all segments is constant. Thus, a new expression for parametric increment of a segment can be obtained. In addition, the number of sub-segments, which a segment can be subdivided is calculated approximately, thus avoiding Gaussian integration.
Findings
The proposed method can use less CPU time to perform the optimal discretization of three-dimensional curves. The results of curves discretization can also meet requirements for mesh generation used in the preprocessing of numerical simulation.
Originality/value
Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the algorithm saves in the process of curve discretization.
The present paper provides a new definition of the dual interpolation curve in a geometric-intuitive way based on adaptive curve refinement techniques. The dual interpolation curve is an ...implementation of the interpolatory subdivision scheme for curve modeling, which comprises polynomial segments of different degrees. Dual interpolation curves maintain various desirable properties of conventional curve modeling methods, such as local adaptive subdivision, high interpolation accuracy and convergence, and continuous and discontinuous boundary representation. In addition, the dual interpolation curve is mainly applied to solve the difficult geometry defeaturing problems for curve modeling in existing computer-aided technology. By adding fictitious and intrinsic nodes inside or at the vertices of interpolation elements, the dual interpolation curve is flexible and convenient for characterizing a set of ordered points or discrete segments. Combined with the Lagrange interpolation polynomial and meshless method, the proposed approach is capable of characterizing the non-smooth boundary for geometry defeaturing. Experimental results are given to verify the validity, robustness, and accuracy of the proposed method.
Excessive wear of gears will not only cause noise and vibration in the transmission system, but also reduce transmission efficiency and accuracy in severe cases, causing irreversible losses to the ...transmission system. It is desirable to develop a micro-gear unit model for evaluating the wear process and predicting the failure time of large gear units (such as wind turbine gear units), reducing losses due to sudden failures. Based on the Buckingham pi-theorem of dimensional analysis and Hertz formula, the similarity ratio of each parameter of the gear wear process was proposed. The maximum equivalent stress is calculated by establishing the FEM model and comparing it with the theoretical contact stress calculated by the Hertz formula, and the results were relatively consistent. Two pairs of gear friction and wear experiments with similar parameters were carried out to compare the wear evolution performance of two similar gears. The friction performance process of the test gears was observed by particle counter and analytical ferrograph. The results show that the friction and wear processes of the two groups of gears with similar parameters have a certain correlation, which was consistent with the proposed similarity model. The similarity model combined with the observation results of abrasive particles has a certain application value for the evaluation of the wear state of the transmission system.
Computer-aided engineering (CAE) has emerged as an indispensable tool for facilitating engineering practices and driving industrial innovation. However, the insufficient quality and efficiency of ...discretizing complex computer-aided design (CAD) models significantly impede the advancement of CAE calculation accuracy and automation. The presence of “dirty” geometry leads to the fact that it is almost impossible to generate a traditional conforming mesh without geometry repair. In most instances, automating geometry repair proves to be even more challenging than meshing. To cope with intricate CAD model with “dirty” geometry, a novel binary tree surface subdivision method (BSSM) is proposed for automatically generated conforming and nonconforming meshes directly on CAD models. In contrast to the conventional conforming mesh, the nonconforming mesh allows for hanging nodes, thereby eliminating the limitations of the mesh conformance. This facilitates rapid transitions in mesh size for automatic mesh generation when dealing with “dirty” geometry. A series of numerical models employing BSSM are presented in this study. Results reveal that BSSM can automatically, efficiently and reliably generate high level quality mesh for arbitrary structures.
CAE/CAD integration has always been the focus of competition among CAE software vendors. For decades, however, despite the large human resource and financial investment from some super international ...companies, CAE/CAD integration has not yet been fully realized. As we know, the boundary integral equation method has advantages of naturally seamless connection with CAD packages. Unfortunately, the conventional implementation of the boundary element method is unsuccessful in engineering application. In this paper, a new method to seamlessly integrate CAE/CAD based on boundary integral equations and nonconforming meshes is introduced. The nonconform mesh can effectively promote automatic CAE analysis development, while the dual interpolation boundary face method provides theoretical support for the above technologies. In addition, a spherical subdivision method is proposed to improve the accuracy and stability of singular and near-singular integrals in BIE. Adaptive cross approximation algorithm can reduce the storage of the dense coefficient matrix effectively and approximate the far-field matrix for large-scale computation. Based on the above theories, the "5aCAE simulation software" is developed. In this software, CAE analysis is performed directly on the CAD model using discontinuous mesh without geometric simplifying and repairing, which is impossible for existing commercial software. There is no need to select element types such as beams, shells elements, because any structure is treated as a complete entity. Automation is another feature of this software, which lowers the threshold for users. This paper presents a comprehensive overview of the dual interpolation boundary surface method and introduces the highlights of "5aCAE simulation software", which can provide technical support for boundary element CAE software development.
•The DiBFM has been presented for solving three-dimensional potential problems.•A new type of elements named the dual interpolation elements are proposed in DiBFM.•The DiBFM can unify the ...conventional continuous and discontinuous elements.•Even with some irregular elements, the DiBFM can exhibit high accuracy behavior.•The DiBFM is flexible to handle real world geometries in a fully automated manner.
A dual interpolation boundary face method (DiBFM) is presented for solving three-dimensional potential problems. The DiBFM is an alternative implementation of the boundary face method (BFM) and inherits all the merits of BFM, which has been proposed to unify the continuous and discontinuous elements, improve the accuracy of the interpolation calculation and alleviate the heavy task of mesh generation. The DiBFM implementation is based on a new type of elements, called the dual interpolation elements, in which the nodes are classified into virtual nodes and source nodes. Despite the introduction of virtual nodes in the dual interpolation elements, only source nodes of each element are taken as the collocation points. Corresponding constraint equations using the MLS approximation are formulated to condense the degrees of freedom for all virtual nodes, which does not result in the scale of final linear system increasing. In addition, even with some irregular elements in numerical simulation, accurate results and high convergence rates can be achieved by the DiBFM. The DiBFM is flexible and convenient to handle more complicated, real world structures without any geometric simplification in a fully automated manner. Numerical results have demonstrated the validity, high accuracy and superior convergence of the proposed method.
In order to realize the automation of surface mesh generation for arbitrary complex models, this paper proposes a binary-tree method (BTM) which can generate discontinuous grids. Compared with ...continuous grids, the adjacency relationship between discontinuous grids generated by BTM is more flexible, so it is easier to discretize “dirty” geometry without geometry repair than continuous grids. The BTM can adaptively generate meshes by features based on the curvature of curves and surfaces, and thus it does not need to construct a sizing field. Anisotropic meshes can also be directly generated by selecting the direction of subdividing meshes. Moreover, according to the periodic characteristics of periodic surfaces, the topological structure of the initial mesh can be designed to achieve mesh generation on periodic surfaces. Successful numerical examples are used to illustrate the effectiveness and robustness of the presented methods for meshing various types of geometric surfaces and reveal the excellent performance of the BTM. In addition, the BTM has been employed by the dual interpolation boundary face method (DiBFM) to solve 3D problems.
In this paper, an adaptive element Subdivision Method based on the Affine transformations and Partitioning techniques (APSM) is presented for evaluating the weakly singular integrals with arbitrary ...shape of elements. The basic idea consists in partitioning the input surface element via affine transformation and then in generating a set of high-quality patches by adaptive binary-tree subdivision. The proposed method has some advantages over the conventional methods based on elements subdivision, i.e. the adaptive element subdivision, an improvement of the accuracy and a straight-forward implementation. By using the domain partitioning technique, the surface element can be divided into several element projection and subdivision regions under affine transformations. It is far more efficient to separately perform the element subdivision for different regions where the desirable patches are required. The ultimate patches in the vicinity of the singular point are calculated numerically by the coordinate transformation technique, while the remaining patches are evaluated accurately by the standard Gaussian quadrature. Several numerical examples are presented in order to validate the accuracy, efficiency and availability of the proposed method.
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