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A dual interpolation boundary face method for exterior acoustic problems based on the Burton-Miller formulation

ENGINEERING ANALYSIS WITH boundary ELEMENTS 2020年 113卷 219-231页

作者： Zhang, Jianming Lin, Weicheng Shu, Xiaomin Zhong, Yudong Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Peoples R China

A dual interpolation boundary face method (DiBFM) based on the Burton-Miller formulation for solving exterior acoustic problems is presented. The method is able to unify the conforming and nonconforming BFM. In DiBFM implementation, the nodes of a conforming element are divided into two categories: source nodes (inside the element) and virtual nodes (on the boundary of the element). Acoustic pressure and its derivative are approximated using conforming elements, in the same way as conforming BFM. However, the Burton-Miller integral equations are just collocated at source nodes, in the same way as nonconforming BFM. To arrive at a square linear system, additional constraint equations established by the moving least-squares approximation are provided to condense the degrees of freedom relating to virtual nodes. Several numerical examples demonstrate the accuracy and efficiency of the proposed method.

关键词： Acoustic problems dual interpolation boundary face method boundary face method Moving least-squares approximation Burton-Miller formulation

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A dual interpolation boundary face method with Hermite-type approximation for potential problems

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APPLIED MATHEMATICAL MODELLING 2020年 81卷 457-472页

作者： Zhang, Jianming He, Rui Chi, Baotao Lin, Weicheng Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

This paper presents the dual interpolation boundary face method combined with a Hermite-type moving-least-squares approximation for solving complex two-dimensional potential problems. Compared to the standard algorithms, this combined method is better suited for structures with small feature sizes such as short edges and small chamfers. The interpolation functions, if constructed in cyclic coordinates, making it difficult to apply this new method to deal with complex structures with small feature sizes in which only one source point is assigned. The Hermite-type approximation formulated in Cartesian coordinates is able to completely overcome this obstacle by searching for source points on adjacent edges. Additionally, an improved and incomplete quadratic polynomial basis is presented to obtain an accurate algorithm for the Hermite-type approximation. We use several numerical examples to demonstrate the high accuracy and efficiency of the proposed method for solving various engineering structures with small feature sizes. (C) 2020 Elsevier Inc. All rights reserved.

关键词： dual interpolation boundary face method Moving-least-squares approximation Hermite-type approximation Thin-wall structure Small feature sizes

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A multi-domain BEM based on dual interpolation boundary face method for 3D elasticity problem

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ENGINEERING ANALYSIS WITH boundary ELEMENTS 2022年 143卷 568-578页

作者： Chai, Pengfei Zhang, Jianming Xiao, Rongxiong He, Rui Lin, WeiCheng Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

The dual interpolation boundary face method with Hermite-type moving-least-squares approximation (DiBFMHMLS), presented recently, has certain advantages in simulating the discontinuous fields. Based on the DiBFMHMLS and the matrix condensation technique, we proposed a multi-domain method for 3D elasticity problems in this paper. This method ensures an accurate interpolation for the multi-domain models with short edges or small chamfers. In the multi-domain DiBFM-HMLS, the virtual points in each subdomain, not as collocation points in the boundary integral equation (BIE), are eliminated by the HMLS approximation separately. Then, only the interfacial source points are reserved by the matrix condensation technique. The node-to-node interfacial condition in previous research is unemployed;instead of the former, a node-to-element format is constructed based on the moving-least-squares approximation (MLS). This mapping scheme possesses the potential for free mesh in the interface. Several numerical examples are used to reflect these advantages mentioned above.

关键词： Multi-domain method Short edge and small chamfers dual interpolation boundary face method Hermite-type approximation

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A new implementation of DRM with dual interpolation boundary face method for Poisson equation

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ENGINEERING ANALYSIS WITH boundary ELEMENTS 2020年 121卷 21-30页

作者： He, Rui Zhang, Jianming Suliman Yang, Le Lin, Weicheng Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Cent South Univ Sch Math & Stat Changsha 410083 Peoples R China

We present a new numerical algorithm combining the dual reciprocity method with the dual interpolation boundary face method for solving the two-dimensional Poisson equations. In this new combined approach, the boundary physical variables and particular solutions are approximated by dual interpolation elements which include source and virtual points. Additionally, this algorithm is implemented by employing the augmented thin plate spline interpolation function to approximate non-homogeneous term and the Hermite-type moving-least-square approximation to approximate physical variables for virtual nodes. Compared with the traditional dual reciprocity boundary element method, this combined method possesses higher accuracy and efficiency and is better suited for structures with small feature sizes. Several numerical examples are given to illustrate the superiority of the proposed method for solving Poisson equations.

关键词： dual reciprocity method Radial basis functions dual interpolation boundary face method Hermite-type approximation Poisson equation

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A dual interpolation boundary face method for elasticity problems

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2019年 73卷 500-511页

作者： Zhang, Jianming Lin, Weicheng Dong, Yunqiao Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China

A dual interpolation boundary face method (DiBFM) is proposed to unify the conforming and nonconforming elements in boundary element method (BEM) implementation. In the DiBFM, the nodes of a conventional conforming element are sorted into two groups: the nodes on the boundary (called virtual nodes) and the internal nodes (called source nodes). Without virtual nodes, the conforming element turns to be a conventional nonconforming element of a lower order. Physical variables are interpolated using the conforming elements, the same way as conforming BEM. boundary integral equations are collocated at source nodes, the same way as nonconforming BEM. To make the final system of linear equations solvable, additional constraint equations are required to condense the degrees of freedom for all the virtual nodes. These constraints are constructed using the moving least-squares (MLS). Besides, both boundary integration and MIS are performed in the parametric spaces of curves, namely, the geometric data, such as coordinates, out normals and Jacobians, are calculated directly from curves rather than from elements. Thus, no geometric errors are introduced no matter how coarse the discretization is. The method has been implemented successfully for solving two-dimensional elasticity problems. A number of numerical examples with real engineering background have demonstrated the accuracy and efficiency of the new method.

关键词： dual interpolation boundary face method boundary element method Moving least-squares approximation

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Implementation of a dual interpolation boundary face method by discontinuous meshes

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ENGINEERING ANALYSIS WITH boundary ELEMENTS 2022年 139卷 152-168页

作者： Zhang, Jianming Chai, Pengfei He, Rui Lin, WeiCheng Ju, Chuangming Chi, Baotao Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Peoples R China

In this paper, the discontinuous meshes are applied to CAE analysis. Besides that, a dual interpolation boundary face method based on the Hermite-type moving-least-squares method (DiBFM-HMLS) for the 3D elasticity problem is firstly proposed. The DiBFM-HMLS offers an interpolation scheme for the hang points in the discontinuous meshes. Different from the previous mesh division method, the binary-tree structure is used to obtain the discontinuous meshes. Our mesh generation method can effectively avoid model repairing and simplification for geometric structures with small features and defects while ensuring a real automatic mesh division. Compared with the continuous mesh, the discontinuous meshes possess strong geometric adaptability for arbitrarily complicated structures and can provide the possibility for the full-automatic CAE analysis. Suc-cessful numerical examples are used to illustrate the accuracy and reliability of the presented methods in solving various kinds of problems and reveal the excellent performance of the discontinuous meshes.

关键词： Discontinuous mesh Binary-tree structure Hang points dual interpolation boundary face method Hermite-type approximation Discontinuous mesh Binary-tree structure Hang points dual interpolation boundary face method Hermite-type approximation

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A dual interpolation boundary face method for 3D elasticity

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ENGINEERING ANALYSIS WITH boundary ELEMENTS 2021年 122卷 102-116页

作者： Zhang, Jianming Ju, Chuanming Wen, Pihua Shu, Xiaomin Lin, Weicheng Chi, Baotao Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Queen Mary Univ London Sch Engn & Mat Sci London E1 4NS England

The dual interpolation boundary face method (DiBFM) proposed recently has been successfully applied to solve various problems in two dimensions. Compared with the conventional boundary element method (BEM), it has been proved that the DiBFM has the advantages of higher accuracy, convergence rate and computational efficiency. In addition, the DiBFM is suitable to unify the conforming and nonconforming elements in the BEM implementation, as well as to approximate both continuous and discontinuous fields. Moreover, there are no geometric errors by the DiBFM in the computational process. In this paper, the DiBFM is extended successfully to solve the elasticity problems in three-dimensions (3D) with formulations derived in details. A number of numerical examples are presented in order to validate the accuracy and convergence rate of the proposed method.

关键词： dual interpolation boundary face method 3D elasticity boundary element method Moving least-squares approximation

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A solution approach for contact problems based on the dual interpolation boundary face method

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APPLIED MATHEMATICAL MODELLING 2019年 70卷 643-658页

作者： Zhang, Jianming Shu, Xiaomin Trevelyan, Jon Lin, Weicheng Chai, Pengfei Hunan Univ State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Univ Durham Dept Engn South Rd Durham DH1 3LE England

The recently proposed dual interpolation boundary face method (DiBFM) has been shown to have a much higher accuracy and improved convergence rates compared with the traditional boundary element method. In addition, the DiBFM has the ability to approximate both continuous and discontinuous fields, and this provides a way to approximate the discontinuous pressure at a contact boundary. This paper presents a solution approach for two dimensional frictionless and frictional contact problems based on the DiBFM. The solution approach is divided into outer and inner iterations. In the outer iteration, the size of the contact zone is determined. Then the elements near the contact boundary are updated to approximate the discontinuous pressure. The inner iteration is used to determine the contact state (sticking or sliding), and is only performed for frictional contact problems. To make the system of equations solvable, the contact constraints and some supplementary equations are also given. Several numerical examples demonstrate the validity and high accuracy of the proposed approach. Furthermore, due to the continuity of elements in DiBFM and the detection of the contact boundary, the pressure oscillations near the contact boundary can be treated. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Contact problems dual interpolation boundary face method Contact boundary detection Weak discontinuity Contact constraints Supplementary equations

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On the evaluation of Poisson equation with dual interpolation boundary face method

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2021年 88卷

作者： Khan, Suliman He, Rui Khan, Feroz Khan, M. Riaz Arshad, Muhammad Shah, Hasrat Hussain Cent South Univ Sch Math & Stat Changsha 410083 Hunan Peoples R China Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Peoples R China Univ Gujrat Dept Math Hafiz Hayat CampusJalapur Rd Gujrat 50700 Pakistan Univ Chinese Acad Sci Chinese Acad Sci Acad Math & Syst Sci LSEC Beijing 100190 Peoples R China Univ Chinese Acad Sci Chinese Acad Sci Acad Math & Syst Sci ICMSEC Beijing 100190 Peoples R China Abbottabad Univ Sci & Technol Dept Math Abbottabad Pakistan Balochistan Univ Informat Technol Engn & Manageme Dept Math Sci Quetta Pakistan

This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpolation is used to interpolate the physical variables, while boundary integrals are evaluated on the source nodes only. Moreover, moving least squares (MLS) interpolation is used and provides additional constraints equations to establish the relationship between source and virtual nodes. Additionally, augmented thin plate spline (ATPS) is used to better interpolate the non-homogeneous term. Finally, it is claimed that the proposed method is much superior to the DRM for Poisson type equation with different geometries, especially for complex geometry. Numerical examples are evaluated and compared with the DRM to ensure the superiority of the proposed method.

关键词： dual reciprocity method dual interpolation boundary face method Augmented thin plate spline Moving least squares interpolation Poisson equation Complex geometry

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A dual interpolation boundary face method with Hermite-type approximation for elasticity problems

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EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2020年 82卷

作者： Zhang, Jianming He, Rui Lin, Weicheng Yang, Le Chi, Baotao Ju, Chuanming Suliman Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China Cent South Univ Sch Math & Stat Changsha 410083 Peoples R China

This paper proposed the dual interpolation boundary face method with Hermite-type approximation for elasticity problems. Considering the physical relationship between displacement and traction, we also firstly present the Hermite-type approximation for elasticity problems. Compared with the standard moving least-squares (MLS) approximation, shape functions in Hermite-type approximation are directly constructed with Cartesian coordinates rather than parameter coordinates. This new approach can attain high accuracy and efficiency, the same as original dual interpolation boundary face method (DiBFM). Furthermore, the influence domain in the Hermite-type approximation can cover multiple edges. Thus, compared with the original DiBFM, this new scheme is more suitable for handling structures with thin walls and small features. Numerical examples with engineering background have illustrated the accuracy, efficiency and practicality of the method.

关键词： Hermite-type approximation dual interpolation boundary face method boundary element method Local stress concentration

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