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Mathematics
Special Issues
Boundary Element Methods in Engineering
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Boundary Element Methods in Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: closed (28 February 2025) | Viewed by 2827

Special Issue Editors

Prof. Dr. Jianming Zhang

E-Mail Website
Guest Editor
College of Mechanical and Vehicle Engineering, Hunan University, Changsha, China
Interests: boundary element method; meshless method; high-performance finite element method; new engineering calculation methods
Dr. Fenglin Zhou

E-Mail Website
Guest Editor
School of Mechanical Engineering, Hunan University of Technology, Zhuzhou, China
Interests: boundary element method; radial basis functions; integral equations; numerical methods; computational mathematics
Dr. Baotao Chi

E-Mail Website
Guest Editor
School of Mechanical Engineering, Shandong University of Technology, Zibo, China
Interests: numeric methods (finite element, boundary element, meshless method, etc.); mechanical CAE

Special Issue Information

Dear Colleagues,

This Special Issue, entitled "Boundary Element Methods in Engineering", focuses on the latest developments in engineering analysis with boundary elements, mesh reduction, and other related innovative and emerging numerical methods. Mathematics was originally focused on the development of the boundary element method. Its scope has since been expanded to include the emerging mesh reduction and meshless methods. The aim of Mathematics is to promote the use of non-traditional, innovative, and emerging computational methods for the analyses of modern engineering problems.

Prof. Dr. Jianming Zhang
Dr. Fenglin Zhou
Dr. Baotao Chi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • boundary element methods
  • finite element methods
  • finite volume methods
  • computer graphics
  • difference and differential equations
  • mathematics and computer science
  • computational and applied mathematics
  • structured and unstructured mesh generation
  • fundamental solution and related methods
  • collocation methods of the radial basis function
  • other mesh reduction and meshless methods
  • particle methods
  • other emerging and non-traditional numerical methods
  • advanced engineering analyses and applications

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Published Papers (3 papers)

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Research

13 pages, 262 KB  
Article
The Basic Formulas Derivation and Degradation Verification of the 3-D Dynamic Elastoplastic TD-BEM
by Weidong Lei, Bingzhen Wu and Hongjun Li
Mathematics 2025, 13(7), 1081; https://doi.org/10.3390/math13071081 - 26 Mar 2025
Viewed by 327
Abstract
In the field of dynamics research, in-depth exploration of three-dimensional (3-D) elastoplastic dynamics is crucial for understanding material behavior under complex dynamic loads. The findings hold significant guiding implications for design optimization in practical engineering domains such as aerospace and mechanical engineering. Current [...] Read more.
In the field of dynamics research, in-depth exploration of three-dimensional (3-D) elastoplastic dynamics is crucial for understanding material behavior under complex dynamic loads. The findings hold significant guiding implications for design optimization in practical engineering domains such as aerospace and mechanical engineering. Current methodologies for solving 3-D dynamic elastoplastic problems face challenges: While traditional finite element methods (FEMs) excel in handling material nonlinearity, they encounter limitations in 3-D dynamic analysis, especially difficulties in simulating infinite domains. Although classical time-domain boundary element methods (TD-BEMs) effectively reduce computational dimensionality through dimension reduction and time-domain fundamental solutions, they remain underdeveloped for 3-D elastoplastic analysis. This study mainly includes the following contributions: First, we derived the 3-D dynamic elastoplastic boundary integral equations using the initial strain method for the first time, which aligns with the physical essence of strain decomposition in elastoplastic theory. Second, kernel functions for displacement, traction, and strain influence coefficients are analytically obtained by integrating time-domain fundamental solutions with physical and geometric equations. To validate the formulation, a 3-D-to-2-D transformation is implemented through an integral degradation method, converting the problem into a verified dynamic plane strain elastoplastic system. Full article
(This article belongs to the Special Issue Boundary Element Methods in Engineering)
27 pages, 1968 KB  
Article
Wave-Power Extraction by an Oscillating Water Column Device over a Step Bottom
by Gagan Sahoo, Harekrushna Behera and Tai-Wen Hsu
Mathematics 2025, 13(7), 1067; https://doi.org/10.3390/math13071067 - 25 Mar 2025
Cited by 2 | Viewed by 1028
Abstract
This study investigates wave-power extraction by an oscillating water column (OWC) device over a porous-to-rigid step bottom using linearized water-wave theory. The interaction between water waves and the OWC device is analyzed by solving the governing boundary-value problem with the eigenfunction expansion method [...] Read more.
This study investigates wave-power extraction by an oscillating water column (OWC) device over a porous-to-rigid step bottom using linearized water-wave theory. The interaction between water waves and the OWC device is analyzed by solving the governing boundary-value problem with the eigenfunction expansion method (EEM) and the boundary element method (BEM). The study examines the effects of key parameters, including the porous effect parameter of the bottom, OWC chamber width, and barrier height, on the device’s efficiency. The results indicate that the porous effect parameter significantly influences OWC performance, affecting resonance characteristics and efficiency oscillations. A wider OWC chamber enhances oscillatory efficiency patterns, leading to multiple peaks of full and zero efficiency. The efficiency shifts towards lower wavenumbers with increasing step depth and barrier height but becomes independent of these parameters at higher wavenumbers. Additionally, incident angle plays a crucial role, decreasing efficiency at lower angles and exhibiting oscillatory behavior at higher angles. Furthermore, susceptance and conductance follow an oscillatory pattern concerning the gap between the porous bottom and the OWC chamber as well as chamber width. The porous effect parameter strongly modulates these oscillations. The findings provide new insights for enhancing OWC efficiency with complex bottom topography. Full article
(This article belongs to the Special Issue Boundary Element Methods in Engineering)
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14 pages, 2840 KB  
Article
Estimation of Stress Intensity Factor by Using a New Fast Multipole Dual-Boundary Element Method
by Cong Li, Yan Meng, Bin Hu and Zhongrong Niu
Mathematics 2025, 13(5), 842; https://doi.org/10.3390/math13050842 - 3 Mar 2025
Viewed by 707
Abstract
Cracks and defects are inevitable during the long-term use of structures. This study focuses on determining the stress intensity factors of multi-cracked structures by using a new fast multipole dual boundary element method. Numerical examples show that the results of the present method [...] Read more.
Cracks and defects are inevitable during the long-term use of structures. This study focuses on determining the stress intensity factors of multi-cracked structures by using a new fast multipole dual boundary element method. Numerical examples show that the results of the present method agree well with analytic solutions. When the crack distribution changes, the most unfavorable conditions also change. The shape of the defect has an effect on the stress intensity factors of nearby cracks. Among triangular, rectangular, hexagonal, and circular defects, when the area of the defect is identical, the triangular pore is more likely to induce crack propagation, while the circular pore is more secure. The above results can be used as a reference for structural design and optimization. Full article
(This article belongs to the Special Issue Boundary Element Methods in Engineering)
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