Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method
This study extends the calculation of unknown quantities at boundary points to the computation of internal displacements and stresses. The methodological approach is broadly consistent with boundary point calculations. However, the computation of internal unknowns does not involve spatial singularit...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/7/1025 |
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| author | Lihui Li Honjun Li Xiaofei Qin Weidong Lei Yan Liu |
| author_facet | Lihui Li Honjun Li Xiaofei Qin Weidong Lei Yan Liu |
| author_sort | Lihui Li |
| collection | DOAJ |
| description | This study extends the calculation of unknown quantities at boundary points to the computation of internal displacements and stresses. The methodological approach is broadly consistent with boundary point calculations. However, the computation of internal unknowns does not involve spatial singularities; the internal stress boundary integral equation is first derived. Subsequently, the obtained boundary integral equation is numerically processed, requiring discretization in both time and space, followed by assembly and solution. When solving the elements in the influence coefficient matrices, the displacement influence coefficient matrix <b><i>S</i></b> and the traction influence coefficient matrix <b><i>D</i></b> exhibit only wavefront singularities. These wavefront singularities are treated analytically in the time domain, and the spatial integrals are handled using Gaussian numerical integration. The correctness of the algorithm and theory is verified through two classical numerical examples. A theoretically sound and accurate three-dimensional elastodynamic time domain boundary element method and its corresponding computational program are established, providing a reliable tool for guiding engineering design. |
| format | Article |
| id | doaj-art-67580619e8d64ac7b97374f788d6dbb2 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-67580619e8d64ac7b97374f788d6dbb22025-08-20T02:17:00ZengMDPI AGMathematics2227-73902025-03-01137102510.3390/math13071025Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element MethodLihui Li0Honjun Li1Xiaofei Qin2Weidong Lei3Yan Liu4College of Urban and Rural Construction, Hebei Agricultural University, Baoding 071001, ChinaCollege of Urban and Rural Construction, Hebei Agricultural University, Baoding 071001, ChinaCollege of Civil Engineering and Architecture, Henan University of Technology, Zhengzhou 450001, ChinaSchool of Civil and Environmental Engineering, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, ChinaCollege of Urban and Rural Construction, Hebei Agricultural University, Baoding 071001, ChinaThis study extends the calculation of unknown quantities at boundary points to the computation of internal displacements and stresses. The methodological approach is broadly consistent with boundary point calculations. However, the computation of internal unknowns does not involve spatial singularities; the internal stress boundary integral equation is first derived. Subsequently, the obtained boundary integral equation is numerically processed, requiring discretization in both time and space, followed by assembly and solution. When solving the elements in the influence coefficient matrices, the displacement influence coefficient matrix <b><i>S</i></b> and the traction influence coefficient matrix <b><i>D</i></b> exhibit only wavefront singularities. These wavefront singularities are treated analytically in the time domain, and the spatial integrals are handled using Gaussian numerical integration. The correctness of the algorithm and theory is verified through two classical numerical examples. A theoretically sound and accurate three-dimensional elastodynamic time domain boundary element method and its corresponding computational program are established, providing a reliable tool for guiding engineering design.https://www.mdpi.com/2227-7390/13/7/1025internal responsetime domain boundary element methodwavefront singularity |
| spellingShingle | Lihui Li Honjun Li Xiaofei Qin Weidong Lei Yan Liu Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method Mathematics internal response time domain boundary element method wavefront singularity |
| title | Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method |
| title_full | Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method |
| title_fullStr | Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method |
| title_full_unstemmed | Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method |
| title_short | Research on Internal Response in Three-Dimensional Elastodynamic Time Domain Boundary Element Method |
| title_sort | research on internal response in three dimensional elastodynamic time domain boundary element method |
| topic | internal response time domain boundary element method wavefront singularity |
| url | https://www.mdpi.com/2227-7390/13/7/1025 |
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