Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method
In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM wit...
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/22/4323 |
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| author | Dongdong Liu Xing Wei Chengbin Li Chunguang Han Xiaxi Cheng Linlin Sun |
| author_facet | Dongdong Liu Xing Wei Chengbin Li Chunguang Han Xiaxi Cheng Linlin Sun |
| author_sort | Dongdong Liu |
| collection | DOAJ |
| description | In this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM with a linear combination of the fundamental solutions. In order to avoid the perplexing fictitious boundary in the method of fundamental solution (MFS), the SBM places the source point on the physical boundary and eliminates the source singularity of the fundamental solution via the origin intensity factors (OIFs). The EWM is carried out for the inverse Fourier transform, which transforms the frequency-domain solutions into the time-domain solutions. The accuracy and feasibility of the SBM-EWM are verified by three numerical examples. The numerical comparison between the MFS and SBM indicates that the SBM takes a quarter of the time taken by the MFS. |
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| language | English |
| last_indexed | 2024-03-09T18:11:23Z |
| publishDate | 2022-11-01 |
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| series | Mathematics |
| spelling | doaj.art-f60cce4ba4ee437291dec1086af6bcb52023-11-24T09:09:39ZengMDPI AGMathematics2227-73902022-11-011022432310.3390/math10224323Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary MethodDongdong Liu0Xing Wei1Chengbin Li2Chunguang Han3Xiaxi Cheng4Linlin Sun5Jiangxi Key Laboratory of Disaster Prevention, Mitigation and Emergency Management, School of Civil Engineering & Architecture, East China Jiaotong University, Nanchang 330013, ChinaJiangxi Key Laboratory of Disaster Prevention, Mitigation and Emergency Management, School of Civil Engineering & Architecture, East China Jiaotong University, Nanchang 330013, ChinaChina Railway Construction Bridge Engineering Bureau Group Co., Ltd., Tianjin 300000, ChinaChina Railway Construction Bridge Engineering Bureau Group Co., Ltd., Tianjin 300000, ChinaJiangxi Key Laboratory of Disaster Prevention, Mitigation and Emergency Management, School of Civil Engineering & Architecture, East China Jiaotong University, Nanchang 330013, ChinaSchool of Science, Nantong University, Nantong 226019, ChinaIn this paper, the singular boundary method (SBM) in conjunction with the exponential window method (EWM) is firstly extended to simulate the transient dynamic response of two-dimensional saturated soil. The frequency-domain (Fourier space) governing equations of Biot theory is solved by the SBM with a linear combination of the fundamental solutions. In order to avoid the perplexing fictitious boundary in the method of fundamental solution (MFS), the SBM places the source point on the physical boundary and eliminates the source singularity of the fundamental solution via the origin intensity factors (OIFs). The EWM is carried out for the inverse Fourier transform, which transforms the frequency-domain solutions into the time-domain solutions. The accuracy and feasibility of the SBM-EWM are verified by three numerical examples. The numerical comparison between the MFS and SBM indicates that the SBM takes a quarter of the time taken by the MFS.https://www.mdpi.com/2227-7390/10/22/4323singular boundary methodmeshless methodsexponential window methodsaturated soiltransient dynamic response analysis |
| spellingShingle | Dongdong Liu Xing Wei Chengbin Li Chunguang Han Xiaxi Cheng Linlin Sun Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method Mathematics singular boundary method meshless methods exponential window method saturated soil transient dynamic response analysis |
| title | Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method |
| title_full | Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method |
| title_fullStr | Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method |
| title_full_unstemmed | Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method |
| title_short | Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method |
| title_sort | transient dynamic response analysis of two dimensional saturated soil with singular boundary method |
| topic | singular boundary method meshless methods exponential window method saturated soil transient dynamic response analysis |
| url | https://www.mdpi.com/2227-7390/10/22/4323 |
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