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Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition
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Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 March 2024) | Viewed by 5385

Special Issue Editor

Prof. Dr. Miaojuan Peng

E-Mail Website
Guest Editor
School of Mechanics and Engineering Science, Shanghai University, Shanghai 200044, China
Interests: mathematical model; numerical method; numerical simulation; finite element method; meshless method
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Because of the complexity of engineering problems, it is important to present the mathematical model and the corresponding numerical methods. Now partial differential equation with the corresponding boundary and initial conditions is the basic model for engineering problems. Finite element method, boundary element method and meshless method are several kinds of major numerical methods for simulating engineering problems. Various numerical methods are presented for solving the problems in different engineering fields, and the corresponding computational efficiency, accuracy and convergence are studied as well. The applications of the mathematical models and numerical methods in complicated engineering problems also should be studied.

In this Special Issue, we particularly take an interest in manuscripts that report relevance of mathematical models and numerical computation for complicated engineering and social problems. The special issue will become an international forum for researchers to summarize the most recent developments of mathematical models and numerical simulations for engineering problems within the last five years, especially for the mathematical model of new problems. Moreover, the manuscripts on the mathematical theories of mathematical model and numerical computation for complicated science, engineering or social problems are welcome. We also concern the development of the corresponding aspects based on data analysis, including the corresponding theory, numerical method and the applications.

Prof. Dr. Miaojuan Peng
Guest Editor

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

  • mathematical model
  • numerical method
  • numerical simulation
  • engineering problem
  • social problem

Published Papers (6 papers)

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Research

25 pages, 17243 KiB  
Article
RBF-Assisted Hybrid Neural Network for Solving Partial Differential Equations
by Ying Li, Wei Gao and Shihui Ying
Mathematics 2024, 12(11), 1617; https://doi.org/10.3390/math12111617 - 21 May 2024
Viewed by 424
Abstract
In scientific computing, neural networks have been widely used to solve partial differential equations (PDEs). In this paper, we propose a novel RBF-assisted hybrid neural network for approximating solutions to PDEs. Inspired by the tendency of physics-informed neural networks (PINNs) to become local [...] Read more.
In scientific computing, neural networks have been widely used to solve partial differential equations (PDEs). In this paper, we propose a novel RBF-assisted hybrid neural network for approximating solutions to PDEs. Inspired by the tendency of physics-informed neural networks (PINNs) to become local approximations after training, the proposed method utilizes a radial basis function (RBF) to provide the normalization and localization properties to the input data. The objective of this strategy is to assist the network in solving PDEs more effectively. During the RBF-assisted processing part, the method selects the center points and collocation points separately to effectively manage data size and computational complexity. Subsequently, the RBF processed data are put into the network for predicting the solutions to PDEs. Finally, a series of experiments are conducted to evaluate the novel method. The numerical results confirm that the proposed method can accelerate the convergence speed of the loss function and improve predictive accuracy. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)
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17 pages, 12977 KiB  
Article
Mathematical Analysis of the Wind Field Characteristics at a Towering Peak Protruding out of a Steep Mountainside
by Mohammed Nabil, Fengqi Guo, Huan Li and Qiuliang Long
Mathematics 2024, 12(10), 1535; https://doi.org/10.3390/math12101535 - 15 May 2024
Viewed by 691
Abstract
Wind field characteristics in a complex topography are significantly influenced by the nature of the surrounding terrains. This study employs onsite measurements to investigate the wind field characteristics at a towering peak protruding out of a steep mountainside, where butterfly−lookalike landscape platform will [...] Read more.
Wind field characteristics in a complex topography are significantly influenced by the nature of the surrounding terrains. This study employs onsite measurements to investigate the wind field characteristics at a towering peak protruding out of a steep mountainside, where butterfly−lookalike landscape platform will be constructed; the impact of the surrounding topography on the wind flow is highlighted. The results showed that the blocking effect of the mountains in the mountainous side of the valley caused a significant drop in the mean wind speed from that direction. The stationary test (reverse arrangement test) indicated that the wind speed had a strong nonstationary characteristic, necessitating the employment of a steady and nonstationary wind speed model to assess the wind turbulence characteristics. The three directions’ wind turbulence integral scales were critically influenced by the occurrence of the wind speedup effect, unexpectedly resulting in the vertical turbulence integral scale being the greatest of the three. Furthermore, the measured wind turbulence properties under both wind speed models showed certain variations from the recommended specifications. Consequently, the impact of the local terrain and the speedup effect on the wind characteristics must be thoroughly evaluated to ensure the structural stability of structures installed at a similar topography. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)
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19 pages, 7479 KiB  
Article
Aerodynamic Performance and Numerical Analysis of the Coaxial Contra-Rotating Propeller Lift System in eVTOL Vehicles
by Jie Xu, Jiaming Yu, Xinjiang Lu, Zhenkun Long, Yuteng Xu and Hao Sun
Mathematics 2024, 12(7), 1056; https://doi.org/10.3390/math12071056 - 1 Apr 2024
Viewed by 907
Abstract
Electric vertical takeoff and landing (eVTOL) vehicles possess high payload transportation capabilities and compact design features. The traditional method of increasing propeller size to cope with high payload is no longer applicable. Therefore, this study proposes the use of coaxial counter-rotating propellers as [...] Read more.
Electric vertical takeoff and landing (eVTOL) vehicles possess high payload transportation capabilities and compact design features. The traditional method of increasing propeller size to cope with high payload is no longer applicable. Therefore, this study proposes the use of coaxial counter-rotating propellers as the lift system for eVTOL vehicles, consisting of two coaxially mounted, counter-rotating bi-blade propellers. However, if the lift of a single rotating propeller is linearly increased without considering the lift loss caused by the downwash airflow generated by the upper propeller and the torque effect of the lift system, it will significantly impact performance optimization and safety in the eVTOL vehicles design process. To address this issue, this study employed the Moving Reference Frame (MRF) method within Computational Fluid Dynamics (CFD) technology to simulate the lift system, conducting a detailed analysis of the impact of the upper propeller’s downwash flow on the aerodynamic performance of the lower propeller. In addition, the aerodynamic performance indicators of coaxial counter-rotating propellers were quantitatively analyzed under different speed conditions. The results indicated significant lift losses within the coaxial contra-rotating propeller system, which were particularly notable in the lift loss of the lower propeller. Moreover, the total torque decreased by more than 93.8%, and the torque was not completely offset; there was still a small torsional effect in the coaxial counter-rotating propellers. The virtual testing method of this study not only saves a significant amount of time and money but also serves as a vital reference in the design process of eVTOL vehicles. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)
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27 pages, 5219 KiB  
Article
Development of a Relationship between Pavement Condition Index and Riding Quality Index on Rural Roads: A Case Study in China
by Li Li, Dandan Liu, Li Teng and Jie Zhu
Mathematics 2024, 12(3), 410; https://doi.org/10.3390/math12030410 - 26 Jan 2024
Viewed by 966
Abstract
The current standard for evaluating road conditions worldwide relies primarily on the Pavement Condition Index (PCI) and the International Roughness Index (IRI). The IRI can be further calculated to obtain the Riding Quality Index (RQI). To assess pavement damage, various imaging equipment is [...] Read more.
The current standard for evaluating road conditions worldwide relies primarily on the Pavement Condition Index (PCI) and the International Roughness Index (IRI). The IRI can be further calculated to obtain the Riding Quality Index (RQI). To assess pavement damage, various imaging equipment is commonly utilized, providing consistent results that align with actual road conditions. For roughness detection, the Laser Profilometer offers excellent results but may not be suitable for rural roads with poor conditions due to its high inspection cost and the need for a stable environmental setting. Therefore, there is a pressing need to develop cost-effective, rapid, and accurate roughness inspection methods for these roads, which constitute a significant portion of the road network. This study examined the relationship between PCI and RQI using nonlinear regression on 30,088 valid pavement inspection records from various regions in China (totaling 24,624.222 km). Our objective was to estimate RQI solely from PCI data, capitalizing on its broad coverage and superior accuracy. Additionally, we explored how PCI levels impact RQI decay rates. The models in this study were compared to several models published in previous studies at last. Our findings indicate that the model performs best for low-grade roads with low PCI scores, achieving over 90% accuracy for both cement concrete and asphalt concrete pavements. Furthermore, different levels of pavement damage have distinct effects on RQI decay rates, with the most significant impact observed when the pavement is severely damaged. The models in this study outperformed all the other available models in the literature. Consequently, under limited inspection conditions in rural areas, pavement damage inspection results can effectively predict riding quality or roughness, thereby reducing inspection costs. Overall, this study offers valuable insights but has limitations, including limited global generalizability and the model’s applicability to high-grade roads. Future research is needed to address these issues and enhance practical applications. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)
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22 pages, 12443 KiB  
Article
A Novel Prediction Model for Seawall Deformation Based on CPSO-WNN-LSTM
by Sen Zheng, Chongshi Gu, Chenfei Shao, Yating Hu, Yanxin Xu and Xiaoyu Huang
Mathematics 2023, 11(17), 3752; https://doi.org/10.3390/math11173752 - 31 Aug 2023
Cited by 2 | Viewed by 857
Abstract
Admittedly, deformation prediction plays a vital role in ensuring the safety of seawall during its operation period. However, there still is a lack of systematic study of the seawall deformation prediction model currently. Moreover, the absence of the major influencing factor selection is [...] Read more.
Admittedly, deformation prediction plays a vital role in ensuring the safety of seawall during its operation period. However, there still is a lack of systematic study of the seawall deformation prediction model currently. Moreover, the absence of the major influencing factor selection is generally widespread in the existing model. To overcome this problem, the Chaotic Particle Swarm Optimization (CPSO) algorithm is introduced to optimize the wavelet neural network (WNN) model, and the CPSO-WNN model is utilized to determine the major influencing factors of seawall deformation. Afterward, on the basis of major influencing factor determination results, the CPSO algorithm is applied to optimize the parameters of Long Short-Term Memory (LSTM). Subsequently, the monitoring datasets are divided into training samples and test samples to construct the prediction model and validate the effectiveness, respectively. Ultimately, the CPSO-WNN-LSTM model is employed to fit and predict the long-term settlement monitoring data series of an actual seawall located in China. The prediction performances of LSTM and BPNN prediction models were introduced to be comparisons to verify the merits of the proposed model. The analysis results indicate that the proposed model takes advantage of practicality, high efficiency, stable capability, and high precision in seawall deformation prediction. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)
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45 pages, 13262 KiB  
Article
An Exact In-Plane Equilibrium Equation for Transversely Loaded Large Deflection Membranes and Its Application to the Föppl-Hencky Membrane Problem
by Jun-Yi Sun, Ji Wu, Xue Li and Xiao-Ting He
Mathematics 2023, 11(15), 3329; https://doi.org/10.3390/math11153329 - 28 Jul 2023
Cited by 2 | Viewed by 892
Abstract
In the existing literature, there are only two in-plane equilibrium equations for membrane problems; one does not take into account the contribution of deflection to in-plane equilibrium at all, and the other only partly takes it into account. In this paper, a new [...] Read more.
In the existing literature, there are only two in-plane equilibrium equations for membrane problems; one does not take into account the contribution of deflection to in-plane equilibrium at all, and the other only partly takes it into account. In this paper, a new and exact in-plane equilibrium equation is established by fully taking into account the contribution of deflection to in-plane equilibrium, and it is used for the analytical solution to the well-known Föppl-Hencky membrane problem. The power series solutions of the problem are given, but in the form of the Taylor series, so as to overcome the difficulty in convergence. The superiority of using Taylor series expansion over using Maclaurin series expansion is numerically demonstrated. Under the same conditions, the newly established in-plane equilibrium equation is compared numerically with the existing two in-plane equilibrium equations, showing that the new in-plane equilibrium equation has obvious superiority over the existing two. A new finding is obtained from this study, namely, that the power series method of using Taylor series expansion is essentially different from that of using Maclaurin series expansion; therefore, the recurrence formulas for power series coefficients of using Maclaurin series expansion cannot be derived directly from that of using Taylor series expansion. Full article
(This article belongs to the Special Issue Mathematical Modeling and Numerical Simulation in Engineering, 2nd Edition)
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