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Mathematics
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Mathematical Optimization and Computational Mechanics
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Mathematical Optimization and Computational Mechanics

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

Deadline for manuscript submissions: 31 August 2025 | Viewed by 1072

Special Issue Editors

Dr. Hongwei Guo

E-Mail Website
Guest Editor
College of Architecture and Civil Engineering, Beijing University of Technology, Chaoyang District, Beijing 100124, China
Interests: machine learning; deep learning; meta learning; physics; computational method
Dr. Shan Lin

E-Mail Website
Guest Editor
College of Architecture and Civil Engineering, Beijing University of Technology, Chaoyang District, Beijing 100124, China
Interests: machine learning and computational mechanics

Special Issue Information

Dear Colleagues,

Mathematical optimization and computational mechanics are at the heart of advancing engineering applications, from structural stability to material science and geotechnical engineering. This Special Issue aims to bring together a collection of high-quality, peer-reviewed articles that explore the innovative intersection of optimization techniques and computational mechanics, focusing on the mathematical modeling of complex mechanical systems. The proposed topics will highlight research contributions that address the optimization challenges faced in various fields, such as engineering design, structural analysis, material optimization, and computational simulations.

This Special Issue will feature articles of the highest caliber related to the following topics:

  • Mathematical models in optimization and computational mechanics.
  • Numerical methods and algorithms for mechanical systems.
  • Optimization techniques for structural mechanics and stability analysis.
  • Reliability and risk analysis in mechanical and geotechnical systems.
  • Machine learning methods in optimization and mechanics.
  • Advanced computational tools for material modeling and design.
  • Optimization in geotechnical engineering and soil–structure interaction.
  • Multiscale modeling and optimization of mechanical systems.

We invite you to contribute to this dynamic collection of research and look forward to your valuable contributions.

Dr. Hongwei Guo
Dr. Shan Lin
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

  • mathematical optimization
  • computational mechanics
  • structural optimization
  • numerical methods
  • reliability analysis
  • stability analysis
  • geotechnical engineering
  • machine learning in optimization
  • design optimization
  • material modeling

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  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
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  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

18 pages, 11089 KiB  
Article
A Surrogate Model for the Rapid Prediction of Factor of Safety in Slopes with Spatial Variability
by Xitailang Cao, Shan Lin, Miao Dong, Quanke Hu and Hong Zheng
Mathematics 2025, 13(10), 1604; https://doi.org/10.3390/math13101604 - 14 May 2025
Viewed by 154
Abstract
Due to the complexity and long-term nature of geological evolution, geotechnical strength parameters exhibit significant spatial variability, which has a crucial impact on slope stability assessment. While traditional numerical methods combined with Monte Carlo simulations and Gaussian random field theory provide accurate stability [...] Read more.
Due to the complexity and long-term nature of geological evolution, geotechnical strength parameters exhibit significant spatial variability, which has a crucial impact on slope stability assessment. While traditional numerical methods combined with Monte Carlo simulations and Gaussian random field theory provide accurate stability analysis, their high computational cost makes them impractical for large-scale engineering applications. To address this issue, this study proposes an efficient surrogate modeling approach for the rapid prediction of the factor of safety in slopes while considering the spatial variability of geotechnical parameters. The accuracy and robustness of the proposed model are validated through a single-layer slope case study. Results demonstrate that this approach not only ensures computational accuracy but also significantly enhances efficiency. Compared with conventional methods, the surrogate model effectively replaces high-cost numerical simulations, offering a practical and efficient solution for slope stability analysis under complex geological conditions, with high potential for engineering applications. Full article
(This article belongs to the Special Issue Mathematical Optimization and Computational Mechanics)
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37 pages, 19727 KiB  
Article
Shear-Induced Anisotropy Analysis of Rock-like Specimens Containing Different Inclination Angles of Non-Persistent Joints
by Kaiyuan Zhu, Wei Wang, Lu Shi and Guanhua Sun
Mathematics 2025, 13(3), 362; https://doi.org/10.3390/math13030362 - 23 Jan 2025
Viewed by 665
Abstract
Discontinuities in rock mass are usually considered to be important influencing factors for shear failure. As a type of granular material, the macroscopic mechanical behavior of rock masses is closely related to the anisotropy of the contact network. This paper uses the discrete [...] Read more.
Discontinuities in rock mass are usually considered to be important influencing factors for shear failure. As a type of granular material, the macroscopic mechanical behavior of rock masses is closely related to the anisotropy of the contact network. This paper uses the discrete element method (DEM) to simulate direct shear tests of specimens with different joint inclinations and analyzes the evolution of shear-induced fabric anisotropy and contact force anisotropy during the shear process. Three anisotropic tensors aijc, aijn and aijt are defined to characterize the anisotropic behavior of granular materials. The macroscopic mechanical behavior of the specimens is explained from the micromechanical level combined with the evolution laws of the microcracks and energy of the specimens. The research results indicate that, after the appearance of microcracks in the specimens, the joint inclination leads to changes in their macroscopic mechanical behavior such as peak shear stress, peak displacement and failure mode by affecting the development of the fabric and contact anisotropy of the specimens. Meanwhile, a decrease in fabric and contact anisotropy often indicates specimen failure. Full article
(This article belongs to the Special Issue Mathematical Optimization and Computational Mechanics)
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