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Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and...
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Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering, 2nd Edition

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

Deadline for manuscript submissions: 31 August 2024 | Viewed by 1838

Special Issue Editors

Dr. Shujin Laima

E-Mail Website
Guest Editor
School of Civil Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150090, China
Interests: numerical simulation in fluid dynamics; wind engineering; bridge engineering; fluid mechanics; fluid-structrure interaction; machine learning
Special Issues, Collections and Topics in MDPI journals
Dr. Xiaowei Jin

E-Mail Website
Guest Editor
School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China
Interests: bluff body aerodynamics; data-driven modeling for fluid mechanics; physics-informed machine learning for scientific computing
Special Issues, Collections and Topics in MDPI journals
Dr. Hehe Ren

E-Mail Website
Guest Editor
Department of Civil and Airport Engineering, School of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Interests: multi-scale wind field simulation methods; high-resolution typhoon numerical simulation and physical mechanism analysis; airport engineering and offshore wind turbine disaster prevention and mitigation
Special Issues, Collections and Topics in MDPI journals
Dr. Yong Cao

E-Mail Website
Guest Editor
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Interests: computational fluid dynamics; turbulence simulation; wind engineering; extreme weather; bluff-body aerodynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical modeling and numerical solutions are the mainstream way to represent and predict the complex scientific and engineering problems nowadays, leading to the analysis and design of engineering products and systems. It is significantly supported by the fast development of advanced numerical methods and high-performance computers. The computer methods include mathematical models and numerical algorithms related to finite element, finite difference, finite volume, and meshless discretization method. In addition to the traditional methods, artificial intelligence technology is rapidly popularized in the wide fields of science and engineering, and has enormous potential for solution of the complex physical problems.

This Special Issue intends to collect advances in development and use of mathematical models and numerical methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is very wide, and includes papers on the mathematical modeling and numerical simulations in all aspects of mechanics, including solid (structures), fluids, and multiphysics. The novel mathematical models and computational methods based on finite volume, finite element, finite difference, meshless discretization methods, artificial intelligence, parallel computing, as well as probabilistic and stochastic approaches are also useful for this Special Issue.

Dr. Shujin Laima
Dr. Xiaowei Jin
Dr. Hehe Ren
Dr. Yong Cao
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 modeling
  • numerical simulation
  • mechanics
  • engineering
  • finite element method
  • computer fluid dynamics
  • machine learning
  • reduced order modelling
  • inverse problems

Related Special Issue

Published Papers (3 papers)

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Research

17 pages, 4840 KiB  
Article
Accuracy of Modified Johnson–Cook Modelling of the Blanking Process through Experimental and Numerical Analysis
by Lotfi Ben Said, Taoufik Kamoun, Hamdi Hentati and Mondher Wali
Mathematics 2024, 12(8), 1209; https://doi.org/10.3390/math12081209 - 17 Apr 2024
Viewed by 308
Abstract
Metal parts undergo a blanking test that involves experimentation with different process parameters across multiple levels. The presence of uncontrolled burrs (measured as Hbv) significantly affects the precise geometry of the blanked parts, making it a primary concern in precision blanking. Moreover, [...] Read more.
Metal parts undergo a blanking test that involves experimentation with different process parameters across multiple levels. The presence of uncontrolled burrs (measured as Hbv) significantly affects the precise geometry of the blanked parts, making it a primary concern in precision blanking. Moreover, the maximum blanking force (Fmax) holds considerable significance, as it aids in forecasting fracture mechanisms and plays a pivotal role in the design of blanking tools. The aim of this study is to assess the predictive capabilities of an elasto-plastic model coupled with damage in capturing the behavior of sheet material during the blanking process. Additionally, integrating the rate-dependent aspect into the model is crucial for accurately modeling the mechanical behavior of sheet metal. Our focus remains on demonstrating the efficacy of the model in predicting blanking force and burr formation. The numerical model incorporates modified plasticity and damage Johnson–Cook models to achieve this objective, considering the combined effect of strain and strain rate fields in the sheet blanking process. Experimental validation proves the efficacy of the proposed model in accurately predicting blanking outcomes. The experimental results confirm the model’s capability to provide a consistent prediction of the blanking force and burr dimensions. In addition, it was proved experimentally that the sheet thickness has the most influence on Hbv and Fmax. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering, 2nd Edition)
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13 pages, 4922 KiB  
Article
Analytic Solution for Buckling Problem of Rectangular Thin Plates Supported by Four Corners with Four Edges Free Based on the Symplectic Superposition Method
by Yushi Yang, Dian Xu, Jinkui Chu and Rui Li
Mathematics 2024, 12(2), 249; https://doi.org/10.3390/math12020249 - 12 Jan 2024
Viewed by 604
Abstract
The buckling behavior of rectangular thin plates, which are supported at their four corner points with four edges free, is a matter of great concern in the field of plate and shell mechanics. Nevertheless, the complexities arising from the boundary conditions and governing [...] Read more.
The buckling behavior of rectangular thin plates, which are supported at their four corner points with four edges free, is a matter of great concern in the field of plate and shell mechanics. Nevertheless, the complexities arising from the boundary conditions and governing equations present a formidable obstacle to the attainment of analytical solutions for these problems. Despite the availability of various approximate/numerical methods for addressing these challenges, the literature lacks accurate analytic solutions. In this study, we employ the symplectic superposition method, a recently developed method, to effectively analyze the buckling problem of rectangular thin plates analytically. These plates have four supported corners and four free edges. To achieve this, the problem is divided into two sub-problems and solve them separately using variable separation and symplectic eigen expansion, leading to analytical solutions. Finally, we obtain the resolution to the initial issue by superposing the sub-problems. The current solution method can be regarded as a logical, analytical, and rational approach as it begins with the basic governing equation and is systematically derived without assuming the forms of the solutions. To examine various aspect ratios and in-plane load ratios of rectangular thin plates, which are supported at their four corner points with four edges free, we provide numerical examples that demonstrate the buckling loads and typical buckling mode shapes. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering, 2nd Edition)
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22 pages, 8243 KiB  
Article
Mathematical Formulation and Numerical Simulation of the Mechanical Behavior of Ceramic/Metal (TiB/Ti) FG Sheets Subjected to Spherical Indenter
by Amir Kessentini, Marwa Allouch, Hanen Jrad, Jamel Mars, Lotfi Ben Said, Muapper Alhadri, Mondher Wali and Fakhreddine Dammak
Mathematics 2024, 12(2), 209; https://doi.org/10.3390/math12020209 - 08 Jan 2024
Viewed by 658
Abstract
The main motivation for the present work is to provide an improved description of the response of Functionally Graded (FG) structures under a spherical indenter, considering material nonlinearities. This is achieved through the implementation of elastoplastic material behavior using integration points to avoid [...] Read more.
The main motivation for the present work is to provide an improved description of the response of Functionally Graded (FG) structures under a spherical indenter, considering material nonlinearities. This is achieved through the implementation of elastoplastic material behavior using integration points to avoid the division of the structure into multiple layers. The current paper proposes a numerical investigation into the mechanical response of functionally graded materials (FGMs) in contact with a rigid hemispherical head indenter. The numerical model considers both the Mori–Tanaka model and self-consistent formulas of Suquet to accurately model the smooth variation of material properties through the thickness of the elastoplastic FG material. The model execution involves a UMAT user material subroutine to implement the material behavior into ABAQUS/Standard. The user material UMAT subroutine is employed to introduce material properties based on the integration points, allowing for an accurate representation and analysis of the material’s behavior within the simulation. The developed numerical model is validated through a comparison with experimental results from the literature, showing a good correlation that proves the efficiency of the proposed model. Then, a parametric study is conducted to analyze the effect of the indenter dimension, the indentation depth and the gradient index on the indentation force, the contact pressure evolution, von Mises equivalent stress and equivalent plastic strain distributions located on the vicinity of the contact zone. The results showed that the elastoplastic response of TiB/Ti FG plates is significantly influenced by the gradient index, which determines the properties of the FG composite through the thickness. These results may help development engineers choose the optimal gradation for each industrial application in order to avoid contact damage. Full article
(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering, 2nd Edition)
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