Advanced Numerical Modelling and Simulation Techniques in Computational Mechanics

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

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1006

Special Issue Editor


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Guest Editor
1. Senior Lecturer, School of Built Environment, Engineering and Computing, Leeds Beckett University, Leeds, UK
2. Visiting Academic, School of Computing, University of Leeds, Leeds, UK
3. Visiting Lecturer, Department of Civil and Structural Engineering, University of Sheffield, Sheffield, UK
Interests: scientific machine learning; computational fluid dynamics (CFD); discrete element method (DEM) and material-point method (MPM); deep learning: physics-informed neural networks (PINNs); computational mechanics; finite element method (FEM); fluid–structure interaction (FSI); isogeometric analysis (IGA): integration of computer aided design and finite element analysis; spectral/hp method

Special Issue Information

Dear Colleagues,

Computational Mechanics is a field of engineering and applied sciences that uses computational methods and algorithms to study and solve problems in mechanics. Mechanics, in this context, refers to the behaviour of physical systems under the influence of forces. Computational mechanics leverages numerical techniques and computer simulations to analyse the behaviour of structures, materials, and fluids, which can be complex or otherwise difficult to solve analytically.

We are pleased to announce this Special Issue of the journal Mathematics entitled “Advanced Numerical Modelling and Simulation Techniques in Computational Mechanics”. This initiative focuses on advances in algorithmic research and practical applications of computational mechanics techniques and methods, which have been attracting growing interest in recent years due to their effectiveness in solving technical problems.

Potential broad topics for submission include, but are not limited to, the following:

  • Isogeometric Analysis (IGA).
  • Phase-Field Modelling.
  • Deep Learning: including Physics-Informed Neural Networks (PINNs) for integrating deep learning with physical models.
  • Boundary Element Method (BEM).
  • Finite Cell Method (FCM).
  • Material Point Method (MPM).
  • Mesh-Free Methods.
  • Virtual Element Method (VEM).
  • Variational Multiscale Method (VMS).

This Special Issue aims to bring together cutting-edge research and innovative applications in computational mechanics, fostering collaboration and knowledge exchange among researchers and practitioners in the field. We welcome high-quality submissions that contribute to the advancement of numerical modelling and simulation techniques, showcasing their impact on solving real-world engineering problems.

Dr. Yousef Ghaffari Motlagh
Guest Editor

Manuscript Submission Information

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Keywords

  • isogeometric analysis
  • phase-field
  • material point method
  • physics-informed neural networks
  • machine learning
  • variational multi-scale method
  • finite cell method
  • virtual element method.

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Published Papers (1 paper)

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Research

22 pages, 1058 KB  
Article
Application of the DTM to the Elastic Curve Equation in Euler–Bernoulli Beam Theory
by Adrian Ioan Botean
Mathematics 2025, 13(16), 2647; https://doi.org/10.3390/math13162647 - 18 Aug 2025
Viewed by 460
Abstract
This study demonstrates the effectiveness of the differential transform method (DTM) in solving complex solid mechanics problems, focusing on static analysis of beams under various loads and boundary conditions. For cantilever beams (BSM1), DTM provided exact polynomial solutions for deflections and slopes: a [...] Read more.
This study demonstrates the effectiveness of the differential transform method (DTM) in solving complex solid mechanics problems, focusing on static analysis of beams under various loads and boundary conditions. For cantilever beams (BSM1), DTM provided exact polynomial solutions for deflections and slopes: a cubic solution for concentrated end loads, a quadratic distribution for applied moments, and a fourth-degree polynomial for uniformly distributed loads, all matching established theoretical results. For simply supported beams (BSM2), DTM yielded solutions across two intervals for midspan concentrated forces, though required corrective terms for applied moments due to discontinuities. Under uniform loading, the method produced precise polynomial solutions with maximum deflection at midspan. Key advantages include DTM’s high-precision analytical solutions without additional approximations and its adaptability to diverse loading scenarios. However, for cases with pronounced discontinuities like concentrated moments, supplementary methods (e.g., Green’s functions) may be needed. The study highlights DTM’s potential for extension to nonlinear or dynamic problems, while software integration could broaden its engineering applications. This study demonstrates, for the first time, how DTM yields exact polynomial solutions for Euler–Bernoulli beams under discontinuous loads (e.g., concentrated moments), overcoming limitations of traditional numerical methods. The method’s analytical precision and avoidance of discretization errors are highlighted. Traditional methods like FEM require mesh refinement near discontinuities (e.g., concentrated moments), leading to computational inefficiencies. DTM overcomes this by providing exact polynomial solutions with corrective terms, achieving errors below 0.5% with only 4–5 series terms. Full article
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