Structural Optimization and Numerical Modeling of Materials and Engineering

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: 10 October 2026 | Viewed by 542

Special Issue Editors


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Guest Editor
1. Departament d’Enginyeria Civil i Ambiental (DECA), Escola Tècnica Superior d’Enginyers de Camins Canals i Ports de Barcelona (ETSECCPB), Universitat Politècnica de Catalunya—BarcelonaTech (UPC), ETSECCPB, Campus Nord, 08034 Barcelona, Spain
2. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Campus Nord UPC, 08034 Barcelona, Spain
Interests: numerical methods in engineering; finite element method; fatigue; damage

E-Mail Website
Guest Editor
1. Departament d’Enginyeria Civil i Ambiental (DECA), Escola Tècnica Superior d’Enginyers de Camins Canals i Ports de Barcelona (ETSECCPB), Universitat Politècnica de Catalunya—(UPC BarcelonaTech (UPC)), ETSECCPB, Campus Nord, 08034 Barcelona, Spain
2. Centre Internacional de Mètodes Numèrics en Enginyeria International Center for Numerical Methods in Engineering (CIMNE), Campus Nord UPC, 08034 Barcelona, Spain
Interests: FEM; composites; fracture; constitutive modelling

Special Issue Information

Dear Colleagues,

Recent advances in computational mechanics and applied mathematics are reshaping the way engineers design, analyze, and optimize structural systems and advanced materials. High-fidelity numerical methods—such as finite element formulations, multiscale modeling strategies, topology and shape optimization techniques, and advanced constitutive laws—enable the accurate simulation of complex nonlinear behavior in metals, composite materials, and other engineered material systems.

At the same time, the integration of data-driven methodologies, physics-informed machine learning, and high-performance computing is opening new opportunities for accelerating simulations and discovering new models, improving predictive capabilities, and enabling large-scale engineering applications.

This Special Issue, Structural Optimization and Numerical Simulation of Materials and Engineering, aims to collect high-quality contributions addressing theoretical developments, numerical strategies, and engineering applications in structural mechanics, material modeling, and computational optimization. We particularly encourage submissions that combine rigorous mathematical foundations with practical relevance and strong validation, whether numerical, analytical, or experimental.

Topics of interest include, but are not limited to, the following:

  • Numerical methods for structural and material analysis;
  • Finite element procedures and advanced discretization techniques;
  • Fatigue, damage, fracture, and durability modelling;
  • Multiscale and multiphysics simulations;
  • Structural, shape, and topology optimization;
  • Computational modelling of composites and advanced materials;
  • Machine learning-based or hybrid physics-informed models;
  • High-performance computing and large-scale simulations.

This Special Issue welcomes original research papers, review articles, and contributions highlighting emerging trends and innovative engineering applications.

Dr. Sergio Jimenez
Dr. Alejandro Cornejo
Guest Editors

Manuscript Submission Information

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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

  • structural optimization
  • numerical simulation
  • fatigue and damage
  • fracture mechanics
  • composite and advanced materials
  • constitutive modelling
  • data-assisted computational mechanics

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Published Papers (1 paper)

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Research

21 pages, 1400 KB  
Article
Frictional Contact of Functionally Graded Piezoelectric Materials with Arbitrarily Varying Properties
by Xiuli Liu, Kaiwen Xiao, Changyao Zhang, Xinyu Zhou, Lingfeng Gao and Jing Liu
Mathematics 2026, 14(3), 450; https://doi.org/10.3390/math14030450 - 27 Jan 2026
Viewed by 305
Abstract
This study investigates the two-dimensional (2D) steady-state frictional contact behavior of functionally graded piezoelectric material (FGPM) coatings under a high-speed rigid cylindrical punch. An electromechanical coupled contact model considering inertial effects is established, while a layered model is employed to simulate arbitrarily varying [...] Read more.
This study investigates the two-dimensional (2D) steady-state frictional contact behavior of functionally graded piezoelectric material (FGPM) coatings under a high-speed rigid cylindrical punch. An electromechanical coupled contact model considering inertial effects is established, while a layered model is employed to simulate arbitrarily varying material parameters. Based on piezoelectric elasticity theory, the steady-state governing equations for the coupled system are derived. By utilizing the transfer matrix method and the Fourier integral transform, the boundary value problem is converted into a system of coupled Cauchy singular integral equations of the first and second kinds in the frequency domain. These equations are solved semi-analytically, using the least squares method combined with an iterative algorithm. Taking a power-law gradient distribution as a case study, the effects of the gradient index, relative sliding speed, and friction coefficient on the contact pressure, in-plane stress, and electric displacement are systematically analyzed. Furthermore, the contact responses of FGPM coatings with power-law, exponential, and sinusoidal gradient profiles are compared. The findings provide a theoretical foundation for the optimal design of FGPM coatings and for enhancing their operational reliability under high-speed service conditions. Full article
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