Mathematical Modeling and Optimization in Advanced Composite Materials and Structures

Dear Colleagues,

Advanced composite materials and structures are widely used in aerospace, automotive, energy, marine, and biomedical fields because of their low weight, high strength, and design flexibility. However, they often operate under complex conditions that involve high temperature, vibration, impact, and coupled acoustic and aerodynamic loads. Under such conditions, these structures may exhibit excessive resonant responses, frequency drift, and fatigue damage, which ultimately degrade performance and shorten service life. These challenges motivate the development of mathematical modeling and optimization methods for composite materials and structures.

In recent years, rapid advances in multiscale equivalent modeling approach, unified plate and shell theories, the methods and techniques associated with geometric and material nonlinear analysis, digital twins, parameter identification and uncertainty quantification, topology optimization, etc., provide new tools and pathways for efficient prediction and rapid assessment of service reliability of composite materials and structures. However, numerous key problems remain unresolved. For example, the unresolved quantitative estimation issues of interfaces and defects in composite structures on natural frequencies, damping, and time‑ and frequency‑domain responses, the lack of understanding of modal coupling mechanisms when strong nonlinearity, broadband excitation, and time‑varying parameters are considered, the unrevealing mechanism of energy transfer paths and damage evolution under thermo‑vibro‑acoustic and aerodynamic coupling condition, the insufficient optimization of static and dynamic mechanical properties of composite materials and structures that account for manufacturing deviations and engineering verification, etc.

This Special Issue focuses on mathematical modeling and optimization for advanced composites, integrating theoretical methods, numerical algorithms, and experimental validation. Emphasis will be on the following topics: multiscale dynamic modeling, mechanistic modeling of matrix interface interactions and defect effects, dynamics of complex plates, shells, and combined shells, multiphysics coupling modeling and analysis, and impact and fatigue damage analysis and evolution. This Special Issue also welcomes topics such as integrated optimization from the micro to the macro scale, reinforcement and interface design, inversion identification of equivalent material parameter, etc. We seek submissions of innovative, high‑quality manuscripts that advance theory, computation, and experiment in a coordinated manner.

Prof. Dr. Hui Li
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. AppliedMath is an international peer-reviewed open access quarterly 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 1200 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.

• composite materials
• composite structure
• multiphysics coupling
• multiscale modeling
• dynamic modeling
• vibration and damping performance
• interface behavior and delamination
• optimization design