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Symmetry
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Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models,...
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Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models, Numerical Modelling, Experiments, Symmetry and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 2152

Special Issue Editors

Dr. Christian Iandiorio

E-Mail Website
Guest Editor
Department of Enterprise Engineering, University of Rome “Tor Vergata”, 00133 Rome, Italy
Interests: nonlinear mechanics; finite element modelling; flexible multibody; experimental mechanics
Dr. Fabio Botta

E-Mail Website
Guest Editor
Department of Industrial, Electronic and Mechanical Engineering, University of Rome Tre, 00154 Rome, Italy
Interests: mechanical vibrations; mechanics of plates and shells; smart materials; rotor dynamics; turbomachinery
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mechanics is the oldest branch of applied science, yet it continues to experience rapid and ongoing development across various fields, such as in the mechanical, aeronautical, naval, and aerospace engineering fields, as well as in the medical sector. The industrial impact of basic research is vast, and less and less time is required for new ideas and theories to be applied in industry. The important advancements in computational methods, driven by the increasing power of modern computers, combined with cutting-edge manufacturing technologies—particularly additive manufacturing—have made it possible to design and produce complex mechanical systems that were unthinkable just a few years ago. Nonetheless, the fundamental importance of an analytical model remains unquestionable. Even when simplified, such models provide the essential foundation for design, which can then be refined and validated through numerical simulations and experimental testing.

This Special Issue on " Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models, Numerical Modelling, Experiments, Symmetry and Applications " aims to showcase the latest developments in mechanics, within both fundamental research and the industrial sector. It focuses on the essential triad of modern research, namely analytical modeling, numerical validation (such as finite element or multibody analyses), and experimentation.

A noteworthy feature of this issue is the exploration of symmetry as a fundamental concept in both mathematical and numerical modeling. This focus provides a platform for contributions that delve into the intricate balance and contrasts between symmetry and asymmetry, spanning a broad spectrum of mechanical topics, including but not limited to:

  • Nonlinear mathematical models
  • Finite element modeling
  • The dynamics of rigid and flexible multibody systems
  • A kinematic analysis and synthesis of compliant mechanisms
  • The vibrations of beams, plates and shells
  • Experimental mechanics

The goal of this Special Issue is to serve as a comprehensive collection of original research on the mechanics of rigid and deformable systems, providing the scientific community and readers with the latest insights and advancements.

Papers may focus on theory, experimentation, algorithm development, numerical simulations, or practical applications, provided the work is original and advances the field. Papers centered on experimentation, simulations, or applications must do more than simply present results; they should offer insights into the underlying theoretical basis or propose a clear connection to theoretical interpretation.

Dr. Christian Iandiorio
Dr. Fabio Botta
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • mechanics
  • mechanisms
  • flexible structures
  • finite element modelling
  • multibody dynamics
  • experimental mechanics

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

Published Papers (4 papers)

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30 pages, 24914 KiB  
Article
Algorithm to Find and Analyze All Configurations of Four-Bar Linkages with Different Geometric Loci Degenerate Forms
by Giorgio Figliolini, Chiara Lanni and Luciano Tomassi
Symmetry 2025, 17(8), 1171; https://doi.org/10.3390/sym17081171 - 22 Jul 2025
Abstract
A general algorithm to determine the coupler link geometric loci, such as centrodes, inflection and return circles, as well as circling-point and centering-point curves, is formulated to analyze any type of four-bar linkages with the main target to find all mechanism configurations, in [...] Read more.
A general algorithm to determine the coupler link geometric loci, such as centrodes, inflection and return circles, as well as circling-point and centering-point curves, is formulated to analyze any type of four-bar linkages with the main target to find all mechanism configurations, in which at least one of the above-mentioned loci degenerates. Thus, different types of four-bar linkages, such as crank-rocker, double-crank, double-rocker and triple-rocker, are classified according to Grashof’s law, in order to distinguish and analyze their corresponding geometric loci. In particular, the proposed algorithm is based on four diagrams of the angular velocity ratios versus the mechanism driving angle, which consider the links pairs of input/output, input/coupler, and output/coupler, along with those of coupler/input and coupler/output for their relative motion. These diagrams allow the determination of all mechanism configurations according to Freudenstein’s theorems, where the aforementioned geometric loci degenerate into straight lines, including the line at infinity, ϕ-curves, and/or equilateral hyperbolas. This algorithm has been implemented in Matlab in order to run several examples regarding different four-bar linkages, according to Grashof’s law, and analyzing the degenerate forms of their inflection and return circles, as well as the circling-point and centering-point curves, that are also validated by using the collineation axis. Full article
(This article belongs to the Special Issue Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models, Numerical Modelling, Experiments, Symmetry and Applications)
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14 pages, 1694 KiB  
Article
Elastic to Plastic Lattice Structure Homogenization via Finite Element Limit Analysis
by Renato Zona and Vincenzo Minutolo
Symmetry 2025, 17(7), 1120; https://doi.org/10.3390/sym17071120 - 12 Jul 2025
Viewed by 186
Abstract
This work focuses on characterizing structured metamaterials by assessing their elastic law and ultimate strength using finite elements and limit analysis applied to a representative volume element. The elastic and plastic behavior of a reference geometry—the octet truss lattice—is obtained by calculating the [...] Read more.
This work focuses on characterizing structured metamaterials by assessing their elastic law and ultimate strength using finite elements and limit analysis applied to a representative volume element. The elastic and plastic behavior of a reference geometry—the octet truss lattice—is obtained by calculating the response of the representative volume element subjected to prescribed tensor strain bases, namely pure normal strain and pure shear, along the cube symmetry directions. The geometry of the body centered cubic and pure cubic phases of the representative volume element has been analyzed, highlighting that the elastic isotropic behavior depends on the ratio between the stiffnesses of the two phases. The ultimate behavior of the structure has been analyzed through the direct application of the lower bound method of limit analysis. The method has been implemented in a direct finite element environment using the limit analysis procedure developed by the authors. The method was already used and described in previous publications and is briefly recalled. It is based on the identification of the linear operator linking the self-equilibrated stress set to a discrete parameter manifold, accounting for the piecewise continuous distribution of the permanent strain. In the paper, it is highlighted that for different aspect ratios between the body-centered cubic and the pure cubic phase geometry, different ratios between limit shear stress and normal stress arise, the isotropic one assumed to coincide with the von Mises result, where σ0τ0=3. Full article
(This article belongs to the Special Issue Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models, Numerical Modelling, Experiments, Symmetry and Applications)
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14 pages, 6635 KiB  
Article
Slope Calculation Analysis Based on Arbitrary Polygonal Hybrid Stress Elements Considering Gravity
by Chang Liu, Jingjie Tian, Changhao Hu, Fan Xia, Runjie Wang, Xuyang Wei and Ying Xu
Symmetry 2025, 17(2), 265; https://doi.org/10.3390/sym17020265 - 10 Feb 2025
Viewed by 601
Abstract
This article proposes an arbitrary polygonal hybrid stress element considering gravity. It derives an arbitrary polygonal hybrid stress element considering gravity alone for slope stability related engineering analysis. In the stability analysis of slopes, slope disasters caused by gravity erosion have recently become [...] Read more.
This article proposes an arbitrary polygonal hybrid stress element considering gravity. It derives an arbitrary polygonal hybrid stress element considering gravity alone for slope stability related engineering analysis. In the stability analysis of slopes, slope disasters caused by gravity erosion have recently become an urgent problem to be solved through engineering. The traditional finite element analysis of slope stability faces problems such as a large number of divided elements and slow calculation efficiency. By introducing high-order stress fields through stress hybridization elements, accurate results can be simulated using a small number of elements. When dividing the mesh, most of the cell shapes are asymmetric, and the shape of the cell can be any polygon, which can simulate the geometric shape of complex slopes well and more accurately calculate the stress distribution in different parts, thus accurately simulating the stability situation in engineering. By comparing with the corresponding commercial software MARC 2020, the effectiveness and efficiency of the element were verified. It has been proven that any polygonal hybrid stress element has the advantage of flexible mesh division, which can obtain high-order stress fields and stress concentration phenomena with fewer elements. Applying this element to practical problems of slopes in engineering has also achieved good calculation results. Full article
(This article belongs to the Special Issue Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models, Numerical Modelling, Experiments, Symmetry and Applications)
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17 pages, 4976 KiB  
Article
Second-Order Kinematic Invariants for the Design of Compliant Auxetic Symmetrical Structures
by Marco Cirelli, Matteo Autiero, Luca D’Angelo and Pier Paolo Valentini
Symmetry 2025, 17(1), 134; https://doi.org/10.3390/sym17010134 - 17 Jan 2025
Viewed by 828
Abstract
Auxetic structures have great potential in modern engineering, and their design represents an emerging field in industrial applications. The accurate synthesis of the elements of such structures requires multidisciplinary approaches that combine kinematics and structural mechanics. Design methodologies are often based on complex [...] Read more.
Auxetic structures have great potential in modern engineering, and their design represents an emerging field in industrial applications. The accurate synthesis of the elements of such structures requires multidisciplinary approaches that combine kinematics and structural mechanics. Design methodologies are often based on complex time-consuming numerical methods and with considerable computational burden for exploring a large set of alternatives. The aim of the present work is to propose a novel method for designing symmetrical auxetic structures based on the use of pseudo-rigid mechanisms that can reproduce their nonlinear elasto-kinematic behavior with a limited set of parameters. For the definition of these pseudo-rigid mechanisms, the theory of kinematic invariants is proposed. It allows for the deduction of surrogate rigid-link mechanisms with a simpler structure but remarkable accuracy. This approach is an emerging method employed in the generic synthesis and analysis of compliant mechanisms, and, in this study, it is extended for the first time to support the design of auxetic structures. This paper describes the analytical process to deduce the design equations and discusses the example of an application to a symmetrical re-entrant structure, comparing the results with those of a numerical flexible multibody model, a finite element model, and with experimental tests. All the comparisons demonstrate the considerable potential of the proposed methodology, which can also be adapted to other types of auxetic structures. Full article
(This article belongs to the Special Issue Advances in Mechanics of Rigid and Flexible Systems: Mathematical Models, Numerical Modelling, Experiments, Symmetry and Applications)
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