{"title":"Comparative analysis of beam responses via Hencky and fractional models under different mass distributions","authors":"Soner Aydinlik , Ahmet Kiris , Wojciech Sumelka","doi":"10.1016/j.mechrescom.2025.104511","DOIUrl":"10.1016/j.mechrescom.2025.104511","url":null,"abstract":"<div><div>This study presents a comparative analysis of the mechanical responses of beams modeled using Hencky and fractional approaches under various mass distribution conditions. The beam models considered in this study are composed of rigid segments connected by rotational springs, with three distinct mass distribution schemes analyzed: masses concentrated at the joints, masses located at the midpoints of each rigid part, and masses uniformly distributed along each segment. The developed model converges to the Euler–Bernoulli beam theory in the continuum limit, as the number of rigid segments tends to infinity. Closed-form expressions for natural frequencies are derived for simply supported boundary conditions. To approximate the dynamic response of these discrete models and capture their scale-dependent effects, corresponding nonlocal fractional continuum models are formulated using the symmetric Caputo derivative. These models enable precise fractional parameter calibration based on discrete systems’ dispersion relations. The analysis reveals a strong influence of the mass distribution on the dynamic behavior, with stiffening or softening effects emerging depending on the mass arrangement. The proposed fractional framework successfully replicates the dispersion characteristics of each discrete Hencky model and confirms that the accurate selection of fractional derivative parameters effectively models the vibrational behavior of microstructured beams.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104511"},"PeriodicalIF":2.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hygrothermal-induced dynamic behavior of stratified composite plates based on mindlin-reissner analysis","authors":"Saira Javed","doi":"10.1016/j.mechrescom.2025.104519","DOIUrl":"10.1016/j.mechrescom.2025.104519","url":null,"abstract":"<div><div>This study investigates the vibration analysis of stratified composite plates of constant thickness subjected to hygrothermal effects. The analysis considers the impact of temperature and moisture variations on the material properties and structural response of stratified composite plates. Governing equations are derived using Mindlin-Reissner Theory (MRT) to capture transverse shear effects accurately. The hygrothermal effects are incorporated into the constitutive equations through temperature- and moisture-dependent material properties, leading to a coupled thermo-mechanical model. A numerical approach, such as the spline approximation method, is employed to analyse the frequencies and mode shapes under various edge conditions. The results indicate that increased temperature and moisture content reduce the stiffness of the stratified composite plates, leading to a decrease in natural frequencies. Additionally, the influence of material alignment, assembling sequence, and boundary conditions on the vibrational response is examined. The findings provide critical intuitions into the design and reliability of stratified composite structures exposed to varying environmental conditions, such as in aerospace, marine, and automotive applications.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104519"},"PeriodicalIF":2.3,"publicationDate":"2025-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Non-Fourier heat conduction: Discrete vs continuum approaches","authors":"S.L. Sobolev","doi":"10.1016/j.mechrescom.2025.104512","DOIUrl":"10.1016/j.mechrescom.2025.104512","url":null,"abstract":"<div><div>Under far from local-equilibrium conditions, that is on ultra-short space and time scales, the inherent non-locality of the heat conduction process begins to play a crucial role. The discrete variable model (DVM), which assumes that time and space are discrete variables, is one of the most effective approaches to describe the nonlocal effects. Heat conduction equation, energy conservation law, and constitutive equation for the heat flux have been formulated and analyzed in the framework of the DVM. The DVM predicts rather unusual behavior in the spectral characteristics of discrete heat equations on ultrashort time and length scales compared to predictions of continuum approaches. This unusual behavior may serve as a guide for new experimental investigations of high-frequency heat flow regimes, observation of new physical phenomena in solid and thermal materials to expand the range of their technological applications.</div><div>To bridge the gap between the discrete and continuum approaches, two invariants for the continualization procedure, namely, thermal diffusivity and propagation velocity of temperature disturbances, have been employed. It has been demonstrated that in the continuum limit the discrete heat equation contains an infinite hierarchy of partial differential equations including classical Fourier, hyperbolic, Guyer-Krumhansl and Jeffreys heat conduction equations. Generalizations of the DVM to two-dimensional and two-temperature cases have been considered. Possible applications of the discrete approach to heat conduction in nano systems and metamaterials have been discussed.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104512"},"PeriodicalIF":2.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A discrete model for elasticity with microstructure","authors":"D. Polyzos , T.V. Gortsas , S.V. Tsinopoulos , D.E. Beskos","doi":"10.1016/j.mechrescom.2025.104510","DOIUrl":"10.1016/j.mechrescom.2025.104510","url":null,"abstract":"<div><div>In the mid-1960s, Mindlin introduced his theory of strain gradient elasticity (SGE), along with one of its most widely recognized simplified versions, known as SGE-Form II. These enhanced theories were motivated by the need to capture dynamic phenomena that classical elasticity fails to address. Although theoretically elegant, the inclusion of numerous material constants and internal length scale parameters makes the practical application of both SGE and SGE-Form II challenging—even for one-dimensional (1D) problems. A practical approach for identifying these parameters involves validating the theories through lattice models, where both the microstructure and macrostructure are materially and geometrically well-defined. Using a simple 1D lattice model with nearest and next-nearest neighbor spring connections and distributed mass, Polyzos and Fotiadis (Int. J. Solids Struct. 49, 470–480, 2012) were the first to successfully validate Mindlin’s SGE-Form II and to interpret the intrinsic parameters introduced by the theory. Despite significant efforts, no lattice model has yet been shown to fully replicate the behavior described by the general SGE theory, even in 1D cases. This gap is addressed in the present work through the use of a simple 1D lattice model and the implementation of a continualization process similar to that employed by Polyzos and Fotiadis (2012).</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104510"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonlinear electromechanical behaviour of piezoelectric thin sheet actuators under large deformation","authors":"Mostafa Alizadeh, Xiaodong Wang","doi":"10.1016/j.mechrescom.2025.104509","DOIUrl":"10.1016/j.mechrescom.2025.104509","url":null,"abstract":"<div><div>Piezoelectric thin sheet actuators have diverse potential applications in designing advanced structures, such as programmable systems, tunable active metamaterials and buckling-based energy harvesting systems. In this paper, the nonlinear electromechanical behaviour of piezoelectric thin sheet actuators under large deformation is studied based on a generalized elastica model. The presented model is distinct from the classical elastica, notably by considering the extensibility of the actuator and the coupled electromechanical loads. The thin-sheet actuator is treated as an extensible electroelastic Euler–Bernoulli beam, incorporating piezoelectric effects, axial deformation and large deflection. The problem is formulated as a generalized elastica problem and the analytical solution is provided. The general nonlinear behaviour of the actuator is then evaluated and the existence of different deformation modes is discussed. Typical examples are provided to show the effect of the electromechanical loading condition upon the nonlinear response of the actuator. The results from the new model are also compared with those from a simplified nonlinear model of elastic thin sheets to evaluate the effect of large deformation. The comparison shows a very good agreement for small deformation but predicts a significant discrepancy between the two modes when the deformation is large, indicating the necessity of considering the elastica effect when large deformation is to be considered in design. The current work offers fundamental insights into the electromechanical behaviour of thin-sheet piezoelectric actuators with large deformation, thereby advancing their performance for applications in advanced structures.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104509"},"PeriodicalIF":2.3,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145005359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Early traces of the principle of virtual work in Hellenistic texts: Exegesis of problems 1, 2 and 3 in pseudo-Aristotle’s Mechanica Problemata","authors":"Mario Spagnuolo , Francesco dell’Isola","doi":"10.1016/j.mechrescom.2025.104499","DOIUrl":"10.1016/j.mechrescom.2025.104499","url":null,"abstract":"<div><div>Our aim is to try to trace, in the history of mechanics, the first formulation of the principle of virtual work (PVW). This important question is, of course, connected with the origin of the concept of <em>kinematics</em> and its relation with the concept of <em>dynamics</em>. Now it is widely accepted that the Principle of Virtual Velocities (later called Virtual Work) was known in a geometrical form by the author of the Greek text <em>Mechanica Problemata</em> (<em>The Mechanical Problems</em>). Indeed, this text does not appear to be a theoretical treatise but rather a collection of solved exercises, mainly concerning statics, the functioning of machines and some dynamics. In this paper we present our exegesis of the first three problems of the <em>Mechanica Problemata</em>, because we believe that deeply understanding its content may allow us to clarify the Greek origin of the Principle of Virtual Work, to locate in space and time the birth of mathematized mechanics and to prove that Renaissance mechanics derives from Greek sources.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"148 ","pages":"Article 104499"},"PeriodicalIF":2.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"User-friendly Gotoh’s 1977 fourth-order yield function","authors":"W. Tong, I.R. Awad","doi":"10.1016/j.mechrescom.2025.104507","DOIUrl":"10.1016/j.mechrescom.2025.104507","url":null,"abstract":"<div><div>The homogeneous polynomial of fourth order with nine coefficients as originally developed by Gotoh in 1977 is a simple non-quadratic yield function that can model fairly well an orthotropic sheet metal under both uniaxial and biaxial stress states. Unlike Yld2000-2d yield function with eight anisotropic material parameters, however, a Gotoh’s 1977 yield function calibrated by the conventional direct method may not be convex and has thus not been as widely used in sheet metal forming analyses. Four user-friendly methods to develop a strictly convex fourth-order yield function are presented and evaluated in this study. The first three methods decompose Gotoh’s 1977 quartic yield function into a sum of two or more fourth-order polynomials whose convexity may be rather easily established. The last method uses a certain algebraic certificate of sum-of-squares (SOS) convexity to verify directly the convexity of a calibrated Gotoh’s yield function. More importantly, a least-square minimization (with algebraic convex constraints as needed) may also be readily implemented using these methods towards parameter identification of a Gotoh’s yield function with guaranteed convexity. These four methods were subsequently applied to verify the convexity of many calibrated Gotoh’s yield functions reported in the literature. Convexity-constrained parameter identification was also carried out successfully using a set of twelves experimental inputs for one aluminum sheet and one steel sheet. Except the method based on a sum of squares of Hill’s 1948 quadratic yield functions, results of our current study showed that other three methods achieved nearly equal effectiveness. As the SOS-convex method is easiest to use, it is thus recommended as the preferred user-friendly method in developing convex Gotoh’s yield functions for industrial sheet metal forming applications.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"148 ","pages":"Article 104507"},"PeriodicalIF":2.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lin Lin , Shilun Zhao , Yangyang Qu , Yifeng Lin , Nian-Zhong Chen , Haoran Xu
{"title":"Fracture phase-field method based prediction of fatigue crack propagation at a Monopile foundation","authors":"Lin Lin , Shilun Zhao , Yangyang Qu , Yifeng Lin , Nian-Zhong Chen , Haoran Xu","doi":"10.1016/j.mechrescom.2025.104508","DOIUrl":"10.1016/j.mechrescom.2025.104508","url":null,"abstract":"<div><div>A fracture phase-field method based prediction of fatigue crack propagation at a monopile foundation is presented, in which the propagation behavior of surface and embedded cracks at a monopile foundation is investigated. Both surface cracks and embedded cracks are modeled through a diffusive crack representation governed by phase-field variables. Energy-based regularization is employed, where crack evolution is driven by the minimization of total energy, combining elastic strain energy and fracture surface energy. The coupled mechanical-phase field equations are solved to simulate crack initiation and growth without predefined paths, and tensile-compressive energy decomposition is applied to avoid unphysical crack closure. A cycle-jump algorithm is integrated to bypass linear elastic phases and accelerate high-cycle fatigue simulations. Three-dimensional local models are established to analyze crack interactions under stress amplitudes derived from global monopile analysis. Surface cracks, embedded cracks, and their coplanar configurations (with varying thickness- and length-direction spacing) are systematically investigated. Key findings show that surface crack growth rates increase with larger crack depth-to-length ratios, while embedded crack growth is dominated by depth increments. Coplanar crack interactions in the thickness direction accelerate propagation as spacing decreases, whereas increased length-direction separation alters crack paths and delays coalescence.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"148 ","pages":"Article 104508"},"PeriodicalIF":2.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Reliability assessment of critical speed in spinning disks under uncertainty","authors":"H. Nouri, M.A. Foyouzat, M. Mofid","doi":"10.1016/j.mechrescom.2025.104503","DOIUrl":"10.1016/j.mechrescom.2025.104503","url":null,"abstract":"<div><div>Ensuring the structural integrity of spinning disks under uncertain operating conditions is essential for high-speed engineering systems. This study presents a reliability-based assessment of out-of-plane vibrations by incorporating uncertainty in key design parameters. An exact analytical solution from the literature is adopted to compute the first critical speed with high precision. Sensitivity analysis shows that variations in radius, thickness, and elastic modulus significantly affect the onset of dynamic instability. These parameters, together with angular velocity, are treated as independent random variables. A limit state function is defined based on the first critical speed, and the reliability index is evaluated using Monte Carlo simulation. Results indicate a steep decline in the reliability index as angular velocity approaches the critical threshold, emphasizing the importance of accounting for parameter variability in design. This approach provides valuable insight into the probabilistic behavior of spinning disks and supports safer and more efficient designs in demanding applications such as turbines, brake and clutch systems, cutting disks, and data storage devices.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"148 ","pages":"Article 104503"},"PeriodicalIF":2.3,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Parametric Analysis of Porous FGM Core and CNT Distribution Effects on Vibration Behavior of Truncated Conical Sandwich Shells","authors":"Zahra Khoddami Maraghi","doi":"10.1016/j.mechrescom.2025.104505","DOIUrl":"10.1016/j.mechrescom.2025.104505","url":null,"abstract":"<div><div>This study investigates the free vibration behavior of a three-layer sandwich truncated conical shell featuring a functionally graded porous (FG-porous) core between carbon nanotube (CNT)-reinforced composite face sheets. To model material behavior, five CNT distribution profiles and three porosity patterns—symmetric, non-symmetric, and uniform—are considered. Temperature-dependent material properties are incorporated using established micromechanical relations. The structural modeling is based on first-order shear deformation theory (FSDT), which accounts for transverse shear effects through a correction factor. Governing equations are derived using the energy method in conjunction with Hamilton’s principle. A comprehensive parametric analysis is performed to assess the influence of CNT gradation, porosity distribution, and key geometric parameters such as cone angle, radii, layer thicknesses, and shell length on the vibrational response. Numerical results show that increasing CNT volume fraction and adopting the AV distribution model lead to higher natural frequencies, while increased porosity and core thickness generally reduce them. Boundary conditions also significantly influence the dynamic response. These insights contribute to the design optimization of advanced composite conical structures in aerospace, marine, and mechanical applications.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"148 ","pages":"Article 104505"},"PeriodicalIF":2.3,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}