Mechanics of Solids最新文献

{"title":"Reconstruction of Accelerations Domain on the Basis of Limited Array of Measured Accelerations and Unknown External Force Excitation","authors":"A. V. Anisimov,&nbsp;A. Yu. Bondarenko,&nbsp;A. I. Likhoded,&nbsp;A. A. Stets,&nbsp;V. A. Titov","doi":"10.1134/S0025654425605373","DOIUrl":"10.1134/S0025654425605373","url":null,"abstract":"<p>During the operation of engineering structures, in some cases on the basis of the results of measurements of kinematic parameters – accelerations at individual points of the structure or angular accelerations – may the need rise to determine these parameters over the entire structure. In addition, the problem of estimating the external force that caused the dynamic response of the structure is of interest. In cases where the point of application of the external force is known, its magnitude and time history can be determined effectively. This paper addresses a more complex problem: determining accelerations over the entire elastic structure when both the point of application and the time dependence of the external force are unknown, based on acceleration measurements at a limited number of points on the structure. The problem of identifying the location and time-dependent function of the external force is also considered. The solution is based on representing the unknown external force as a complex Fourier series with unknown coefficients and minimizing the discrepancy between the measured and calculated accelerations.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751665","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":"Occurrence of Strong Shocks in the Hill-Type Hyperelastic Media","authors":"A. I. Karakozova,&nbsp;E. N. Egereva,&nbsp;S. G. Mistyukova","doi":"10.1134/S0025654425605233","DOIUrl":"10.1134/S0025654425605233","url":null,"abstract":"<p>The phenomenon of occurring strong shocks at the propagation of smooth harmonic acoustic waves is observed in a hyperelastic compressible medium modelled by the Hill-type hyperelastic potential. The observed strong shocks may explain the kinetic and strain energy attenuation together with heat release at the propagation of shear waves in the considered hyperelastic media. The Cauchy formalism is adopted for solving equations of motion and equations of energy balance.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751949","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":"Kinematically Optimal Control of Reorientation of Solid Body (Spacecraft) Taking Account of The Loading of Construction, and Analytical Approximate Solution of the Dynamic Problem of Rotation","authors":"M. V. Levskii","doi":"10.1134/S0025654425603337","DOIUrl":"10.1134/S0025654425603337","url":null,"abstract":"<p>Quaternion solution of the problem on optimal control of a turn of a spacecraft (as solid body) from an arbitrary initial into the prescribed angular position taking account the loading of the construction is presented. To optimize the process of control, we use the combined functional of quality that combines in a given proportion the sum of the integral of kinetic factor (quadratic form relative to angular velocity) and rotation time spent on spacecraft reorientation. Analytical solution of optimal control problem is obtained on the base of quaternion models of the solid body motion controlled. The properties of optimal motion are represented in analytic form. The formalized equations and calculation formulas are written to construct the optimal program of rotation, and the computational scheme for solving the boundary-value problem of a turn is described also. Analytical equations and relations for finding the optimal control are presented. Key relations that determine the optimal values of the parameters of rotation control algorithm are given. A numerical example and results of mathematical modeling that confirm the practical feasibility of the developed method for control of spacecraft attitude are given.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751109","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":"Experimental Study of Penetration Resistance of Composite Layered Structures Including Flexible Auxetic Metamaterials","authors":"S. Yu. Ivanova,&nbsp;K. Yu. Osipenko,&nbsp;N. V. Banichuk,&nbsp;D. S. Lisovenko","doi":"10.1134/S0025654426601424","DOIUrl":"10.1134/S0025654426601424","url":null,"abstract":"<p>The ability of composite structures incorporating flexible metamaterials with a cell-based structure in the form of a convex or concave hexagon to mechanically resist penetration by a rigid spherical striker was experimentally studied. In some experiments, solid layered samples with layers having different internal structures were penetrated. In other cases, the penetrated samples consisted of separate, unconnected layers. The samples were 3D-printed from flexible TPU 95A plastic (thermoplastic polyurethane) and represented metamaterials with various mechanical properties, including auxetic ones. The prepared barriers, similar in total mass, differed in the sequence of laying solid or separate layers and were compared for their ability to reduce the kinetic energy of strikers at a speed of approximately 190 m/s and a temperature of 25°C. Under the chosen experimental conditions, it was found that separate layers better reduce the kinetic energy of the striker. The most efficient order of laying layers in barriers was also determined.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751725","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":"The Analytical Solution of a Problem of Hollow Cylinder Torsion Taking Account of the Postcritical Deformation of Material and Loading System Stiffness","authors":"A. I. Mugatarov","doi":"10.1134/S0025654426602697","DOIUrl":"10.1134/S0025654426602697","url":null,"abstract":"<p>The problem of the hollow cylinder torsion is considered, taking into account the postcritical deformation of the material and the loading system stiffness. The complete stress-strain curve of the material under pure shear is presented as the n-link piecewise linear function. The dependence of the torque on the torsion angle is defined. The conditions of the complete loading diagram realization are determined. The influence of the cylinder geometry on the loading diagram is studied. The possibility of identifying additional deformation reserves by taking into account the material softening is demonstrated. The conclusion is made on the rationality of the postcritical deformation and the loading system stiffness consideration in design.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751582","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":"Mathematical Models of the Wave Solid-State Gyroscope Resonator Dynamics for Objects Moving at High Angular Velocities","authors":"D. A. Maslov","doi":"10.1134/S0025654425604896","DOIUrl":"10.1134/S0025654425604896","url":null,"abstract":"<p>This article develops a nonlinear mathematical model of the resonator dynamics of a wave solid-state gyroscope in slow variables, taking into account the high angular velocities of moving objects. A case is considered in which the cubic nonlinearity inherent in the equations of the resonator dynamics of wave solid-state gyroscopes is taken into account. Mathematical modeling of the resonator dynamics at high angular velocities is performed, demonstrating the adequacy and sufficient accuracy of the proposed mathematical model. It is shown that in addition to the constant angular drift velocity of the wave solid-state gyroscope, caused by the nonlinearity of oscillations and independent of the angular velocity of the moving object, an additional constant component of the angular drift velocity appears, which depends on the angular velocity of the moving object.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751584","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":"Mechanical and Structural Properties of GaN/AlN/GaN/AlN and AlN/GaN/AlN Heterostructures on SiC/Si(111) and Al2O3 Substrates","authors":"A. S. Grashchenko,&nbsp;S. A. Kukushkin,&nbsp;Sh. Sh. Sharofidinov","doi":"10.1134/S0025654425605889","DOIUrl":"10.1134/S0025654425605889","url":null,"abstract":"<p>This article presents a comprehensive analysis of the mechanical and structural characteristics of multilayer GaN/AlN/GaN/AlN and AlN/GaN/AlN heterostructures formed by chloride-hydride epitaxy on hybrid SiC/Si(111) and single-crystal Al₂O₃ substrates. Nanoindentation was used to measure the mechanical properties. Atomic force microscopy was employed to analyze the surface morphology. It was found that the morphological and mechanical properties significantly depend on the substrate type. GaN/AlN/GaN/AlN heterostructures on an Al₂O₃ substrate are characterized by the formation of deep etch pits up to 1500 nm deep, whereas on SiC/Si(111) substrates these structures are devoid of obvious defects and are distinguished by a uniform distribution of irregularities close to normal. Moreover, the AlN/GaN/AlN heterostructures on both substrates exhibit a hilly surface relief with a comparable degree of smoothness. Nanoindentation data revealed differences in the mechanical characteristics. On SiC/Si(111) substrates, the mechanical properties remain stable throughout the entire indentation depth, with an elastic modulus of up to 320 GPa for the GaN/AlN/GaN/AlN structure and up to 340 GPa for AlN/GaN/AlN. At the same time, Al₂O₃ substrates exhibit higher elastic modulus values: up to 397 GPa for GaN/AlN/GaN/AlN and up to 428 GPa for AlN/GaN/AlN, and also exhibit a strain hardening effect. An analysis of the mechanisms of property formation showed that the porous structure of the SiC/Si(111) substrate promotes stress relaxation but increases the dispersion of mechanical characteristics, while the monolithic Al₂O₃ substrate provides higher quality of surface layers but forms a gradient of mechanical stresses across the thickness of the heterostructure.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751726","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 Optimization of an Auxetic Star-Shaped Structure using the Grey Wolf Optimizer (GWO) Algorithm","authors":"Vladimir Sinđelić,&nbsp;Snežana Ćirić-Kostić,&nbsp;Aleksandar Nikolić,&nbsp;Nebojša Bogojević,&nbsp;Giangiacomo Minak","doi":"10.1134/S0025654425607244","DOIUrl":"10.1134/S0025654425607244","url":null,"abstract":"<p>In this study, a parametric optimization of the Star-Shaped Auxetic Structure (SSAS) was performed using the metaheuristic Grey Wolf Optimizer (GWO) algorithm. The main objective was to enhance the Poisson’s ratio while maintaining the volume and mechanical characteristics of the structure. Based on the defined geometric parameters, an analytical model was developed using Castigliano’s second theorem to determine the effective mechanical properties, including relative density, Poisson’s ratio, and Young’s modulus. The optimization was carried out in MATLAB, where the GWO algorithm was employed to identify the optimal combination of geometric parameters, under the constraint that deviations in Young’s modulus and volume did not exceed 1% from the target values. The obtained results show a significant improvement in the negative Poisson’s ratio compared to the analytical model, while the Young’s modulus and relative density remained nearly unchanged. The accuracy of the optimized model was verified through finite element simulations in ANSYS Mechanical, showing very good agreement between analytical, optimized, and FEM results. The proposed approach demonstrates a strong potential for designing lightweight and biomedical auxetic materials requiring controlled deformation within a limited spatial domain.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751138","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":"Post-Buckling of Tapered Functionally Graded Bumped Doubly Curved Shells under Thermal Loads with Variable Thickness Using Isogeometric Analysis","authors":"Sajjad Etehadi,&nbsp;Alireza Shaterzadeh","doi":"10.1134/S0025654425607347","DOIUrl":"10.1134/S0025654425607347","url":null,"abstract":"<p>The present study employs isogeometric analysis (IGA) to investigate the post-buckling behavior of tapered functionally graded (TFG) bump-stiffened doubly curved shells under thermal loading. The high order shear deformation theory (HSDT) is utilized, specifically employing Reddy’s third-order shear deformation theory to describe the shell kinematics. The formulation incorporates von Kármán nonlinearity to account for small strains and moderate rotations. Material properties, varying through the shell thickness are defined using a rule of mixtures and are assumed to be either temperature-dependent or temperature-independent. The governing equations are derived from the principle of virtual work and subsequently discretized using the IGA approach, which naturally and efficiently satisfies the C²-continuity requirement. Newton’s iterative technique in conjunction with the arc-length method is used to trace the post-buckling equilibrium paths. Comprehensive parametric studies are conducted to examine the influences of material gradation, geometric parameters, thickness ratios, tapering configurations, boundary conditions, and temperature distribution on the post-buckling response of the shells.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751265","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":"Influence of the Jacket on Projectile Penetration into Typical Semi-infinite Metallic Targets","authors":"Xie Chengjuan,&nbsp;Ma Minghui,&nbsp;Wu Yiding,&nbsp;Lu Wencheng,&nbsp;Sun Xinyu,&nbsp;Gao Guangfa","doi":"10.1134/S0025654426600492","DOIUrl":"10.1134/S0025654426600492","url":null,"abstract":"<p>Existing research on the penetration of metallic targets by armor-piercing projectiles has predominantly focused on the mechanical behavior of the core, while the role of the jacket encasing the core during penetration is often simplified or even neglected. However, as the first component to contact the target, the jacket accounts for a considerable proportion of the projectile’s mass and undergoes severe deformation, which may significantly influence penetration efficiency and target failure modes. This paper investigates the influence of the projectile jacket on the penetration process of a 12.7 mm API projectile into different metallic target plates through combined experimental and numerical simulation methods. Comparative ballistic tests were conducted using the complete projectile and the bare core against 2A12-T4 aluminum alloy and Q235 steel targets. LS-DYNA simulations were employed to systematically analyze the dynamic behavior and energy dissipation mechanisms of the jacket during penetration. The results show that the presence of the jacket significantly affects penetration performance and crater morphology: for the aluminum alloy target, the penetration depth of the jacketed projectile is approximately 17.84% lower than that of the bare core; for the steel target, the reduction is about 11.84%. The jacket consumes a substantial amount of kinetic energy through its own plastic deformation, fragmentation, and friction with the target, with approximately 85% of its initial energy dissipated as internal energy and heat within the jacket. Furthermore, the jacket transforms the crater morphology from sharp, serrated edges induced by the bare core into smoother, shallower expansion profiles and suppresses the formation of adiabatic shear bands. The study demonstrates that although the jacket increases the initial kinetic energy of the projectile, it reduces penetration efficiency. Its primary role lies in modulating the failure mode of the target and the energy distribution pathway, providing important insights for the evaluation of armor-piercing projectile effects and the design of protective structures.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 2","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751137","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}