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On Two Effective Numerical-Analytical Methods in Axially Symmetric Dynamic Contact Torsion Problems for an Elastic Foundation 弹性地基轴对称动态接触扭转问题的两种有效数值解析方法
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654425607530
M. A. Sumbatyan, A. V. Sahakyan
{"title":"On Two Effective Numerical-Analytical Methods in Axially Symmetric Dynamic Contact Torsion Problems for an Elastic Foundation","authors":"M. A. Sumbatyan,&nbsp;A. V. Sahakyan","doi":"10.1134/S0025654425607530","DOIUrl":"10.1134/S0025654425607530","url":null,"abstract":"<p>This paper examines two effective methods for solving integral equations arising in axially symmetric dynamic problems of linear elasticity theory for an elastic foundation with mixed boundary conditions. These methods are classified as numerical-analytical (sometimes – referred to as semi-analytical) methods and represent simple numerical approaches to solving integral equations with a kernel whose characteristic part is expressed as a discontinuous integral of the Weber-Schafheitlin type. Such problems arise in contact problems, problems involving cracks, inclusions, overlays, stringers, and other thin amplifiers in semi-bounded domains such as a half-space, layer, or a multilayered half-space. The first method is a mechanical quadrature method based on a quadrature formula for calculating an integral with the above-mentioned kernel in the presence of a square-root singularity of the solution. The second method is a direct collocation method. Both methods reduce the problem to a certain SLAE. The stability of the methods is analyzed by applying them to a simple problem of the described type, for various combinations of physical and geometric parameters, and a comparative analysis is given.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132487","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}
引用次数: 0
Acoustic Black Holes in Hyperelastic Media Defined by Arruda–Boyce Potentials 由Arruda-Boyce势定义的超弹性介质中的声黑洞
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654425605403
A. V. Ilyashenko
{"title":"Acoustic Black Holes in Hyperelastic Media Defined by Arruda–Boyce Potentials","authors":"A. V. Ilyashenko","doi":"10.1134/S0025654425605403","DOIUrl":"10.1134/S0025654425605403","url":null,"abstract":"<p>It has been established that a hyperelastic material with a smooth variation of elastic properties with deformation can serve as an acoustic black hole (ABH) with respect to oscillating acoustic waves propagating in the corresponding hyperelastic medium modeled by Arruda–Boyce potentials. The study is based on a thermodynamic analysis of nonlinear effects that accompany wave propagation and are associated with the formation of strong shock waves in the medium, as well as on the formalization of the Cauchy problem and its numerical solution using an explicit finite-difference Lax–Wendroff scheme in the time domain and the finite element method in the spatial domain. The observed phenomena clarify the appearance of ABHs in media with Arruda–Boyce potentials and can be applied in the development of new types of vibration and seismic isolators that provide dissipation of mechanical energy in a purely elastic dynamic system.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132488","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}
引用次数: 0
Investigation of Elastic Properties of Single Crystals of a Nickel-Based Superalloy under Bending and Torsion by the Method of Speckle Interferometry 用散斑干涉法研究镍基高温合金单晶在弯曲和扭转下的弹性特性
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654426601825
A. I. Epishin, I. N. Odintsev, D. S. Lisovenko
{"title":"Investigation of Elastic Properties of Single Crystals of a Nickel-Based Superalloy under Bending and Torsion by the Method of Speckle Interferometry","authors":"A. I. Epishin,&nbsp;I. N. Odintsev,&nbsp;D. S. Lisovenko","doi":"10.1134/S0025654426601825","DOIUrl":"10.1134/S0025654426601825","url":null,"abstract":"<p>The speckle interferometry has been used to investigate the elastic deformations of samples in the shape of thin narrow single-crystal plates of different crystallographic orientations made of a 2nd generation nickel-based superalloy under pure bending and torsion. The obtained basic values of the elastic characteristics are in good agreement with the literature data for alloys of this class. The investigation of samples with the chosen orientations made it possible to register extreme and special values of Young’s modulus <i>E</i>, shear modulus <i>G</i> and Poisson’s ratio <span>({v})</span>. For Young’s modulus: <span>({{E}_{{{text{min}}}}} = {{E}_{{langle 001rangle }}})</span> = 126 GPa and <span>({{E}_{{{text{max}}}}} = {{E}_{{langle 111rangle }}} = )</span> 307 GPa, for the shear modulus <span>({{G}_{{{text{min}}}}} = {{G}_{{left{ {011} right}langle 01bar {1}rangle }}} = )</span> 44 GPa and <span>({{G}_{{{text{max}}}}} = {{G}_{{left{ {001} right}langle arb bot rangle }}})</span> = 128 GPa, for Poisson’s ratio <span>({{nu }_{{{text{min}}}}} = {{nu }_{{langle 011rangle langle 01bar {1}rangle }}})</span> = –0.10, <span>({{nu }_{{langle 001rangle langle arb bot rangle }}} = )</span> 0.39 and <span>({{nu }_{{{text{max}}}}} = {{nu }_{{langle 011rangle langle 100rangle }}} = )</span> 0.70. That is, cubic crystals of the investigated nickel-based superalloy are highly elastically anisotropic and represent partial auxetics (<span>({{nu }_{{{text{min}}}}} &lt; 0)</span> and <span>({{nu }_{{{text{max}}}}} &gt; 0)</span>), like many cubic crystals of metals.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132490","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}
引用次数: 0
Equilibrium of a Pair of Heavy Articulated Bodies Supported by Rough Horizontal Steps 粗糙水平台阶支撑的一对重铰接体的平衡
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654425606081
A. A. Burov, M. A. Munitsyna, V. I. Nikonov
{"title":"Equilibrium of a Pair of Heavy Articulated Bodies Supported by Rough Horizontal Steps","authors":"A. A. Burov,&nbsp;M. A. Munitsyna,&nbsp;V. I. Nikonov","doi":"10.1134/S0025654425606081","DOIUrl":"10.1134/S0025654425606081","url":null,"abstract":"<p>The problem on equilibrium of a pair of heavy articulated bodies supported by horizontal rough steps is considered. It is assumed that the system remains in the vertical plane, and the joint is frictionless. The equilibrium conditions are written out and studied. Within additional assumptions, regions corresponding to the conditions of existence of equilibria are depicted in the parameter space.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132491","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}
引用次数: 0
Contact of a Punch with a Functionally Graded Coating Taking Into Account Adhesive Friction 考虑黏着摩擦的功能梯度涂层与冲床的接触
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654425606111
S. S. Volkov, A. S. Vasiliev, A. L. Nikolaev, E. V. Sadyrin
{"title":"Contact of a Punch with a Functionally Graded Coating Taking Into Account Adhesive Friction","authors":"S. S. Volkov,&nbsp;A. S. Vasiliev,&nbsp;A. L. Nikolaev,&nbsp;E. V. Sadyrin","doi":"10.1134/S0025654425606111","DOIUrl":"10.1134/S0025654425606111","url":null,"abstract":"<p>A plane contact problem involving the indentation and sliding of a punch on the surface of an elastic half-plane with a functionally graded coating is considered. Adhesive friction acts at the contact. Young’s modulus and Poisson’s ratio of the coating vary with depth according to arbitrary, independent laws. The normal force is applied with some eccentricity to maintain parallelism of the punch motion. The problem is reduced to solving a system of dual integral equations in Fourier transforms for two unknown functions—even and odd. A unique approximate analytical method is used to solve these equations. After inverting the Fourier transform, approximate analytical expressions for the contact stresses and eccentricity are obtained.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132483","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}
引用次数: 0
On Reducing of the Cyclic Machines Input Link Rotation Irregularity by Non-Circular Gears 用非圆齿轮减小循环机床输入连杆转动不均匀性的研究
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654425604847
A. A. Prikhodko, A. V. Novitskii
{"title":"On Reducing of the Cyclic Machines Input Link Rotation Irregularity by Non-Circular Gears","authors":"A. A. Prikhodko,&nbsp;A. V. Novitskii","doi":"10.1134/S0025654425604847","DOIUrl":"10.1134/S0025654425604847","url":null,"abstract":"<p>Cyclic machines play a vital role in the functioning of many sectors of the economy. A key aspect in the design of this class of machines is reducing the input link rotational irregularity caused by the nonlinear load on the machine’s working element and the kinematic features of the actuator. This paper considers the dynamic synthesis of noncircular gears installed between the motor and the actuator, which can significantly reduce rotational irregularity. The dynamics of a cyclic machine are studied using a piston compressor as an example. Centroids of the noncircular gears are constructed based on the law of motion, and the rotational irregularity is studied taking into account the inclusion of the developed gears in the machine design. The resulting method reduces rotational irregularity to δ = 0.11, while the mass of the moving machine links is reduced by 56% compared to a traditional flywheel installation. An experimental test of the proposed method confirms the reduction in input link speed fluctuations.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132318","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}
引用次数: 0
The Hyperbolicity of Coupled Equations in the Mathematical Theory of Plasticity 塑性数学理论中耦合方程的双曲性
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S002565442670007X
Y. N. Radayev
{"title":"The Hyperbolicity of Coupled Equations in the Mathematical Theory of Plasticity","authors":"Y. N. Radayev","doi":"10.1134/S002565442670007X","DOIUrl":"10.1134/S002565442670007X","url":null,"abstract":"<p>The stress-strain state of a rigid-plastic solid with a scattered anisotropic microdamage field is considered. Damage is represented by a symmetric second-rank damage tensor of which the principal axes coincide with the principal axes of the stress tensor. A closed system of static and kinematic equations of coupled plastic strain-damage theory has been obtained in the isostatic coordinate net with respect to the principal stress increments, principal plastic strain rates, and displacement increments, which is particularly convenient to represent and analyze the equations of the coupled problem. In the case of plane plastic deformation has been considered, and it has been demonstrated that the system of fundamental relations is of hyperbolic type, that enables us to extent of the slip-line field concept to the case of coupled states.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132485","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}
引用次数: 0
Experimental Study of the Penetration Resistance of TPU Plastic Plates Made on 3D Printer Using Various Filling Patterns 3D打印TPU塑料板材不同填充方式的渗透阻力实验研究
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654426602533
S. Yu. Ivanova, K. Yu. Osipenko, N. V. Banichuk, D. S. Lisovenko
{"title":"Experimental Study of the Penetration Resistance of TPU Plastic Plates Made on 3D Printer Using Various Filling Patterns","authors":"S. Yu. Ivanova,&nbsp;K. Yu. Osipenko,&nbsp;N. V. Banichuk,&nbsp;D. S. Lisovenko","doi":"10.1134/S0025654426602533","DOIUrl":"10.1134/S0025654426602533","url":null,"abstract":"<p>A series of experiments on the penetration of plate-shaped specimens of thermoplastic polyurethane (flexible TPU 95A plastic), manufactured using various 3D printing infilling patterns, by a rigid spherical striker were conducted. The ability of such specimens to resist penetration and reduce the kinetic energy of strikers at a speed of approximately 190 m/s and a temperature of 25°C was experimentally studied. Four standard 3D printer infilling patterns for continuous filling of a given volume with material were used in preparing the specimens: “line,” “triangle,” “gyroid,” and “cube.” For each pattern, the filling density of the specimens with material varied from 25 to 100 percent. For the selected experimental conditions, it was found that plate-shaped specimens of TPU 95A plastic, printed on a 3D printer using the continuous filling “line” pattern, best reduce the kinetic energy of the striker at the maximum filling density.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132486","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}
引用次数: 0
Hemitropic Micropolar Elastic Energy Form Diagonalization by the Jacobi Multidimensional Rotations Method Jacobi多维旋转法的半偏微极弹性能量形式对角化
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654426700068
E. V. Murashkin, Yu. N. Radaev
{"title":"Hemitropic Micropolar Elastic Energy Form Diagonalization by the Jacobi Multidimensional Rotations Method","authors":"E. V. Murashkin,&nbsp;Yu. N. Radaev","doi":"10.1134/S0025654426700068","DOIUrl":"10.1134/S0025654426700068","url":null,"abstract":"<p>Thе paper is devoted to obtaining the canonical diagonal energy form of a hemitropic micropolar elastic solid. The strain energy is a quadratic form depending on the asymmetric strain and wryness tensors. For the purposes of this study, the A-representation of the strain energy of the hemitropic micropolar elastic medium, characterized by 9 mechanical moduli, is the most convenient. The quadratic form of the strain energy is diagonalized by the method of successive two-dimensional Jacobi rotations. Uncoupled two-dimensional rotations can be represented as a single multidimensional rotation by their composition. Only 5 distinct rotations are sufficient to diagonalize the quadratic-form matrix. As a result of application of the Jacobi method, a diagonal matrix similar to the matrix of the quadratic energy form has been obtained. Moreover, the eigenvalues are situated on the principal diagonal. The composition of 5 indicated rotations, defined as similarity transformations, determines the transition to new canonical variables. The canonical form of the strain energy makes it possible to formulate the equilibrium stability criteria for a hemitropic micropolar elastic solid in an explicit and particularly simple form. Unilateral constraints on the constitutive constants have been obtained, that ensure the positive definiteness of the quadratic form and thereby guarantee the equilibrium stability of the hemitropic micropolar elastic solid. The equivalence of the systems of inequalities, obtained by the Lagrange method and the Jacobi method, has been demonstrated.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132317","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}
引用次数: 0
The Effect of Rheology of the Liquid Mass in Aneurysm on its Deformation 动脉瘤内液质流变对其变形的影响
IF 1 4区 工程技术
Mechanics of Solids Pub Date : 2026-10-05 DOI: 10.1134/S0025654426602223
N. A. Verezub, D. V. Gandilyan, D. S. Lisovenko, A. I. Prostomolotov
{"title":"The Effect of Rheology of the Liquid Mass in Aneurysm on its Deformation","authors":"N. A. Verezub,&nbsp;D. V. Gandilyan,&nbsp;D. S. Lisovenko,&nbsp;A. I. Prostomolotov","doi":"10.1134/S0025654426602223","DOIUrl":"10.1134/S0025654426602223","url":null,"abstract":"<p>This paper presents a numerical analysis of the biomechanical behavior of the abdominal aortic wall and aneurysm. The problem is considered in an axisymmetric formulation, where vascular wall deformation is caused by the hydrodynamic effects of pulsating blood flow, which is described using the Carreau model that takes into account the dependence of viscosity on shear rate. Finite element analysis is used to calculate the relationship between hemodynamic loads and the stress-strain state of the aorta. Particular attention is paid to how changes in the mechanical characteristics of the aneurysm affect on the distribution of local strains and stresses within it.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"61 3","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132484","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}
引用次数: 0
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