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Computing a Transfer Function of the Poincaré–Steklov Operator for a Functionally Graded Elastic Strip 计算功能分级弹性带的 Poincaré-Steklov 算子的传递函数
IF 0.3 Q4 MECHANICS Pub Date : 2023-12-21 DOI: 10.3103/S0027133023050023
A. A. Bobylev

A boundary value problem is considered in a functionally gradedelastic strip. A three-term asymptotic expansion of a transferfunction is obtained for the Poincaré–Steklov operator thatmaps normal stresses to normal displacements on a part of thestrip boundary. Padé approximations are determined for theobtained asymptotic series. An approach to computing the transferfunction using the asymptotic series and the Padé approximationsis proposed, which reduces computational costs.

摘要 研究了功能分级弹性带材的边界值问题。为将法向应力映射为带状边界部分的法向位移的 Poincaré-Steklov 算子求得了传递函数的三项渐近展开。对得到的渐近级数确定了帕代近似值。提出了使用渐近级数和 Padé 近似值计算传递函数的方法,从而降低了计算成本。
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引用次数: 0
Quasi-Self-Similar Solutions to Some Parabolic Problems in the Theory of Viscoplastic Flow 粘塑性流动理论中一些抛物型问题的拟自相似解
IF 0.3 Q4 Engineering Pub Date : 2023-11-13 DOI: 10.3103/S0027133023040027
V. A. Banko, D. V. Georgievskii

The initial-boundary value problems of acceleration from a state of rest of a two-constant viscoplastic medium (Bingham body) in a half-plane is investigated when the tangential stress is given at the boundary as a piecewise continuous monotonically nondecreasing function of time. As an additional condition at an unknown interface between a flow zone that increases with time in thickness and a stationary semi-infinite rigid zone, the requirement is chosen that the solution of this problem with a tendency to zero of the yield strength of the material at each point and at each moment of time tends to the solution of the corresponding viscous flow problem known as the generalized vortex layer diffusion problem. The exact analytical solutions are found for tangential stress and velocity profiles in nonstationary one-dimensional flow. The cases of self-similarity and so-called quasi-self-similarity are distinguished. The nature of the tendency at (ttoinfty) of the thickness of the layer, in which the shear is realized, to infinity is of particular interest.

研究了半平面上双常粘塑性介质(宾厄姆体)在边界处的切向应力作为时间的分段连续单调非递减函数给定时,在静止状态下加速度的初边值问题。在厚度随时间增加的流动区与固定的半无限刚性区之间的未知界面处,作为附加条件,选择要求该问题的解在每个点和每个时刻材料的屈服强度趋于零时,其解趋向于相应的粘性流动问题的解,即广义涡层扩散问题。得到了非平稳一维流动中切向应力和速度分布的精确解析解。区分了自相似和所谓的准自相似的情况。特别令人感兴趣的是,在(ttoinfty)处发生剪切的层的厚度趋向于无穷大的性质。
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引用次数: 0
Generalized Cesàro Formulas and Third-Order Compatibility Equations 广义Cesàro公式与三阶相容方程
IF 0.3 Q4 Engineering Pub Date : 2023-11-13 DOI: 10.3103/S0027133023040040
S. A. Lurie, P. A. Belov

We consider the classical problem of elasticity theory concerning the conditions of strain compatibility, which ensure the determination of a continuous field of displacements of an elastic body by the strain field. We construct generalized Cesàro representations that allow defining the displacement field through integrodifferential operators on the components of the strain tensor deviator with an accuracy up to quadratic polynomials. It has been established that the quadratures both for the pseudovector of local rotations and for the bulk strain are completely determined by the strain deviator field. We present the conditions for the existence of the listed quadratures, which are written in the form of five third differential order compatibility equations for the five components of the strain deviator tensor.

考虑弹性理论中有关应变相容条件的经典问题,该条件保证了弹性物体的连续位移场是由应变场确定的。我们构造了广义的Cesàro表示,允许通过应变张量偏差分量上的积分微分算子以二次多项式的精度定义位移场。证明了局部旋转伪向量的正交和体应变的正交完全由应变偏差场决定。我们给出了列示正交存在的条件,这些条件用应变偏差张量的五个分量的五个三阶相容方程的形式表示。
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引用次数: 0
On the Variational Principle of Lagrange in the Micropolar Theory of Elasticity at Nonisothermal Processes 非等温过程弹性微极理论中的拉格朗日变分原理
IF 0.3 Q4 Engineering Pub Date : 2023-11-13 DOI: 10.3103/S0027133023040052
A. V. Romanov

In this paper, a variational principle of Lagrange, the Ritzmethod, and piecewise polynomial serendipity shape functions areused to obtain a stiffness matrix and a system of linear algebraicequations in the micropolar theory of elasticity for anisotropic,isotropic, and centrally symmetric material in case of anonisothermal process.

本文利用拉格朗日变分原理、里兹方法和分段多项式偶然性形状函数,得到了各向异性、各向同性和中心对称材料在非等温过程中的弹性微极理论中的刚度矩阵和线性代数方程组。
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引用次数: 0
Equilibrium Point and Phase Portrait of a Model for Flow of Tixotropic Media Accounting for Structure Evolution 考虑结构演化的转向介质流动模型的平衡点和相图
IF 0.3 Q4 Engineering Pub Date : 2023-11-13 DOI: 10.3103/S0027133023040039
A. V. Khokhlov

We continue the systematic analytical study of a nonlinear Maxwell-type constitutive equation for shear flow for thixotropic viscoelastic media accounting for interaction of deformation process and structure evolution, namely, the influence of the kinetics formation and breakage of chain cross-links, agglomerations of molecules and crystallites on viscosity and shear modulus and deformation influence on the kinetics. We formulated it in the previous article and reduced it to the set of two nonlinear autonomous differential equations for two unknown functions (namely, the stress and relative cross-links density). We examine the phase portrait of the system for arbitrary (increasing) material function and six (positive) material parameters governing the model and prove that the (unique) equilibrium point is stable and the only three cases are realized: the equilibrium point is either a stable sink, or a degenerated stable sink, or a stable spiral sink. We found criteria for every case in the form of explicit restrictions on the material function and parameters and shear rate.

我们继续系统地分析研究了触变粘弹性介质剪切流动的非线性maxwell型本构方程,该方程考虑了变形过程和结构演化的相互作用,即链交联的形成和断裂、分子和晶体的团聚对粘度和剪切模量的动力学影响以及变形对动力学的影响。我们在前一篇文章中将其表述为两个未知函数(即应力和相对交联密度)的两个非线性自治微分方程的集合。我们研究了任意(增加)材料函数和控制模型的六个(正)材料参数的系统相肖像,并证明了(唯一)平衡点是稳定的,并且只有三种情况是实现的:平衡点要么是稳定汇,要么是退化稳定汇,要么是稳定螺旋汇。我们找到了每种情况的标准,以明确限制材料功能和参数以及剪切速率的形式。
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引用次数: 0
On the Method for Identifying Inhomogeneous Fields of Residual Stresses 非均匀残余应力场识别方法研究
IF 0.3 Q4 Engineering Pub Date : 2023-08-15 DOI: 10.3103/S0027133023030044
E. B. Zavoychinskaya, A. S. Plotnikov

A numerical-analytical method for three-axial inhomogeneous elastic residual stress determination based on the data of the displacement optical measurement during the incremental hole drilling method is presented. The constitutive relations for the displacements as the three variable functions (in plane of the hole and along its depth) are represented by the Volterra integral operators. A method for finding the basic functions is given. The stress tensor components recovered by the proposed method are in good agreement with the well-known solution of a problem where the residual stresses are formed by bending an elastic-perfectly plastic beam.

提出了一种基于增量钻孔法位移光学测量数据的三轴非均匀弹性残余应力的数值解析方法。位移作为三个变量函数(在孔的平面上和沿孔的深度)的本构关系用Volterra积分算子表示。给出了一种求基本函数的方法。该方法恢复的应力张量分量与已知的完全弹塑性梁弯曲产生残余应力问题的解很好地吻合。
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引用次数: 0
Constitutive Equations with Dissipative Stresses 具有耗散应力的本构方程
IF 0.3 Q4 Engineering Pub Date : 2023-08-15 DOI: 10.3103/S0027133023030032
I. N. Molodtsov

A new class of constitutive equations for complex loading processes is obtained. It has three state functionals. A new method of mathematical modeling and mathematical principle is formulated. According to them, physically correct equations of state are changed by introducing gyroscopic terms that do not perform mechanical work. The constitutive equations of complex loading processes with two state functionals under conditions of force and kinematic loading are constructed. Their connection with the Il’yushin formula and modern theories of plastic flow is obtained. A mathematical model of the domain mechanism of plasticity is formulated. It represents a real deformable continuum as a mixture of an elastoplastic continuum and a Cosserat continuum—flat veinlets (domains of plastic deformation that are the zones of large relative rotations). A physical justification for the inclusion of the asymmetric part of the stress and rotation tensor in the composition of the thermodynamic parameters of the model is given.

得到了一类新的复杂加载过程本构方程。它有三个状态函数。提出了一种新的数学建模方法和数学原理。根据他们的观点,通过引入不做功的陀螺项来改变物理上正确的状态方程。建立了具有两种状态泛函的复杂加载过程在力和运动加载条件下的本构方程。得到了它们与伊留申公式和现代塑性流动理论的联系。建立了塑性区域机理的数学模型。它代表了一个真正的可变形连续体,它是弹塑性连续体和Cosserat连续体-平坦脉(相对旋转较大的塑性变形区域)的混合物。给出了在模型的热力学参数组成中包含应力和旋转张量的不对称部分的物理理由。
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引用次数: 0
On Some Properties of the Kalman Filter in the Pedestrian Navigation Problem 行人导航问题中卡尔曼滤波的若干性质
IF 0.3 Q4 Engineering Pub Date : 2023-08-15 DOI: 10.3103/S0027133023030020
Yu. V. Bolotin, A. V. Bragin

A pedestrian navigation system consisting of two foot-mounted strapdown inertial navigation systems (SINS)s is considered. The zero velocity conditions of the foot in the stance phase of a step and a limited distance between the feet are used for SINS corrections. The aim of the work is to study some consistency properties of the extended Kalman filter. It is shown that this consistency depends on a form of the error equations.

研究了一种由两个脚踏捷联惯性导航系统组成的行人导航系统。在一个台阶的站立阶段,脚的零速度条件和脚之间的有限距离用于捷联惯导系统的修正。本文的目的是研究扩展卡尔曼滤波器的一些一致性。结果表明,这种一致性取决于误差方程的一种形式。
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引用次数: 0
Displacement Discontinuity Method Taking into Account the Curvature of the Crack 考虑裂纹曲率的位移不连续法
IF 0.3 Q4 Engineering Pub Date : 2023-08-15 DOI: 10.3103/S0027133023030056
A. V. Zvyagin, D. D. Novov

The paper is devoted to the development of the displacement discontinuity method for plane problems of fracture mechanics in consideration of the curvature of crack lines. In this paper, some new representations of biharmonic functions are found. This is necessary to obtain the analytical solutions of problems for an elastic plane weakened by a crack in the form of a circular arc. A numerical method is proposed on the basis of these analytical solutions. The numerical values of the stress intensity factor are compared with its known analytical value.

本文研究了考虑裂纹线曲率的平面断裂力学问题的位移不连续方法。本文给出了双调和函数的一些新的表示形式。这对于得到被圆弧形式的裂纹削弱的弹性平面问题的解析解是必要的。在这些解析解的基础上,提出了一种数值方法。将应力强度因子的数值与已知的解析值进行了比较。
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引用次数: 0
Free Oscillations of a Conical Shell 锥形壳的自由振动
IF 0.3 Q4 Engineering Pub Date : 2023-06-22 DOI: 10.3103/S0027133023020024
S. D. Algazin, A. A. Sinitsyn

Free oscillations of a conical shell of finite length are considered. This problem was formulated in the 1960s. A modern algorithm without saturation is given in this paper, and specific calculations which show its high efficiency are discussed.

研究了有限长度圆锥壳的自由振动问题。这个问题是在20世纪60年代提出的。本文给出了一种无饱和的现代算法,并讨论了具体的计算结果,说明了该算法的高效性。
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引用次数: 0
期刊
Moscow University Mechanics Bulletin
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