Dynamic Deformation of a Curved Plate with a Rigid Insert

A general solution is obtained for dynamic bending of ideal rigid-plastic plates with a clamped or simply supported curved contour containing an absolutely rigid insert of an arbitrary shape. The plate is affected by a short-time high-intensity explosive dynamic load uniformly distributed over the surface. It is shown that there are several mechanisms of plate deformation. Equations for dynamic deformation are derived for each mechanism, and conditions of occurrence are analyzed. Examples of numerical solutions are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 126–138, March–April, 2006.     

Periodic Orbits for Planar Piecewise Smooth Systems with a Line of Discontinuity

In this work we examine the existence of periodic orbits for planar piecewise smooth dynamical systems with a line of discontinuity. Unlike existing works, we consider the case where the line does not contain the equilibrium point. Most of the analysis is for a family of piecewise linear systems, and we discover new phenomena which produce the birth of periodic orbits, as well as new bifurcation phenomena of the periodic orbits themselves. A model nonlinear piecewise smooth systems is examined as well.     

平面薄壁回旋曲线梁变形分析

薄壁缓和曲线梁在桥梁工程中存在广泛应用,其力学特性复杂,变形分析困难.基于Vlasov薄壁梁理论,假定曲梁截面形心和剪心重合,并忽略剪切变形的影响,建立了回旋线型等截面薄壁缓和曲线梁的变形微分方程,并与已有模型进行对比分析.该模型平面内变形与平面外变形是不耦联的,可以独立求解.采用微分求积法求解该模型,给出一两端固定的回旋曲线梁在自重作用下的变形算例,进行平面外的变形和内力反应分析,并给出了相应的结论.     

Short-Term Microdamage of a Granular Material under Physically Nonlinear Deformation

The structural theory of short-term damage is generalized to the case where the undamaged components of a granular composite deform nonlinearly. The basis for this generalization is the stochastic elasticity equations for a granular composite with porous components whose skeletons deform nonlinearly. Microvolumes of the composite components meet the Huber–Mises failure criterion. Damaged microvolume balance equations are derived for the physically nonlinear materials of the components. Together with the equations relating macrostresses and macrostrains of a granular composite with porous nonlinear components, they constitute a closed-form system. The system describes the coupled processes of physically nonlinear deformation and microdamage. Algorithms for calculating the microdamage–macrostrain relationship and plotting deformation diagrams are proposed. Uniaxial tension curves are plotted for the case where microdamages occur in the linearly hardened matrix and do not in the inclusions, which are linearly elastic     

Influence of Physically Nonlinear Deformation on Short-Term Microdamage of a Laminar Material

The structural theory of short-term damage is generalized to the case where the undamaged components of an N-component laminar composite deform nonlinearly. The basis for this generalization is the stochastic elasticity equations for an N-component laminar composite with porous components whose skeleton deforms nonlinearly. Microvolumes of the composite components meet the Huber–Mises failure criterion. Damaged microvolume balance equations are derived for the physically nonlinear materials of the composite components. Together with the equations relating macrostresses and macrostrains of the laminar composite with porous nonlinear components, they constitute a closed-form system. This system describes the coupled processes of physically nonlinear deformation and microdamage. For a two-component laminar composite, algorithms for calculating the microdamage–macrostrain relationship and plotting deformation curves are proposed. Uniaxial tension curves are plotted for the case where microdamages occur in the linearly hardening component and do not in the linearly elastic component     

Deformation of a shallow shell of revolution into a circular plate

If the curvature of a shell changes under the action of an external force, then the shell can enter a strain state in which it acquires the shape of a plate. In the framework of physical and geometrical linearity, we suggest a solution of the axisymmetric problem about the stress-strain state of a shallow shell of revolution transformed into a circular plate.     

Theory of Short-Term Microdamageability for a Homogeneous Material under Physically Nonlinear Deformation

The structural theory of short-term damageability is generalized to the case of physically nonlinear deformation of an undamaged material. The stochastic elasticity equations for a porous medium whose skeleton deforms nonlinearly are used. The failure criterion for a microvolume of the material is assumed to be in the Huber–Mises form. The microdamage balance equation for a physically nonlinear material is derived. This equation and the macrostress–macrostrain relation for a porous physically nonlinear material constitute a closed-form system describing the coupled processes of physically nonlinear deformation and microdamage. An algorithm is constructed for computing microdamage–macrostrain relationships and plotting deformation curves. Such curves are plotted for the case of uniaxial tension     

Isogeometric Analysis of the Nonlinear Deformation of Planar Flexible Beams with Snap-back

Based on the continuity of the derivatives of the Non-Uniform Rational B-Splines(NURBS) curve and the Jaumann strain measure, the present paper adopted the position coordinates of the control points as the degrees of freedom and developed a planar rotation-free Euler-Bernoulli beam element for isogeometric analysis, where the derivatives of the field variables with respect to the arc-length were expressed as the sum of the weighted sum of the position coordinates of the control points, and the NURBS basis functions were used as the weight functions. Furthermore, the concept of bending strip was used to involve the rigid connection between multiple patches. Several typical examples with geometric nonlinearities were used to demonstrate the accuracy and effectiveness of the proposed algorithm. The presented formulation fully accounts for the geometric nonlinearities and can be used to study the snap-through and snap-back phenomena of flexible beams.     

Planar problem of penetration of thin elastic cylindrical shells into a compressible fluid

Institute of Mechanics, Academy of Sciences of the UkrSSR, Kiev. Kiev Automobile-Highways Institute, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 9, pp. 66–75, September, 1990.     

复合材料粘接件热变形问题实验研究

本文采用云纹干涉法,对复合材料粘接件承受温度载荷作用,粘接板热膨胀失配造成的胶层剪应变及其随温度的变化特进行了分析,提出了用复合材料两个方向膨胀系数分别取代各向同性体问题的热膨胀系数,为云纹干涉法在复合材料热变形问题的热膨胀系数,为云纹干涉法在复合材料热变形问题的应用打下了基础.     

A Normal Force on the Free Surface of a Coated Material

The three-dimensional theoretical solution of a concentrated normal force acting on the free surface of a coated material has been deduced by applying the reflection method. It is found that all stress functions defined in the local coordinate systems with their origins placed at each mirror point can be deduced from the fundamental solution of a concentrated normal force acting on the free surface of a semi-infinite homogeneous medium. The structure of the elastic solution has been illustrated by numerical analysis. It is found that only the stress functions corresponding to the first few mirror points are influential. It is also found that the effect of material combination on the stress field shall be described by three parameters, the two Dundurs' parameters and one additional parameter.     

Deformation of the Free Surface in a Moving Locally-Heated Thin Liquid Layer

Liquid film flow on a vertical surface is studied experimentally and theoretically under the determining influence of the thermocapillary forces. In the two-dimensional steady-state case the shape of the film surface is calculated numerically within the thin layer approximation with allowance for the temperature dependence of the viscosity of the liquid and redistribution of the heat flux in the heating element. A local heat source was used in the experiments to produce temperature gradients up to 10 K/mm on the liquid surface. The film thickness was determined by means of the schlieren method with reflection. The relative thickness of the roller in the upper heater edge zone, characteristic of the formation of regular structures, is measured. The thickness is h/h ₀=1.32 ±0.07, which agrees satisfactorily with the results of numerical calculations.     

Deformation of liquid jets and drops injected into a gas stream

The process of deformation of liquid drops and jets is examined on a broad interval of two-phase flow parameters. The shape of a jet penetrating a gas stream directed at an angle to the jet-particle velocity vector is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 82–88, May–June, 1971.In conclusion the authors thank A. K. Simonovskii for his useful comments.     

Slip and Macroparameter Jumps of a Polyatomic Gas with Rotational Degrees of Freedom on a Weakly Curved Spherical Surface

The problem of the slip of a temperature-inhomogeneous polyatomic gas along a spherical surface of small curvature is solved. The solution is obtained using the half-space moment method on the basis of a previously proposed model kinetic equation which takes into account the rotational degrees of freedom of the polyatomic gas. Both the first- and second-order (in the Knudsen number) slip coefficients and the polyatomic gas macroparameter jump coefficients on the phase interface are obtained. These coefficients are given as functions of the tangential momentum accommodation coefficients, the translational and rotational energy accommodation coefficients, and the Prandtl number. The kinetic coefficients are calculated for certain polyatomic gases.     

润滑接触中弹性变形的快速数值计算

研究了弹性变形的计算特点 ,并在简单回顾卷积算法的基础上给出了一种利用快速傅立叶变换 (FFT)和离散圆卷积计算弹性变形的方法 .计算表明 ,通过对压力信号和影响系数 -响应函数 (Green函数 )进行简单的预处理 ,可以获得准确的弹性变形 ,其计算精度和多层网格积分法相当 ,而计算速度则是多层网格积分法的 3倍左右 ,是一种准确、高效的数值计算方法     

Evaluation of Volume Deformation from Surface DIC Measurement

Stereo-DIC allows to track with a high accuracy the shape change and the surface displacement field of objects during deformation processes. When multiple camera arrangements are used, the shape and deformation measurement can be performed over the whole surface of the object. We submit that, in the case of intact specimens, with no internal defects and/or discontinuities, such boundary information can be used to estimate the internal displacement field by using proper interpolation functions. This calculation could serve, for instance, to evaluate the strain localization that occurs in metal specimens subjected to plastic deformation, hence allowing to get a better insight in the necking initiation and fracture propagation processes. In this paper, an interpolation method based on Bézier curves is developed and tested using simulated and real experiments on specimens with flat and cylindrical geometries. In particular, the deformation behaviour in the necking zone was investigated in the case of highly ductile and anisotropic materials. Numerical models were used to validate the method while the application to two real experiments demonstrated its feasibility in practical cases. The applicability of the method to more complex loading cases (e.g., bending, torsion, mixed-loads) or different initial shapes (e.g., curved beams, notches) will be investigated in future studies.