权函数法研究高速旋转厚壁筒的应力强度因子

采用厚壁筒在内压作用下的应力强度因子作为参考载荷的应力强度因子,通过权函数方法推导出了内壁带二维径向边裂纹的旋转厚壁筒的应力强度因子公式．这些公式可用于计算旋转厚壁筒在不同裂纹深度、转速、材料和尺寸情况下的应力强度因子．算例表明该文的公式具有良好的精度．同时还研究了旋转圆筒应力强度因子随裂纹深度和内外径比之间的变化规律,方便了工程应用．     

圆筒受余弦分布压力之解及其k→0的极限

本文得到一个新的应力函数。用此解答了圆筒受余弦分布压力的问题,并为解决圆筒在轴向受任意分布荷载作用的空间轴对称问题打下了基础。根据求出的解答,取压力沿轴向不变化时的极限,就导出了厚壁圆筒的Lamè公式。     

人体动脉瘤生成与破裂的力学分析

在大变形超弹性理论框架下研究了内压、轴向拉伸和扭转联合作用下人体动脉壁的力学响应,应用结构不稳定性理论对动脉瘤生成的可能性进行了解释,应用材料强度理论对动脉瘤破裂的可能性进行了分析．考虑动脉壁中残余应力和平滑肌主动作用的影响,用纤维加强各向异性不可压超弹性复合材料两层厚壁圆筒模型来模拟动脉壁的力学特性．给出了正常和几种非正常状态下动脉壁的变形曲线和应力分布．变形和稳定性分析结果表明该文模型可以模拟正常状态下动脉壁的均匀变形,还可以模拟在动脉壁中弹性蛋白纤维和胶原蛋白纤维强度降低的非正常状态下动脉瘤生成的可能性及动脉瘤的增长．应力和强度分析结果表明该文模型可以模拟当动脉瘤中的最大应力超过管壁的强度时动脉瘤破裂的可能性．     

多层厚壁圆筒频率方程的简化及一类贝塞尔函数递推公式

本文从理论上研究了相同材料的多层厚壁圆筒径向振动的频率方程,证明若干层相互接触的层筒的整体频率方程,可以用单个厚壁圆筒的频率方程替代,从而大大简化了求解过程.并从该实际问题出发,推导出了一类贝塞尔函数的递推公式.     

加捻纤维复合材料三维残余应力分析

本文提供一种对于含有加捻纤维束的复合材料由于固化而产生的热残余应力的分析研究.纤维束中的纤维经过加捻产生了一种螺旋形状,这种形状所产生的三维热弹性力学问题可以利用能量法获得解答.这个问题的热残余应力场可以表示为纤维、基体材料的性质以及纤维束几何参数的函数.纤维/基体界面上的残余应力(包括环向和径向的应力)都可以从这些分析中得到.本文分析的结果表明:加捻纤维束构成的复合材料,由于纤维的适当加捻,可以减弱由于纤维与基体各具不同的热膨胀系数而产生的热固化残余应力.     

玻壳成型过程诱导残余应力的数值预测

建立了玻壳压制成型固化过程中残余应力预测的数值模拟模型,采用平行平板间玻璃熔体的固化问题来描述成型过程中残余应力形成的机理,并假定材料为热流变简单粘弹性材料．基于板壳理论,将产品视为平板单元的组合,并采用有限元法来求解,这种方法可以象全三维计算一样一层层地计算残余应力,非常适合复杂形状的薄压制成型产品．最后通过实验比较验证了所提出的模型和方法．     

Simplification of Frequency Equation of Multilayered Cylinders and Some Recursion Formulae of Bessel Functions

本文从理论上研究了相同材料的多层厚壁圆筒径向振动的频率方程, 证明若干层相互接触的层筒的整体频率方程, 可以用单个厚壁圆筒的频率方程替代, 从而大大简化了求解过程。并从该实际问题出发,推导出了一类贝塞尔函数的递推公式。     

两炮喇叭口爆炸成形强化护环拐点离上端近时残余应力的解析解

对两炮喇叭口爆炸成形强化护环拐点离上端近的情况进行分析,采用轴对称圆柱薄壳有矩理论,构造新的位移函数,得出该情况下残余应力的解析解.这就为求解拐点上移后残余应力的解析解打下了基础,其在理论和工程实际中都有很大的价值.     

动脉管壁切应力的确定

血管为了适应所处力学环境的变化会产生结构和功能的变化,血液流动作用于血管壁上的切应力在这种血管重建中起着重要的作用.目前直接测量活体血管壁切应力存在着许多技术上的困难.通过分析动脉中血液脉动流的特性,提出一种利用测量管轴上的血流速度,计算血管壁切应力的方法,为定量确定血管壁切应力,进而讨论血管壁切应力对血管重建的影响提供必要的手段.     

残余界面应力对粒子填充热弹性纳米复合材料有效热膨胀系数的影响

根据黄筑平等人提出的基于“3个构形”的表/界面能理论,研究了热弹性纳米复合材料的有效性质,重点讨论了残余界面应力对纳米尺度夹杂填充的热弹性复合材料有效热膨胀系数的影响．首先,给出了由第一类Piola-Kirchhoff界面应力表示的热弹性界面本构关系和Lagrange描述下的Young-Laplace方程;其次,采用Hashin复合球作为代表性体积单元,推导了在参考构形下复合球内部由残余界面应力诱导的残余弹性场,并进一步计算了从参考构形到当前构形的变形场;最后,基于以上计算得到了热弹性复合材料有效体积模量和有效热膨胀系数的解析表达式．研究表明,残余表/界面应力对复合材料的热膨胀系数有重要影响．     

Axially symmetric temperature stresses in an elastic isotropic cylinder of finite length

We consider an axially symmetric problem of the thermostressed state of a solid cylinder of finite length with a load-free surface. Using the method of superposition, we have constructed the complete analytical solution of this problem, which is reduced to the solution of a system of linear algebraic equations. We have proposed a method for determining the asymptotic behavior of coefficients in these systems, which enables us to develop an efficient algorithm for the calculation of stresses in the cylinder, including regions near its end-face circles. Typical examples are considered.     

Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium

Within the framework of the piecewise homogeneous body model with utilization of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the mathematical modeling of the torsional wave propagation in the initially stressed infinite body containing an initially stressed circular solid cylinder (case 1) and circular hollow cylinder (case 2) are proposed. In these cases, it has been assumed that in the constituents of the considered systems there exist only the normal homogeneous tensional or compressional initial stress acting along the cylinder, i.e. in the direction of wave propagation. In the case where the mentioned initial stresses are not present, the proposed mathematical modeling coincides with that proposed and investigated by other authors within the classical linear theory of elastic waves. The mechanical properties of the cylinder and surrounding infinite medium have been described by the Murnaghan potential. The numerical results related to the torsional wave dispersion and the influence of the mentioned initial stresses on this dispersion are presented and discussed.     

On the Incorporation of Residual Stresses in Arterial Walls

The present work deals with the incorporation of residual stresses existing in circumferential direction of arterial walls. For the consideration of the residual stresses a novel model will be presented. This model is based on the assumption that residual stresses decrease the stress gradients through the thickness of the arterial wall. Since arterial walls exhibit a pronounced material behavior in fiber direction, the radial gradients of the fiber stresses are considered for the definition of the residual stresses. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural residual stresses in oriented glass-reinforced plastics

A previously proposed method is used to obtain expressions for calculating the residual stresses as a function of the physicomechanical properties of the polymer matrix and the reinforcement ratio. The calculation results are presented and the corresponding state of stress and strain analyzed. There are considerable deviations (in the magnitude and distribution of the stresses) from models that neglect or only take partly into account the interaction of the fibers.Moscow Ordzhonikidze Aviation Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1051–1058, November–December, 1968.     

Application of fibre BRAGG grating sensors for residual stress analysis

Residual stresses are important by the manufacturing of the most components. The analysis of residual stresses using the hole-drilling method is complicated and is based at the moment solely on strain measurement on the surface. Now, an approach is described where the residual stresses can be calculated on the basis of strain measured in several plains. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of residual stresses in components made out of laminated and fibrous composites during the hardening process

Conclusions The application of the theory of the viscoelasticity of unstable media to the calculation of the residual stresses enables one to reveal effects due to the change in the properties of a solidifying binder under different sets of operating conditions for the technological process. At the same time, it once again confirms that thermal shrinkage makes a significantly larger contribution to the magnitude of the residual stresses than chemical shrinkage. The absolute values of the stresses are in satisfactory agreement with results that were obtained using simpler calculational schemes.Moscow Power Institute. Translated from Mekhanika Polimerov, No. 5, pp. 790–795, September–October, 1976.     

Temperature stresses in an inhomogeneous cylinder of finite length

An analytic method of determining the temperature stresses in circular cylinders is described. In the solution of the problem, based on a collocation method, together with the finite length of the cylinder its arbitrary inhomogeneity is also taken into account. In a particular case this may be caused by the effect of temperature on the mechanical constants of the material, which is especially typical of polymers at negative temperatures. The results of a calculation of the stresses in a hollow cylinder of finite length with a variable modulus of elasticity are presented as an example.Dzherzhinskii Military Engineering Academy. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 710–715, July–August, 1968.     

Calculation of contact stresses in axisymmetric underwater explosions

The problem of an underwater electrical explosion in a long layered elastoplastic cylinder is solved. The solution is obtained numerically with use of artificial viscosity. The law for energy produced by the explosion is determined experimentally and residual stresses are determined by the establishment method. Contact stress is presented as a function of explosion energy for various cylinders.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 106–109, 1989.     

Dual-weighted residual adaptivity for phase-field fracture propagation

In this study, we consider phase-field-based fracture propagation in solid mechanics. The phase-field model is based on a thermodynamically-consistent version proposed by Miehe, Welschinger, Hofacker. The main focus is on goal-oriented functional evaluations using a partition-of-unity dual-weighted residual estimator for accurate measurement of, for example, point values, stresses, or crack opening displacements. Our developments are substantiated with a numerical test. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)