Effect of the Stress State on the Critical Load and Load-Carrying Capacity of Shells with Axisymmetrical Dents

A method of approximate determination of critical stresses in elastic near-cylindrical shells with the use of equations in terms of displacements is proposed. Analytical expressions to estimate critical stresses in membrane unstiffened shells were obtained. Two distributions of internal forces, namely, the forces constant and variable in magnitude, were analyzed.     

Stability and Load-Carrying Capacity of Elastic Reinforced Cylindrical Shells

By using the equilibrium equations in displacements, we develop an analytic method for the evaluation of upper critical loads in elastic cylindrical shells with transverse reinforcement. As a result, we deduce analytic expressions for the evaluation of critical stresses in momentless shells and propose a procedure for the evaluation of the lower limit of the load-carrying capacity of shells based on the application of the method of reduced stiffness. The numerical results are compared with the available theoretical and experimental data. __________ Translated from Problemy Prochnosti, No. 6, pp. 103 – 113, November – December, 2005.     

Load-Carrying Capacity of a Cracked Plate under Biaxial Tension

The paper presents the findings of an experimental investigation into the possibility of estimating the load-carrying capacity of sheet materials with a central through crack under biaxial tension at low temperatures from the fracture-toughness parameters determined in uniaxial tests.     

A Refined Asymptotic Theory for the Nonlinear Analysis of Laminated Cylindrical Shells

Within the framework of the three-dimensional (3D) nonlinear elasticity, a refined asymptotic theory is developed for the nonlinear analysis of laminated circular cylindrical shells. In the present formulation, the basic equations including the nonlinear relations between the finite strains (Green strains) and displacements, the nonlinear equilibrium equations in terms of the Kirchhoff stress components and the generalized Hooke's law for a monoclinic elastic material are considered. After using proper nondimensionalization, asymptotic expansion, successive integration and then bringing the effects of transverse shear deformation into the leading-order level, we obtain recursive sets of the governing equations for various orders. It is shown that the von Karman-type first-order shear deformation theory (FSDT) is derived as a first-order approximation to the 3D nonlinear theory. The differential operators in the linear terms of governing equations for the leading order problem remain identical to those for the higher-order problems. The nonlinear terms related to the unknowns of the current order appear in a regular pattern and the other nonhomogeneous terms can be calculated by the lower-order solutions. It is also illustrated that the nonlinear analysis of laminated circular cylindrical shells can be made in a hierarchic and consistent way.     

Modification of the Wilkins Method to Study the Dynamics of Axisymmetric Thick-Wall Shells with a Spiral Orthotropy

Modification of the Wilkins method has been performed for numerical investigation into dynamics of thick-wall cylindrical shells with a spiral orthotropy. Test calculations are shown to agree well with the known solutions. New physical effects have been found, which are absent from isotropic and cylindrically orthotropic bodies.     

Range of the Applicability of the Wilkins Method to the Investigation of the Dynamic Stress-Strain State of Anisotropic Elastic Axisymmetric Shells

The exactness and stability of the Wilkins method in the investigation of the stress-strain state of axisymmetric anisotropic elastic shells, including thick-walled ones, have been studied for different values of artificial viscosity, pulse load rise and fall time, and different deformation process durations. A comparison of numerical calculations, performed by means of an application software package developed by V. A. Romashchenko on the basis of the Wilkins method, with experimental results, known numerical data, and with calculations using the computation kernel LS-DYNA 3D has been carried out.     

Stability of Cylindrical Shells with Regard for Dispersed Cracking in the Material

The problems of bifurcation stability of cylindrical shells are stated and solved with regard for the damage to a material in the subcritical stressed state. The appearance of defects in the material is explained by the inhomogeneity of its microstrength. The defects are simulated by a system of plane elliptic and circular cracks statistically uniformly and isotropically distributed over the volume of a shell. The mathematical statement of the problem is performed within the framework of the Kirchhoff–Love hypotheses by using the concept of continued loading. The solution of the problem is constructed for the case of uniform compression of the shell.     

高速旋转圆柱壳的自然频率和临界转速

应用能量法导出对应于任一转速的自然频率和临界转速的计算公式。结果表明每一阶主振动都有正向反向的两种频率。只有在长径比较小条件下才有环向第一阶正向临界转速且数值很大。反向临界转速则在环向第一和第二阶都存在。     

Elastic cylinder with helicoidal orthotropy: Theory and applications

The elasticity equations are derived for a helicoidally symmetric cylinder. An isotropic cylinder in the center is wrapped by a thick layer of a material with helicoidal anisotropy formed by spiraling of fibers around the core. Such structures are seen in springs, armored cables, trusses, composites, and biostructures. Structure under axial loading and pure bending are considered. The analytical expressions for displacements are obtained from equations of three-dimensional elasticity. The results are verified numerically via the finite element method. The stiffness matrix for an equivalent simplified model that links the displacements of the ends with the applied force and momentum is formulated. A coupling effect is revealed: the bar twists and elongates when axially loaded.The developed technique is used to explain an evolution of structure in nature. A pine trunk with spiralling grain is investigated from an optimization of a mechanical construction viewpoint. We model the trunk as an anisotropic cylinder with helicoidal symmetry and compute the displacements and stresses using nonlinear finite element model. An optimized spiralling angle of the grains accounts for a composite failure, transverse deflection, and fluid transportation. We suggest a combined criterion that could explain this spiralling morphology.     

T形配钢型钢混凝土构件正截面承载力计算方法

基于塑性理论下限定理提出了T形配钢型钢混凝土构件在压、弯复合受力状态下的正截面承载力计算方法。将正截面承载力分为混凝土部分、钢筋部分和型钢部分,分析得出各部分的承载力方程,采用叠加强度法建立了T型配钢型钢混凝土构件的N-M相关曲线,并给出了相应计算公式。进行了5个1/2比例T形配钢型钢混凝土柱的低周反复加载试验,对是否配置拉结筋、不同配箍率和不同轴压力下的受力特点、破坏形态、承载能力进行了研究,其中4个试件发生了正截面受弯破坏,部分计算结果与试验数据符合较好。结果表明,所提出的计算方法简单易行,可供实际工程设计参考。     

Nonlinear Response of Imperfect Eccentrically Stiffened Ceramic-Metal-Ceramic Sigmoid Functionally Graded Material (S-FGM) Thin Circular Cylindrical Shells Surrounded on Elastic Foundations Under Uniform Radial Load

This article researches nonlinear response of imperfect eccentrically stiffened symmetric FGM thin circular cylindrical shells with ceramic-metal-ceramic layers, which are symmetric through the middle surface by Sigmoid-law distribution (S-FGM) and have stiffeners surrounded on elastic foundations under uniform radial load. The Donnell classical shell theory, stress function, and Galerkin method are used for investigation of the nonlinear stability of the S-FGM shell. The obtained results show the effects of the stiffeners, elastic foundations, mechanical load, and material parameters on the nonlinear buckling response of symmetric S-FGM circular cylindrical shells.     

一类具复杂偏差变元的Liénard方程的周期解

研究了一类具复杂偏差变元的Lienard型泛函微分方程x"(t)+f(x(t),x'(t))x'(t)+g(t,x(t-τ-(t,x(t))))=0周期解的存在性。分别在阻尼系数有界和无界的条件下,得出了方程周期解的存在定理。     

电线电缆包装盘包装容量的计算

指出用传统的计算电缆包装盘包装容量公式的弊端及其原因所在,提出更切合现场实际的计算公式,为合理选用电线电缆包装盘提供理论基础;同时也丰富了有关缠绕计算理论。     

双壳纲三角帆蚌贝壳的三维微结构及其化学组成研究

通过场发射扫描电镜(FE-SEM)、傅里叶变换红外(FTIR)光谱、X射线粉晶衍射(XRD)对淡水三角帆蚌贝壳各壳层的微结构特征及化学组成进行较系统的对比研究。结果表明:在贝壳的垂直生长层方向,最外层的角质层可细化为外角质层与矿化区,其中在贝壳的不同区域中该角质层的厚度存在明显差异;棱柱层中的棱柱与外层的角质层及内层的珍珠层文石板片呈近垂直交接,棱柱层的厚度在贝壳的不同位置同样存在差异;首次发现珍珠层中文石板片的厚度从接近棱柱层一端至珍珠层内侧面逐渐变厚,该结论与前人的文献报道恰好相反。基于本研究的结论,推测贝壳中复合的微纳米结构与化学组成共同决定了软体动物贝壳优异的力学性能。     

周期桁架结构浮筏隔振特性分析与实验研究

利用周期结构特性和波形转换作用,提出一种新型周期桁架结构浮筏。首先利用有限元方法建立浮筏结构的数值模型并计算其频响特性,通过频响函数综合建立包含机组、浮筏和基础的振动传递模型,在隔振系统中评价新型桁架浮筏的性能,然后在此基础上,对新型桁架浮筏隔振系统进行实验验证。结果表明：周期桁架结构浮筏比传统浮筏能够更有效地抑制振动传递,组成浮筏隔振系统后,在与浮筏上下层隔振器的共同作用下,整个隔振系统在更宽的频段内对振动传递产生抑制作用。     

非对称横电磁波传输室分布电容和特性阻抗的计算

本推导了一种计算非对称横电磁波传输室分布电容和特性阻抗的简单，有效的方法。此法物理意义明确，既能计算主段，又能计算过渡段的分布电容；既能计算大型又能计算中小型横电磁波室。经适当修正不但可计算有限厚度内导体横电磁波室，亦可近似计算零厚度内导体板横电磁波室的分布电容和特性阻抗。     

Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part I: Theory and solutions

Buckling and postbuckling behavior are presented for fiber reinforced composite (FRC) laminated cylindrical shells subjected to axial compression or a uniform external pressure in thermal environments. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The governing equations are based on a higher order shear deformation shell theory with von Kármán-type of kinematic non-linearity and including the extension-twist, extension-flexural and flexural-twist couplings. The thermal effects are also included, and the material properties of FRC laminated cylindrical shells are estimated through a micromechanical model and are assumed to be temperature dependent. The non-linear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths of FRC laminated cylindrical shells.     

基于有效线导纳的单筋圆柱壳振动声辐射分析

周向激励下加筋圆柱壳体振动和声辐射特性的研究是预测水下航行器壳体噪声的关键环节。基于有效线导纳理论和有效线导纳对简单圆柱壳体分析的基础，建立周向激励下单筋圆柱壳体的受力模型，得到振动响应计算公式，并对单筋圆柱壳体的振动响应和声辐射功率级进行实例计算和分析。计算结果表明：壳体表面加强筋处的局部振动响应得到有效抑制，幅度可降至原来的1％，但对整个壳体结构声辐射影响较小，功率仅降低1％左右。同时表明有效线导纳的理论能够正确有效地对周向激励下加筋圆柱壳体的振动响应和声辐射进行预报和分析。     

带有周期系数和时滞的细胞神经网络模型的周期解的存在性和全局指数稳定性

本文运用非奇异M矩阵的性质,不等式分析法和建立在重合度基础上的连续性定理,得到了带有周期系数和周期时滞的细胞神经网络的周期解的存在性以及全局指数稳定性的新判据。并且给出了指数收敛率的估计。