内压椭球壳塑性变形的发生部位与扩展过程分析

对内压椭球的就发布作了图形描述，指出椭球壳上一点的应力状态只与壳体的轴比λ和该点在壳体上的位置有关，并进一步分析了内压椭球壳的塑性变形的发生部位及其扩展过程。     

Flow-induced deformation of an elastic membrane adhering to a wall

The flow-induced deformation of a two-dimensional membrane with a circular unstressed shape clamped at the two ends on a plane wall at an arbitrary contact angle is considered. Working under the auspices of generalized shell theory, the membrane is allowed to develop in-plane tensions, transverse tensions, and bending moments determined by the curvature of the resting and deformed shapes. A system of ordinary differential equations governing the membrane shape is formulated, and the associated boundary-value problem is solved by numerical methods. Numerical results are presented to illustrate the deformation of a clamped membrane due to gravity or a negative transmural pressure. The shell formulation is coupled with a boundary-integral formulation for Stokes flow, and an efficient iterative scheme is developed to describe deformed equilibrium shapes of a membrane attached to a plane wall in the presence of an overpassing shear flow. Computations for different contact angles and shear rates reveal a wide variety of profiles and illustrate the distribution of the membrane tension developing due to the flow-induced deformation.     

椭球壳体液压成形的塑性变形规律的研究

采用大变形弹塑性有限元法对椭球壳体的液压成形过程进行了模拟，结果表明壳体成形时，各点塑性变形不是同时发生的，并对壳体塑性变形的扩展过程和点的加载轨迹进行了研究，证明了壳体在胀形时焊缝区受到弯曲作用的影响，同时还成形后的椭球壳体的壁厚分布及壳体尺寸进行了预测。     

Elastoplastic state of nonshallow flexible ellipsoidal shells under concentric loading

The elastoplastic stress-strain state of flexible ellipsoidal shells under concentric loading is investigated by the solution of nonlinear boundary-value problems. Numerical results are presented for open shells in the case of a free (unsupported) edge and a shell with a central opening (the periphery of the opening is supported by a thin ring). Solutions of the problems in linear and nonlinear statements are analyzed. Numerical results for ellipsoidal and spherical shells are compared. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 54–60, April, 1999.     

Stress Analysis of Anisotropic Inhomogeneous Shells of Revolution Subjected to Centrifugal Forces

An approach is proposed to analyze the stress state of thin shells of revolution under centrifugal loads with regard for anisotropy, the meridional variability of geometrical and mechanical parameters, and the eccentricity of the axis of revolution relative to the axis of geometric symmetry. Allowance is also made for the change in the dimensions of the shell due to deformation, which results in a nonaxisymmetric distribution of stresses and strains and their nonlinear dependence on the squared frequency of rotation. By separating variables, the problem is made one-dimensional and then solved numerically. The stress state of an ellipsoidal filament-winded composite shell is analyzed     

水平圆柱薄壳非轴对称载荷作用内力分析

近年来大直径圆柱形薄壳结构烟风煤粉管道的使用呈增长趋势.水平圆柱薄壳在非轴对称载荷作用下的内力常按整体梁理论或壳的无矩理论计算,无法反映载荷作用边界的弯曲应力.本文结合圆柱壳的无矩理论和弯矩理论,得到了简支水平圆柱薄壳在任意高度内部积灰(粉)、风、雪、自重、地震作用下的内力解析解,且理论解与三维有限元分析结果非常接近.研究结果可推广到类似的非轴对称变形圆柱壳,并为水平薄壁圆柱壳结构设计提供依据.     

壳体初始形状对球形容器液压胀形结果的影响

借助于数值模拟研究了锥台形壳体液压胀形过程中可能出现的质量问题，以及壳体的初始形状对成形结果的影响，在此基础上提出了锥台形壳体的改进方案，以避免壳体的起皱，并最终获得预期的球形容器或椭球形容器。     

Effect of structural and mechanical characteristics of the composite material on the deformation of a reflector antenna

This is a study of the effect of structural and mechanical characteristics of a composite material on the stress–strain state of a reflector antenna shaped as a composite thin shell of revolution subjected to gravity, wind, and temperature loads. The boundaryvalue problem for the system of partial differential equations governing the behavior of this structure is reduced to a sequence of boundaryvalue problems for inhomogeneous systems of ordinary differential equations with variable coefficients. The resulting stiff systems of equations are solved by Godunov's method of discrete orthogonalization.     

矩形弹性壳液耦合系统中的重力波分析

根据非线性动力学理论,建立了矩形壳液耦合系统的非线性振动方程组,通过数值求解,发现当激振频率为壳体固有频率与重力波频率之和,且激振力足够大时,会产生大幅低频重力波,通过实验验证,发现了壳液耦合系统中存在的大幅低频重力波现象,实验结果与理论结果基本吻合。     

Wrinkled membrane element based on the wrinkling potential

For a membrane structure, wrinkles have an important effect on its mechanical behaviors. Wrinkling level characterizes the development of wrinkles and reflects the performance of a membrane in its service, and it plays a very significant role in the wrinkling analysis. The shell elements combined with the stability theory would be an ideal solution to the wrinkling problem. However, this approach requires a dense mesh and the computation is very time consuming. Also the wrinkling parameters are very sensitive to the size of shell elements. Existing wrinkling models based on membrane elements are derived from the Tension Field Theory which are incapable of describing fully the wrinkling behaviors.A new wrinkling model adopting the wrinkling strain as a measure of the wrinkling level is proposed in this paper to address these issues. According to the analogy between the wrinkling strain and the elasto-plastic strain, a wrinkling potential surface is assumed to exist and its normal direction defines the direction of the wrinkling strain tensor by virtue of the flow rule. Based on the consistent condition of the wrinkling potential surface, a modified constitutive tensor is obtained. To avoid the switching of the wrinkling state in the numerical solution, a new wrinkling criterion is proposed, in which the predominant influence of the previous state is included. Besides, a new approach to determine the wrinkling orientation is given to improve the efficiency of convergence in the slack region. The objectivity of the wrinkling coordinate frame is also demonstrated as an accompanying set of results. Finally, two benchmark problems are analyzed with the proposed wrinkling model, and their results are compared with those in the literatures. Results indicate that the proposed wrinkling model is valid and accurate to characterize the wrinkling level of a membrane and it exhibits efficient convergence even in the slack region.     

A formulation of the centre of twist and shear for nonhomogeneous beam

A formula will be derived for the torsional stiffness of conical membrane shell made from linear elastic homogeneous isotropic material. The torsional stiffness of the truncated conical membrane shell is defined by the following manner: it is that value which is obtained as the square of the applied torque divided by two times strain energy in the state of pure torsion.     

Hybrid theoretical,experimental and numerical study of vibration and buckling of composite shells with scatter in elastic moduli

Hybrid theoretical, experimental and numerical method is proposed for free vibration and buckling of composite shell with unavoidable scatter in elastic moduli. Based on the Goggin’s measurement techniques, the elastic moduli for material T300-QY8911 are measured, and a set of experimental points are obtained. The measurements of elastic moduli are quantified by either (1) the smallest ellipsoid and (2) the smallest four-dimensional uncertainty hyper-rectangle. Then uncertainty propagation in vibration and buckling problems of composite shell by ellipsoidal analysis and interval analysis are, respectively, studied from the theoretical standpoint. Comparison between these analyses is performed numerically.     

An approximation to red blood cells with a model of three-center-combined shells

Red blood cells present a biconcave shape and bear an inner pressure (osmotic pressure) when they are in the static state. In this paper, a model of “three-center-combined shells”, which consists of two spherical shells and a toroidal shell, is employed to describe the geometric shape of red blood cells. Surface area and volume of the combined shells model are very close to those measured from experiment. The stress distribution in the cell membrane is formulized as a closed form according to the Novozhilov's theory of the three-center-combined shells. Calculating results in terms of Novozhilov's formula give a good agreement with the numerical results given by ABAQUS when using actual measurements. It is concluded that the combined shells model can well approximate to the biconcave structure of red blood cells. In addition, stress calculation shows that the membrane of biconcave red blood cells can carry bending moments, and the moments reach a maximum value in the vicinity of joint line of the spherical shell and the toroidal shell in the combined shells model.     

Dynamics of ellipsoidal cavities in fluid

A mathematical model of the hydrodynamics of free closed surfaces in a fluid is expounded. It is used for studying the dynamics of ellipsoidal cavities during their development. The model is based on a system of differential equations that accounts for the influence exerted on the dynamics of cavities by various perturbations such as gravity, surface tension, viscosity, and geometrical features of the cavity. Solving this system makes it possible to determine the hydrodynamic characteristics of the flow around the cavity and to plot cavity shapes depending on time and flow regimes. Characteristic features of the development of such cavities under gravity and surface tension are established __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 24–31, February 2006.     

Cooperative entry of nanoparticles into the cell

Interaction of nanoparticles (NPs) with cell membrane is a crucial issue in studying drug delivery, photodynamic therapy system and cytotoxicity. Single NP with relatively small size cannot be fully wrapped by the cell membrane, which prohibits its uptake. One feasible way is cooperative entry, i.e., recruiting and assembling multiple small NPs to form a larger NP cluster to enter into a cell. In this work, we present theoretical analysis about the cooperative entry of multiple NPs. Through free energy calculation we investigate how the NPs׳ size, shape, interval and NP/cell interfacial binding energy influence the feasibility of entry. Interestingly we find that the cooperative entry of oblate ellipsoidal NPs can get larger energy compensation than individual ones as well as spherical ones. We also propose that soft NPs have preference in cooperative entry of the cell. Our work can be used to actively design and transfer NPs in applications such as drug delivery as well as to understand the shape effect on toxic mechanism of ellipsoidal NPs.     

Numerical analysis of cracked inelastic shells with large displacements or mixed mode loading

The trend in higher utilization of structural materials leads to a need for accurate numerical tools for reliable predictions of structural response. In some instances both material and geometrical nonlinearities are allowed for, typically in assessments of structural collapse or residual strength in damaged conditions. Dynamically loaded structures are prone to fatigue cracking; this has to be accounted for when computing nonlinear structural response. The present study addresses the performance of cracked inelastic shells with out-of-plane displacement not negligible compared to shell thickness. This situation leads to membrane force effects in the shell. Hence, a cracked part of the shell will be subjected to a nonproportional history of bending moment and membrane force, and e.g. fracture mechanics parameters (J-integral ) are affected. A Mindlin shell finite element based nonlinear program is developed and utilized herein. The cracked parts are accounted for by means of inelastic line spring elements. These elements also account for possible mode II deformations.     

Submerged fluid-filled cylindrical shell subjected to a shock wave: Fluid–structure interaction effects

A submerged fluid-filled circular cylindrical shell subjected to a shock wave propagating in the external fluid is considered. The study focuses on a number of acoustic and structural effects taking place during the interaction. Specifically, the influence of the acoustic phenomena in the fluid on the stress–strain state of the shell is analysed using two different visualization techniques. The effect that the parameters of the shell have on the internal acoustic field is addressed as well, and the ‘shock transparency’ of various shells is discussed. Special attention is paid to the analysis of the contribution of the terms in the shell equations representing bending stiffness, and the limits of applicability of the membrane theory of thin shells are discussed in the fluid–structure interaction context. The possibility of cavitation in the internal fluid is investigated, and the effect that cavitation could have on the structural dynamics of the shell is discussed. The present paper is a follow-up of the author's earlier study of the interaction between fluid-filled cylindrical shells and external shock waves.     

Equations of heterophase equilibrium of a biomembrane

Summary Phase transitions in a shell are considered within the frame example work of a biomembrane of a general shape divided into parts containing different phases. The configuration of a boundary separating these phases is determined by the condition of minimum of the total membrane free energy with respect to its position. Equations of equilibrium for both the membrane phases and the phase boundary are deduced. They allow to describe the heterophase state of the biomembrane. Received 11 December 1997; accepted for publication 31 July 1998     

Interaction of an Ellipsoidal Inclusion with an Elliptic Crack in an Elastic Medium

An approach is considered to how to allow for the interaction between an ellipsoidal heterogeneity (inclusion) and an elliptic crack in an elastic medium. Using the superposition of perturbed stress states, the boundary conditions are satisfied on the ellipsoidal surface by the method of equivalent inclusion and on the crack surface by the least-squares method. A numerical analysis is carried out. Typical mechanical effects are revealed. In the calculations, the stress state near the ellipsoidal heterogeneity is approximated by a polynomial of the second degree in Cartesian coordinates, whereas the load on the crack surface is simulated by a polynomial of the fourth degree in Cartesian coordinates. In particular cases, the results are in good agreement with the data obtained by other authors     

Finite deformation of an ideal rigid-plastic membrane

We consider finite deformation of a membrane which is a cylinder in the initial state under a pressure uniformly distributed over the inner surface. The problem is solved using the model of deformation of an incompressible rigid-plastic material with full plasticity. Exact analytical relations are obtained for the pressure and kinematic characteristics as functions of the rotation angle of the normal on the contour of the shell. Elongations and displacements are found as functions of the radial coordinate. The time of reaching the maximum value of the external pressure is determined. It is shown that the change in the membrane thickness along the radial coordinate is constant.