High-temperature long-term strength of shells in aggressive media with regard for the mass exchange

We study the long-term strength of long cylindrical shells placed in aggressive media under the conditions of complex stressed states. The influence of these states on the long-term strength of the shells is described with the help of equivalent scalar stresses. The time to fracture of the shell is found according to the Rabotnov kinetic theory by using two parameters, namely, the degree of damage to the material and the concentration of the medium in the material of the shell. As the boundary condition on the fracture front, we use the condition of mass exchange. We study the interaction between the diffusion and fracture fronts. The time to fracture of the shell is found by using the solution of a system of integrodifferential equations. Under the assumption of mean level of concentration of the medium, we deduce explicit relationships between the times to fracture of the shell in aggressive and neutral media. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 43, No. 2, pp. 17–24, March–April, 2007.     

改型等强度壳的理论与工程应用

提出一种新型连接结构:在相邻的两段不同直径圆柱壳之间嵌入一段"改型等强度壳",构成"柱-改型-柱"组合壳,使得两段不同直径的圆柱壳光顺地连接,可以大幅度降低结合部的局部弯曲应力。应用旋转壳有矩理论分析了这些组合壳的应力分布,对其工程应用——作为连接结构的"改型等强度壳"几何参数的选择提出了建议。     

开口及边界条件对复合材料三分之一柱面壳压缩屈曲性能的影响

研究了完整、开口周边加强及开口加口盖3种型式的复合材料三分之一柱面壳的压缩屈曲性能,考查了3种典型复合材料柱面壳的轴压屈曲强度,分析了开口及口盖对柱面壳压缩稳定性的影响.结果表明:开口大大降低了柱面壳的轴压屈曲强度;口盖可以部分恢复其强度,但很难达到开口之前的水平.进行了开口加口盖经编织物铺层三分之一柱面壳轴向压缩试验,其轴压屈曲强度比用平面织物制造的相同结构的降低很多.为了探究其轴压屈曲强度比同类结构偏低很多的原因,进行了非均匀加载复合材料柱面壳模型有限元分析.结果表明:柱面壳边界不均匀加载会降低其承载能力,根据柱面壳刚度分布制定边界载荷可以提高其承载能力.     

Criterion analysis of the fracture of cylindrical shell structures loaded by internal pressure induced by localized thermal impacts

We present experimental results of the investigation of the strength of cylindrical shells loaded by internal pressure formed as a result of a localized thermal impact caused by laser radiation. The types of fracture of shells recorded in the experiments are characterized either by the loss of gas-tightness as a result of the formation of cracks (or holes) or by the total fracture of a shell. We performed the criterion analysis of the experimental results by using the methods of the theory of similarity. The amount of conveyed radiant energy and the level of excess internal pressure are the main factors responsible for the fracture of shells. We suggest a formula which establishes a relationship between these factors and which can be regarded as a helpful criterion in comparing the results of testing of various models under different loading modes and application of these results to actual objects. Translated from Problemy Prochnosti, No. 5, pp. 51–57, September–October, 1997.     

Criterion analysis of the fracture of cylindrical shell structures loaded by internal pressure induced by localized thermal impacts

We present experimental results of the investigation of the strength of cylindrical shells loaded by internal pressure formed as a result of a localized thermal impact caused by laser radiation. The types of fracture of shells recorded in the experiments are characterized either by the loss of gas-tightness as a result of the formation of cracks (or holes) or by the total fracture of a shell. We performed the criterion analysis of the experimental results by using the methods of the theory of similarity. The amount of conveyed radiant energy and the level of excess internal pressure are the main factors responsible for the fracture of shells. We suggest a formula which establishes a relationship between these factors and which can be regarded as a helpful criterion in comparing the results of testing of various models under different loading modes and application of these results to actual objects.     

Numerical and analytical study of severity of cracks in cylindrical and spherical shells

The present study deals with the severity of cracks in pressure equipments, where such defects are often involved. Our work is particularly concerned with the problem of cylindrical shells and also the little well-known problem of spherical shells, including all sorts of practical defects, namely axisymmetric or semi-elliptic, both internal and external cracks. The stress intensity factor in the linear elastic domain and the J integral in the elastoplastic range are performed using the finite element method and compared to the results provided by the application of the semi-analytical A16 or R6 simplified criteria, depending on a limit load calculation. The nocivity of the defects depends on the crack shape and size and other structural geometrical parameters. Use is made of a polynomial decomposition of the stress field in the vicinity of the crack in order to cover all industrial loadings. All the numerical results, for a wide range of shell and crack geometries, are depicted using appropriate tables and curves in order to check the fracture criteria more easily.     

非均匀加筋圆柱薄壳圆截面内振动的径向模态机械阻抗分析

提出圆柱薄壳的圆截面内运动假设,从声学角度将环肋对壳体的作用等效为径向作用力,根据Hamilton原理建立了简支非均匀加筋圆柱壳的振动控制方程,利用驻波形式解对其径向模态机械阻抗进行了研究。分析表明:对于加筋圆柱壳,环肋与圆柱薄壳的径向模态机械阻抗具有串联连接方式,通过调整环肋的几何参数增大环肋自身的径向模态机械阻抗,可以达到壳体减振降噪的目的,并指出了利用环肋的反共振特性进行加筋圆柱壳结构减振的设计方向。     

Forced response of cylindrical shells coupled with nonlinear shape-memory-alloy (SMA) actuators regulated by sinusoidal and saw-tooth temperature profiles

Dynamic responses of cylindrical shells coupled with shape-memory alloy (SMA) ring segments placed at critical locations are investigated. Since the SMA actuators are highly nonlinear and governed by the temperate-dependent stiffness and martensite/austenite fraction, input shaping and phase shift of temperature profiles are incorporated to control the shell vibrations. Open-loop equations of an elastic cylindrical shell panel are defined first and then used with assumed mode-shape functions satisfying specified boundary conditions in the free-vibration analysis. Modal-analysis data are used to determine spatial strain distributions of natural modes. Distributed modal-signal characteristics suggest optimal placements of SMA actuator segment(s) for each given mnth mode. Based on the modal-expansion method, the open-loop control force induced by the SMA ring segments applied to a simply supported cylindrical shell panel is formulated. This formulation indicates that only the odd modes in the circumferential direction can be controlled. Longitudinal modes are controlled via placing specific number, depending on the mode, of actuator segments along the panel length. To predict control effects of the nonlinear SMA ring segments, the modal participation factor response is determined for an external harmonic excitation applied to the shell along with induced SMA control forces, via sinusoidal and saw-tooth temperature profiles to generate desirable control forces and to eliminate the unwanted effects. Analysis results suggest that with proper choice of temperature waveform function to the SMA ring segments and minor modifications to frequency and phase, the SMA ring segments can attenuate unwanted external vibrations of cylindrical shells.     

Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support

Summary In this paper, a study on the vibration of thin cylindrical shells with ring supports made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The cylindrical shells have ring supports which are arbitrarily placed along the shell and which impose a zero lateral deflection. The study is carried out based on third order shear deformation shell theory (T.S.D.T). The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. The analysis is carried out with strains-displacement relations from Love's shell theory. The governing equations are obtained using an energy functional with the Rayleigh-Ritz method. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.     

Effect of Static Preloading on the Dynamic Buckling of Laminated Cylinders Under Sudden Pressure

This article presents the results obtained while investigating the behavior of cylindrical laminated shells under suddenly applied lateral pressure. The investigations were based on a finite-element approach using an explicit time integration scheme. The Budiansky-Roth and phase-plane criteria were used to assess buckling. The response of the shells was investigated with and without statically applied preloading. Results are presented for different values of shell length, imperfection amplitude, shell total thickness, and laminae stacking sequences, and for different magnitudes of the static preloading. The results presented here can be used in the design of shell structures and can help better realize the influence of the variations in the system parameters upon the shell strength and stability.     

Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads

Considering rotary, in-plane inertias, and fluid velocity potential, the dynamic characteristics of fluid-conveying functionally graded materials (FGMs) cylindrical shells subjected to dynamic mechanical and thermal loads are investigated, where material properties of FGM shells are considered as graded distribution across the shell thickness according to a power-law, and dynamic thermal loads applied on the shell is considered as non-linear distribution across the thickness of the shell. The linear response characteristics of fluid-conveying FGM cylindrical shells are obtained by using modal superposition and Newmark’s direct time integration method.     

含预裂缝复合材料缠绕圆柱壳轴压承载特性分析

为探究穿透裂缝对复合材料缠绕圆柱壳承载能力及失效模式的影响,首先开展不同壁厚含预裂缝复合材料缠绕圆柱壳轴向压缩试验。对于A系列厚壁圆柱壳,裂缝导致承载能力下降53.96%,失效模式由局部屈曲转化为裂缝扩展、脆性断裂;而B系列薄壁圆柱壳均发生局部屈曲,裂缝使承载能力下降12.59%。其次,采用有限元软件ABAQUS 6.14,基于非线性RIKS算法,建立轴压作用下含预裂缝复合材料圆柱壳极限承载能力计算模型,通过引入Hashin失效准则及损伤演化判据,预测结构渐进破坏模式及极限荷载。数值结果与试验数据吻合良好,最大误差为7.01%,验证了数值算法的可靠性。在此基础上,探讨裂缝方向、缠绕角度对含预裂缝复合材料圆柱壳极限承载的影响,可知:对于±55°螺旋铺层复合材料圆柱壳,随裂缝角度α增加,极限承载能力先升高再降低,当α=45°时,具备最大承载能力;对于含开缝角α=15°、45°、55°缠绕圆柱壳,随缠绕角θ增加,其承载能力呈先上升后下降趋势。且开缝角越小,缠绕角度对极限荷载的影响越大,当缠绕角θ=30°时,达到最大承载能力。     

金属圆柱壳参数变化对缓冲吸能的影响

根据能量守恒以及角度增量叠缩法研究得到了圆柱壳在采用不同的材料以及不同几何参数时的冲击块的速度位移曲线、圆柱壳的载荷以及瞬时载荷位移历程曲线，计算结果说明改变圆柱壳的材料以及几何参数可以确定合理的平均载荷以及瞬时载荷位移历程曲线，还可以通过增加圆柱壳的数量减少圆柱壳在塑性变形叠缩过程中的垂直位移。     

Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation

In this study, the mechanical buckling of functionally graded material cylindrical shell that is embedded in an outer elastic medium and subjected to combined axial and radial compressive loads is investigated. The material properties are assumed to vary smoothly through the shell thickness according to a power law distribution of the volume fraction of constituent materials. Theoretical formulations are presented based on a higher-order shear deformation shell theory (HSDT) considering the transverse shear strains. Using the nonlinear strain–displacement relations of FGMs cylindrical shells, the governing equations are derived. The elastic foundation is modelled by two parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The boundary condition is considered to be simply-supported. The novelty of the present work is to achieve the closed-form solutions for the critical mechanical buckling loads of the FGM cylindrical shells surrounded by elastic medium. The effects of shell geometry, the volume fraction exponent, and the foundation parameters on the critical buckling load are investigated. The numerical results reveal that the elastic foundation has significant effect on the critical buckling load.     

复合材料柱面壳压缩性能分析

对三分之一复合材料柱面壳进行压缩性能试验研究与理论分析, 试验得到柱面壳的破坏方式为屈曲破坏。利用有限元法对其建模分析和静强度分析, 得到的静强度远大于屈曲强度, 因此柱壳应该首先发生屈曲破坏, 这与试验结果相符; 且理论计算所得的屈曲强度与试验结果相符, 说明该模型可以用来分析整个复合材料柱壳的压缩破坏行为, 研究结果可为柱壳的结构设计提供参考。对比某一载荷下理论模型与实际模型上对应点的应变, 发现二者结果相符, 证明有限元建模有效。然后分别对理论模型进行屈曲分析。      

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.     

Application of an analog of the δc-model to the analysis of strength of elastoplastic cracked shellsto the analysis of strength of elastoplastic cracked shells

We propose a method for the investigation of the limiting equilibrium of elastoplastic shells with systems of interacting cracks. It can be described as follows: By using an analog of the δ_c-model, the elastoplastic problem is reduced to an elastic problem of the limiting equilibrium of a shell with cracks of unknown length whose lips are subjected to the action of unknown forces and moments satisfying the conditions of plasticity for thin shells. By using equations of the general moment theory of shells and the theory of generalized functions, we reduce the problem to the solution of a system of singular integral equations with unknown limits of integration and singular right-hand sides. We construct an algorithm for the numerical solution of systems of this sort supplemented by the conditions of boundedness of stresses and conditions of plasticity. We investigate crack tip opening displacements in a closed cylindrical shell with a regular system of longitudinal cracks or two transverse cracks. For a cylindrical shell with a single crack, we present an approximate relation for the determination of the critical load or crack length. Pidstryhach Institute of Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 32, No. 3, pp. 5–15, May–June, 1996.     

The effect of moisture content on the mechanical properties of a seed shell

The mechanical properties of the seed shells of the African mongongo nut, Schinziophyton rautenenii (Euphorbiaceae), were measured by compressive C-ring tests in an air-dry condition and also after soaking in distilled water. Young's modulus was found to be about 5 GPa and the fracture strength was 40–50 MPa, for both conditions. However, fracture toughness was affected significantly by moisture content. The critical stress intensity factor, K _IC, of air-dried specimens was 27% greater and the work of fracture, R, 69% greater than those of wet specimens. This difference corresponded well with microscopic observations of the complexity of the fracture surface. Viewed either by scanning electron microscopy or confocal microscopy, cracks in the wet shell deviated neatly around individual fibres, while cracks in air-dried shells either crossed individual fibres or ran obliquely across the outer layers of the secondary cell wall leaving a feathered appearance. It is proposed that the increase in toughness of shells which would be obtained from air-drying may help protect embryonic seed tissues from predation by larger animals (e.g. vertebrates such as rodents) after abcission from the parent plant.     

Analytical model of sound transmission through relatively thick FGM cylindrical shells considering third order shear deformation theory

This work presents an analytical solution for acoustic transmission through relatively thick FGM cylindrical shells using third order shear deformation theory (TSDT). An infinitely long FGM cylindrical shell composed of metal and ceramic with power-law distribution of volume fraction through the thickness is considered. The shell is immersed in a fluid with an external airflow and an oblique plane wave impinges on the external sidewall of the shell. Comparing the results of present study with those of previous models (CST and FSDT) for thin shells, similar results are observed due to limited effects of shear and rotation on transmission loss (TL). However, for relatively thick shells where the shear and rotation effects become more important in lower R/h, TSDT presents more accurate results caused by its higher order model. In addition, the results show proportional change in TL according to distribution of material properties through the thickness of FG cylindrical shells.     

Creation of dense hydroxyapatite (synthetic bone) by hydrothermal conversion of seashells

Strombus gigas (conch) shells and Tridacna gigas (Giant clam) shells have dense, tailored structures that impart excellent mechanical properties to these shells. In this study, conch and clam seashells were converted to hydroxyapatite (HAP) by a hydrothermal method at different temperatures and for different conversion durations. Dense HAP structures were created from these shells throughout the majority of the samples. High temperatures were found to accelerate the conversion process, however, cracks were found on the surface of the samples converted at high temperature or for very long conversion times. The conversion at 180 °C, refreshing the diammonium hydrogen phosphate [(NH₄)₂HPO₄] solution every 2 days, produced samples of good quality. Different morphologies of HAP were found in different regions of the converted shells, which may be caused by different structural morphologies and in different amounts of porosity in the original shells. Partially converted shell samples with dense HAP layers on the surface growing inward and original shell structures inside have an average fracture stress about 137–218 MPa, which is close to the mechanical strength of compact human bone.