Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

The stress state around circular openings,such as boreholes,shafts,and tunnels,is usually needed to be evaluated.Solutions for stresses,strains and ultimate bearing capacities of pressurized hollow cylinder are common cases.Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given.The power series method of complex function is used.The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted.The distributions of normal and tangential contact stress along the interface,tangential stress on the inner boundary and stresses in the radial direction at θ=0°,45° and 90°,are obtained.An example indicates that,when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer,the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials.In that way,stress concentration at the inner surface can be alleviated and the stress distribution is more uniform.This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.

Simulation on flow, heat transfer and stress characteristics of large-diameter thick-walled gas cylinders in quenching process under different water spray volumes

Cooling strength is one of the important factors affecting microstructure and properties of gas cylinders during quenching process,and reasonable water spray volume can effectively improve the quality of gas cylinders and reduce production costs.To find the optimal water spray parameters,a fluid-solid coupling model with three-phase flow was established in consideration of water-vapor conversion.The inner and outer walls of gas cylinder with the dimensions of d914 mm×38 mm×12000 mm were quenched using multi-nozzle water spray system.The internal pressure,average heat transfer coefficient(have)and stress of the gas cylinder under different water spray volumes during quenching process were studied.Finally,the mathematical model was experimentally verified.The results show that both the internal pressure and have increase along with the increase of spray volume.The internal pressure increases slowly first and then rapidly,but have increases rapidly first and then slowly.To satisfy hardenability of gas cylinders,the minimum spray volume should not be less than 40 m^3/(h·m).The results of stress indicate that water spray quenching will not cause deformation of bottle body in the range of water volume from 40 to 290 m^3/(h·m).

Limit analysis of viscoplastic thick-walled cylinder and spherical shell under internal pressure using a strain gradient plasticity theory

Plastic limit load of viscoplastic thick-walled cylinder and spherical shell subjected to internal pressure is investigated analytically using a strain gradient plasticity theory. As a result, the current solutions can capture the size effect at the micron scale. Numerical results show that the smaller the inner radius of the cylinder or spherical shell, the more significant the scale effects. Results also show that the size effect is more evident with increasing strain or strain-rate sensitivity index. The classical plastic-based solutions of the same problems are shown to be a special case of the present solution.

Reduction of the residual stresses in cold expanded thick-walled cylinders by plastic compression

We suppose that in order to maintain high accuracy of holes and to lower residual stresses after cold expansion of thick-walled cylinders, which undergo cross-section plastic deformation, it is necessary to perform axial plastic compression and subsequent cold expansion with small interferences. To test this hypothesis, we studied hoop, radial and axial residual stresses in cylinders made of carbon steel AISI 1050 with hole diameter of 5 mm, outer diameter of 15 mm and length of 30 mm by Sachs method as well as accuracy of expanded holes. It is found that double cold expansion with total interference equal to 5.1% generates hoop residual stresses with largest absolute value equal to 284 MPa and ensures high holes accuracy(IT7). After plastic compression with strain equal to 0.5 and 1% the mentioned stresses reduced to 120 and 75 MPa respectively,and accuracy of the holes reduced as well. Subsequent cold expansion with small interference equal to 0.9% helps to restore holes accuracy(IT7)gained by double cold expansion and ensure that absolute value of hoop residual stresses(177 MPa) is lower compared to double cold expansion.

Study on scour around vertical large-size cylinder base due to combined action of wave and current

Based on the mechanism of local scour around vertical large-sized cylinder due to combined action of wave and current,the sour morphology,scour process and the maximum scour depth around the cylinders are studied experimentally.The influence of various ocean environmental parameters on local scour around the cylinder is considered in physical model test.The experimental results indicate that the principal effect factors on the scour in fine-sand seabed are wave height,wavelength,current velocity,ratio of diameter to wavelength and ratio of depth to wavelength when the ratio of cylinder diameter to wavelength is from 0.2 to 0.8.In this paper,dimensional analysis theory is utilized to establish a theoretical equation for forecasting maximum scour depth around large-sized round cylinder base due to the combined action of wave and current.The results computed with the theoretical equation are compared with the experimental results,and found to be in good consistency.The results in this studies can be used to estimate the maximum sour depth around analogous structures.

A Numerical Investigation of Vortex-Induced Vibration Response and Fatigue Damage for Flexible Cylinders Under Combined Uniform and Oscillatory Flow

Vortex-induced vibration(VIV)for flexible cylinders under combined uniform and oscillatory flow is a challenging and practical issue in ocean engineering.In this paper,a time domain numerical model is adopted to investigate the characteristics of cross-flow VIV response and fatigue damage under different combined flow cases.Firstly,the adopted VIV model and fatigue analysis procedure are validated well against the published experimental results of a4-m cylinder model under pure oscillatory flows.Then,forty-five combined flow cases of the same cylinder model are designed to reveal the VIV response characteristics with different non-dimensional oscillation period T^*and combined ratio r.The combined flow cases are classified into three categories to investigate the effect of r on cylinder’s dynamic response,and the effect of T*is described under long and short period cases.Finally,fatigue analysis is carried out to investigate how the structural fatigue damage varies with the variations of r and T^*.The captured characteristics of structural response and fatigue damage are explained through the VIV mechanism analysis.

A borehole stability study by newly designed laboratory tests on thick-walled hollow cylinders

At several mineral exploration drilling sites in Australia, weakly consolidated formations mainly consistof sand particles that are poorly bonded by cementing agents such as clay, iron oxide cement or calcite.These formations are being encountered when drilling boreholes to the depth of up to 2 0 0 m. To studythe behaviour of these materials, thick-walled hollow cylinder （TWHC） and solid cylindrical syntheticspecimens were designed and prepared by adding Portland cement and water to sand grains. The effectsof different parameters such as water and cement contents, grain size distribution and mixture curingtime on the characteristics of the samples were studied to identify the mixture closely resembling theformation at the drilling site. The Hoek triaxia! cell was modified to allow the visual monitoring of graindebonding and borehole breakout processes during the laboratory tests. The results showed the significanceof real-time visual monitoring in determining the initiation of the borehole breakout. The sizescaleeffect study on TWHC specimens revealed that with the increasing borehole size, the ductility ofthe specimen decreases, however, the axial and lateral stiffnesses of the TWHC specimen remain unchanged.Under different confining pressures the lateral strain at the initiation point of boreholebreakout is considerably lower in a larger size borehole （2 0 mm） compared to that in a smaller one（10 mm）. Also, it was observed that the level of peak strength increment in TWHC specimens decreaseswith the increasing confining pressure.

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.

Ringlike failure experiment of thick-walled limestone cylinder specimens in triaxial unloading tests

In order to study the failure of surrounding rock under high in situ stress in deep underground engineering projects, disturbed by excavation unloading, we carried out triaxial unloading experiments using thickwalled cylinder specimens on a TATW-2000 rock servo-controlled triaxial testing machine in a laboratory. The specimens were made of limestone material, taken from Tongshan county, Xuzhou city, Jiangsu province, China. In our experiments, rock deformation and failure behavior was studied through loading and unloading of inner hole pressure of thick-walled cylinder specimens. At first, the axial stress, confining pressure and inner pressure were increased simultaneously to a specified designed state of stress. Then, keeping the axial stress and confining pressure stable, the pressure on the inner hole was decreased until the specimen was fractured. When the inner pressure was released completely but the specimen did not fracture, the confining pressure was decreased subsequently until complete failure occurred. Our experimental results suggest that traces of major circular ringlike fractures with a number of radial cracks often appear in thick cylinder walls. This type of ringlike failure phenomenon, similar to intermittent zonal fracturing characteristics of deep exploitation, has, so far, not been published. Our experimental results show that rock deformation and failure behavior of thick-walled limestone cylinders vary under different stress paths between loading and unloading. Tensile failure and orderly failure surfaces occur under unloading conditions while irregular damaged rock blocks are produced during loading failure. This type of triaxial unloading experiment provides for new research methodology and approach for thorough investigations on intermittent zonal fracturing in deep underground excavations.

Research on Strengthening Method of Concave Cone-toroid-cylinder Combined Shell with Initial Imperfection

As a new joint structure,the impact of initial imperfection to stress of Concave cone-toroid-cylinder combined shell was analyzed. Firstly the location and shape of combined shell's initial imperfection caused by welding was studied. Secondly dominated stress was chosen after comparing varioustypical stress. Then it was analyzed that the influence of imperfection to dominated stress via changing the shape of frame's deflection and shell's concave-convex. At last the strengthening case for combined shell with imperfection was pointed out. The conclusions are:(1) Stress of frame 9 is more sensitive to initial imperfection than circumferential stress of toroidmidsurface,which is a new concern;(2) To strength the frames in the sides of toroid not only can decrease the stress of frame,but also can reduce the circumference stress of toroid's midsurface.

Parameter matching and experiment of the combined cyclone separation and cylinder sieve cleaning system for rape combine harvester

Existing rape combine harvester with a cyclone separation cleaning device has the challenge that the loss rate and the cleaning rate increase and decrease simultaneously.A cleaning process route was proposed,which involves the cyclone separation cleaning device removing light and tiny impurities,and the cylinder sieve device removing coarse and long impurities such as pod shells and short stems.A novel cleaning system combining the cyclone separation cleaning device and cylinder sieve cleaning devices was designed.The ranges of the structure and operation parameters for each component were analyzed based on kinematics and dynamic analysis.A four-factor five-level quadratic orthogonal test was carried out,in which the loss rate and cleaning rate were taken as the evaluation indexes.The velocity at the suction port,the rotation speed of the cylinder sieve,the screw pitch of the spiral blade and the diameter of the sieve hole were taken as the influencing factors.The orthogonal test results showed that the cleaning system performed best at a rotation speed of the winnower is 600 r/min,an airflow velocity at the suction port is 18.25 m/s,a rotation speed of the cylinder sieve is 87 r/min,a screw pitch of the spiral blade is 440 mm and a diameter of the sieve hole is 4.48 mm.At this time,the loss rate of the cleaning system is 3.22%,and the cleaning rate is 95.67%.Compared to the conventional cyclone separation cleaning device,the loss rate is reduced by 2.17%and the cleaning rate is increased by 1.05%.This study can provide a reference for the optimal cleaning system design for rape combine harvesters.

ELASTOPLASTIC ANALYSIS OF THICK-WALLCYLINDER CONSIDERING THE MATERIAL'S DILATANCY CHARACTER

Impermeable bentonite or its mixtures have been proposed as candidate materials to be used in the geotechnical disposal of radioactive nuclear waste. These materials are filled in the space between a canister containing radioactive nuclear waste and an underground chamber to absorb the radionuclide emitting from the canister and simultaneously retard its migration accompanying the perrneation of underground water to prevent the surrounding environment from po1lution. On the basis of the established elastoplastic strain-hardening mechanical model considering the material’s dilatancy character,the authors carry out the stress-strain analysis of a thick-wa1l cylinder in a plane strain state subJected to a pressure difference between internal and external pressures. The analysis may be expected to be a theoretical basis for developing a coupled shear and permeability test apparatus for conducting a permeability test along a sheared plane in a specimen. The apparatus will be used to study the effects of shear strain on the variation of geotechnical materials’ permeability coefficient in order to evaluate the influence of shear strain caused by nonuniform deformation and/or earthquake on the long-term safety of the disposal system of radioactive nuclear waste. The theoretlcal analysls methods in this paper can be directly spread to the analysis of the deformation and stability of tunnels or roadways driven in soft soils or high moisture-bearing soft rocks.

Effect of Optimum Plastic Depth on Stresses and Load-bearing Capacity of Autofrettaged Cylinder

Autofrettage is an effective measure to even distribution of stresses and raise load-bearing capacity for （ultra-）high pressure apparatus. Currently, the research on autofrettage has focused mostly on specific engineering problems, while general theoretical study is rarely done. To discover the general law contained in autofrettage theory, by the aid of the authors’ previous work and according to the third strength theory, theoretical problems about autofrettage are studied including residual stresses and their equivalent stress, total stresses and their equivalent stress, etc. Because of the equation of optimum depth of plastic zone which is presented in the authors’ previous work, the equations for the residual stresses and their equivalent stress as well as the total stress and their equivalent stress are simplified greatly. Thus the law of distribution of the residual stresses and their equivalent stress as well as the total stress and their equivalent stress and the varying tendency of these stresses are discovered. The relation among various parameters are revealed. The safe and optimum load-bearing conditions for cylinders are obtained. According to the results obtained by theoretical analysis, it is shown that if the two parameters, namely ratio of outside to inside radius, k, and depth of plastic zone, kj, meet the equation of optimum depth of plastic zone, when the pressure contained in an autofrettaged cylinder is lower than two times the initial yield pressure of the unautofrettaged cylinder, the equivalent residual stress and the equivalent total stress at the inside surface as well as the elastic-plastic juncture of a cylinder are lower than yield strength. When an autofrettaged cylinder is subjected to just two times the initial yield pressure of the unautofrettaged cylinder, the equivalent total stress within the whole plastic zone is just identically equal to the yield strength, or it is a constant. The proposed research theoretically depicts the stress state of ultra-）high pressure autofrettaged cylinder more accurately and more reasonably and provides the reference for design of （ultra-）high pressure apparatus.

Axisymmetric smooth contact for an elastic isotropic infinite hollow cylinder compressed by an outer rigid ring with circular profile

A contact problem for an infinitely long hollow cylinder is considered. The cylinder is compressed by an outer rigid ring with a circular profile. The material of the cylinder is linearly elastic and isotropic. The extent of the contact region and the pressure distribution are sought. Governing equations of the elasticity theory for the axisymmetric problem in cylindrical coordinates are solved by Fourier transforms and general expressions for the displacements are obtained. Using the boundary conditions, the formulation is reduced to a singular integral equation. This equation is solved by using the Gaussian quadrature. Then the pressure distribution on the contact region is determined. Numerical results for the contact pressure and the distance characterizing the contact area are given in graphical form.

SIMULATION OF HOLE FLANGING PROCESS ON HEAVY CYLINDERS AND PARAMETER OPTIMIZATION

The forming mechanism of hole flanging on a thick-wall heavy cylinder forging is simulated by DEFORM3D. The cylinder is 4 390 mm in diameter and 390 mm in thickness. The results show that the compound deformation with bending and expanding happens in the process of hole flanging. The diameter of pre-hole of the workpiece is one of the key parameters in the process of hole flanging. The optimal diameter is obtained for reverse-conical hole of average diameter 40 mm by simulation of hole flanging process on 5 pre-holes with different diameters and 3 pre-holes with different shapes. The results can provide the scientific base for engineering application of the process.

Analysis of a functionally graded piezothermoelastic hollow cylinder

A long thick-walled hollow cylinder of piezothermoelastic materials was studied in this work. The gradient prop- erty of the piezoelectric parameter g31 was taken into account. The theory of elasticity was applied to obtain the exact solutions of the cylinder subjected simultaneously to thermal and electric loadings. As an application, these solutions have been success- fully used to study the inverse problems of the material. For comparison, numerical results have been carried out for both graded and double-layered cylinders.

Improved Circularity Metrology of Small Cylindrical Workpieces by the Segmenting-stitching Technique

To address the alignment and measuring force problem in the segmenting-stitching technique for the circularity metrology of small cylindrical workpieces(diameter less than 1.5 mm and length less than 10 mm),a magnet combination jig method is proposed.A small round magnet is attached between the round magnetic jig and small cylinder,and the other end of the small cylindrical workpiece is attached to some cylindrical magnets.Thus,the smaller cylinder can be put in the V-groove and measured successfully with the magnet combination.For verifying the advantage of the magnet combination jig,four measurement quality evaluations are proposed:the circumferential deviation of neighbor arc contours,radial deviation of neighbor arc contours,angle of inclination between the V-groove and small cylinder,and curvature of the obtained arc.The results show that the matching coefficient is enhanced by 98%,the Euclidean distance of overlap parts of neighbor arc contours is reduced by 68%,the position error is reduced 27%,and the average curvature of the arc contours is improved.It can be concluded that the measuring quality can be enhanced prominently by this magnet combination method for the segmenting-stitching method.

内层钢板外层高强度混凝土复合井壁受力特性与支护结构参数优化分析

针对内层钢板外层高强度混凝土复合井壁的厚度设计,以受均匀围压的内层钢板外层高强度混凝土复合井壁得出的弹性解析解为基础,对内层钢板采用Mises屈服准则,外层高强度混凝土采用统一强度理论,研究复合井壁的初始屈服临界状态.以内层钢板和外层高强度混凝土均未屈服为条件,提出复合井壁的设计流程.结果表明,当内半径、围压以及材料给定时,存在外半径和分层半径的最佳取值范围,在此范围内选择外半径和对应的分层半径,内层钢板和外层高强度混凝土均不会达到屈服.与模型试验进行对比,发现试验中内半径、外半径、分层半径和材料给定的复合井壁,当围压等于设计围压时,外半径和分层半径处于最佳取值范围;当围压继续增大时,外层高强度混凝土先于内层钢板屈服.弹性解与屈服准则相结合,得到复合井壁设计流程为:通过规范及工程地质条件确定井壁内半径和围压值,选定复合井壁的材料,采用屈服准则求得外半径和分层半径的最佳取值范围.

均匀流作用下半潜式养殖网箱立柱和网衣耦合水动力数值研究

为满足水产养殖场向深远海扩张的趋势,近年来一系列新型网箱概念被提出。该文以半潜式网箱的基本组成单元,立柱—网衣组合结构为研究对象,对其在均匀流下的水动力耦合特性开展了数值研究。采用多孔介质模型对网衣结构进行建模,采用k-ε湍流模型进行数值计算;测量了仅立柱、仅网衣和立柱—网衣组合结构的升阻力特性,初步揭示了立柱和网衣之间的水动力耦合机理。研究结果表明:网衣结构的存在总会使立柱所受阻力增加,这主要与立柱前侧表面压强增大有关;相反,立柱结构的阻塞作用会影响网衣区域的局部流场,使网衣所受阻力增大,其对网衣升力的影响主要与来流角度有关。该研究表明,对新型半潜式网箱等海洋结构物进行水动力分析时,应当考虑立柱和网衣之间的水动力相互作用。

Theoretical and numerical research on the dynamic launch response of carbon fiber composite cartridges

Understanding the dynamic response of composite material cartridges during the firing process is of great significance for improving their reliability and safety.A theoretical model describing the dynamic response of composite material cartridges is established based on the thick-walled cylinder theory and rate-dependent constitutive model of composite materials.The correctness of the theoretical model is validated through finite element simulations of cartridge deformation.The influence of chamber pressure and cartridge wall thickness on the cartridge's deformation process and stress distribution is analyzed.The results indicate that the primary deformation of composite material cartridges inside the chamber is elastic deformation.Compared to metal cartridges,composite material cartridges require higher pressure for touching-chamber and are more prone to developing gaps after unloading to ensure smooth extraction.During the deformation process,the touching-chamber behavior of the cartridge can improve the stress distribution.Under the same chamber pressure,the touching-chamber behavior can reduce the circumferential stress by approximately 30%.The inner wall surface of the cartridge is a critical area that requires attention.The touching-chamber behavior can be facilitated by appropriately reducing the cartridge wall thickness while ensuring overall strength.This study can provide guidance for the optimization design of composite material cartridges.