Effect of lamination sequence on the localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

Effect of lamination sequence on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element, and is based on the assumption of layer-wise linear displacements distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. Hitherto unavailable numerical results pertaining to the influence of lamination sequence on the localization of buckling patterns and the ensuing shear crippling instability are also presented.     

Effects of fiber misalignment and transverse shear modulus on localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

The effect of transverse shear modulus on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. The present study is primarily motivated to obtain the hitherto unavailable results pertaining to the effect of reduced transverse shear modulus, , of a lamina weakened by the presence of randomly distributed fiber misalignments. A simple expression for the reduced transverse shear modulus, , of a layer material is derived in terms of the average fiber misalignment angle. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element and is based on the assumption of layer-wise linear displacement distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. The interaction of a micro-structural defect in the form of initial fiber misalignments with its macro-structural counterpart represented by a modal imperfection is a key to understanding this meso-structural level phenomenon. Hitherto unavailable numerical results pertaining to the influence of this effect on the localization of buckling patterns and the ensuing shear crippling instability are also presented.     

Effects of thickness and modal imperfection amplitude on elastic collapse pressure of a cross-ply imperfect ring

Effects of thickness and modal imperfection amplitude on mode 2 elastic collapse pressures of thin, moderately thick and thick cross-ply perfect and imperfect rings are investigated in detail. A recently developed nonlinear resonance (eigenvalue) based semi-analytical solution technique is employed here for computation of the elastic mode 2 collapse pressures of thin to thick cross-ply rings, weakened by modal or harmonic type imperfections. A von Karman type iterative nonlinear analysis, which is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the perfect/imperfect cross-ply ring. Interesting and hitherto unavailable numerical results pertaining to the effects of thickness and amplitude of modal imperfection on the hydrostatic collapse pressures of imperfect cross-ply rings and comparison with their perfect counterparts are also presented.     

Use of material grading for enhanced buckling design of thin-walled composite rings/long cylinders under external pressure

This paper presents a mathematical model for enhancing the buckling stability of composite, thin-walled rings/long cylinders under external pressure using radial material grading concept. The main structure to be analyzed is built of multi-angle fibrous laminated lay-ups having different volume fractions of the constituent materials within the individual plies. This leads to a piecewise grading of the material in the radial direction. The objective is to maximize the critical buckling pressure while preserving the total structural mass at a constant value equal to that of a baseline design. The fiber volume fractions are included among the standard design variables such as fiber orientation angles and ply thicknesses, which are used by many investigators in the field. The model employs the classical lamination theory, where an analytical solution that accounts for the effective axial and flexural stiffness separately is given. The critical buckling pressure contours subject to the mass equality constraint are given for several types of anisotropic rings/long cylinders showing the functional dependence of the constrained objective function on the selected design variables. It is shown that material grading can have significant contribution to the whole optimization process in achieving the required structural designs with enhanced stability limits.     

On instability failure of corroded rings under external hydrostatic pressure

Analytical formulations were derived for bifurcation pressure and non-linear static analysis of a corroded ring under external pressure. The mid-surface inextensional condition was included in the derivation which resulted in much improved accuracy in the prediction of bifurcation pressure. Afterwards, an analytical method was presented to solve the non-linear deformation problem of a corroded ring with initial ovality included under external pressure. A finite element analysis was carried out to verify the accuracy of the developed model. By setting the initial yielding as the failure criterion, a parametric study was carried out to study the effect of corrosion depth and corrosion angular extent. Moreover, the interaction effect of two circumferential corroded regions on the critical pressure was studied. Finally, some comments on the analytical methods were given to consider the case of continuously varying thickness and an alternative perturbative method was proposed. This research is intended to enhance the understanding of instability and failure for a corroded tube under external pressure mainly applicable to offshore industry.     

Non-linear buckling and postbuckling of shear deformable anisotropic laminated cylindrical shell subjected to varying external pressure loads

Non-linear buckling and postbuckling of a moderately thick anisotropic laminated cylindrical shell of finite length subjected to lateral pressure, hydrostatic pressure and external liquid pressure has been presented in the paper. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic non-linearity and including the extension/twist, extension/flexural and flexural/twist couplings. The non-linear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a circumferential stress along with an associate shear stress when the shell is subjected to external pressure.     

Delamination buckling and postbuckling in composite cylindrical shells under combined axial compression and external pressure

A series of finite element analyses on the delaminated composite cylindrical shells subject to combined axial compression and pressure are carried out varying the delamination thickness and length, material properties and stacking sequence. Based on the FE results, the characteristics of the buckling and postbuckling behaviour of delaminated composite cylindrical shells are investigated. The combined double-layer and single-layer of shell elements are employed which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the local strain energy release rate along the delamination front. The results are compared with the previous results obtained by the author on the buckling and postbuckling of delaminated composite cylindrical shells under the axial compression and external pressure, applied individually.     

A generalized higher-order theory for buckling of thick multi-layered composite plates with normal and transverse shear strains

The onset of buckling in square laminated multi-layered composite plates, subject to unidirectional in-plane loads, is investigated within the framework of a generalized higher-order shear deformation theory suitable to capture significant transverse shear and thickness-wise deformation effects. The displacement field is expanded in a Taylor series of the thickness coordinate with arbitrary polynomial degree; in turn, the series coefficients, expressed as a superposition of admissible functions, are determined according to the Rayleigh–Ritz method. Truly higher-order polynomial terms, along with a sufficient number of in-plane admissible functions, are shown to be necessary for convergence towards the fundamental buckling load multiplier. As a by-product, reduced-order models are identified for various plate geometries and lamination schemes. The sensitivity of the lowest buckling load with respect to the nondimensional parameters (the thickness ratio, the ratio between the elastic moduli, the ply angle) is investigated. In particular, the attention is focused on the cross-over phenomenon between the lowest two buckling eigenvalues in multi-layered composite square plates with different lamination schemes. The presented results shed light onto the buckling behavior of thick shear-deformable multi-layered plates.     

Reliability-based load and resistance factor design of composite pressure vessel under external hydrostatic pressure

A reliability-based load and resistance factor design procedure for subsea composite pressure vessel subjected to external hydrostatic pressure is presented. The failure criterion for defining the performance function is considered as buckling. A sensitivity analysis is conducted to research influences of statistical characteristics of variables on the partial safety factors and the thickness of pressure vessel. The results shows the longitudinal modulus, inside radius of composite layers, unsupported length and external pressure significantly affect the design results, whereas transversal modulus, Poisson’s ratio, shear modulus and winding angle have little effects. In order to validate the design results, a filament-wound composite pressure vessel is manufactured, and the buckling test is performed. It is observed that when the applied external hydrostatic pressure is a little more than the designed critical buckling pressure, the buckling and subsequent burst behaviours occur, which shows a good agreement between the experimental and analytical results.     

Gas pressure effects on thickness uniformity and circumvented deposition during sputter deposition process

In sputter deposition processes, the thickness distribution of the film is affected by experimental conditions such as gas pressure, target-substrate (T-S) distance and target elements. To study these effects, we have designed a sample holder with three quartz crystal microbalance (QCM) thickness monitors on its surface and measured the distribution of the depositing flux around the sample holder, including the circumvented deposition onto the back face. As for the gas pressure dependence for a T-S distance of about 50 mm, the relative deposition flux on the back face was found to be at its maximum at pressures of 1-2 Pa. Above this pressure, the uniformity of the flux on the front face became gradually worse. The observed characteristics could be reproduced by a Monte-Carlo simulation of the particle transport process. The reduction of the circumvented deposition and the uniformity degradation at high gas pressures were ascribed to the start of thermalization of sputtered particles and the shrinkage of its spatial profile toward the target.     

纤维缠绕复合材料气瓶内衬的屈曲分析

为深入了解纤维缠绕复合材料气瓶的内衬屈曲情况,基于ANSYS有限元软件,运用数值模拟方法对纤维缠绕复合材料气瓶的金属内衬结构进行屈曲分析,建立了复合气瓶内衬结构的有限元模型,采用特征值法分析得出内衬1~10阶的屈曲模态,并利用非线性稳定法绘出内衬位移量随外压变化曲线.结果表明,计算得到的内衬临界失稳外压为0.199 MPa,与复合气瓶内衬外压试验结果相符合,证实了本文对于复合气瓶内衬屈曲分析的可靠性.     

Analytical study on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure

This article focuses on the buckling of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. First, combining the method of separation of variables, perturbation method, and Fourier series expansion, an analytical method for the buckling analysis of cylindrical shells with axisymmetric thickness variation subjected to external pressure is established. The method is verified by comparing with the previous results. Then, the stepwise variable thickness of cylindrical shells is described exactly by the arc tangent function. Finally, using the presented method, a general formula for the critical buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure is derived. This general formula is compared and discussed with some empirical formulae in the current design standards. This study lays a theoretical foundation for the calculation of the buckling load of cylindrical shells with stepwise variable thickness subjected to uniform external pressure. Moreover, it provides a reference and guidance for the further revision of related standards.     

Effect of thickness of ZnO active layer on ZnO-TFT's characteristics

We have investigated the electrical characteristics of ZnO thin film transistors with respect to the thickness of ZnO active layers. The ZnO layers with the thickness of 30 nm to 150 nm were deposited on bottom gate patterned Si substrate by RF sputtering at room temperature. The low-temperature oxide served as gate dielectric. As ZnO channel layer got thicker, the leakage current at V_DS = 30 V and V_G = 0 V greatly increased from 10^− 10 A to 10^− 6 A, while the threshold voltage decreased from 15 V to 10 V. On the other hand, the field effect mobility got around 0.15 cm²/V s except for the 30-nm-thick channel. Overall, the 55-nm-thick ZnO channel layer showed the best performance.     

Elasticity, shell theory and finite element results for the buckling of long sandwich cylindrical shells under external pressure

The buckling of a sandwich cylindrical shell under uniform external hydrostatic pressure is studied in three ways. The simplifying assumption of a long shell is made (or, equivalently, ‘ring’ assumption), in which the buckling modes are assumed to be two-dimensional, i.e. no axial component of the displacement field, and no axial dependence of the radial and hoop displacement components. All constituent phases of the sandwich structure, i.e. the facings and the core, are assumed to be orthotropic. First, the structure is considered a three-dimensional (3D) elastic body, the corresponding problem is formulated and the solution is derived by solving a set of two linear homogeneous ordinary differential equations of the second-order in r (the radial coordinate), i.e. an eigenvalue problem for differential equations, with the external pressure, p the parameter/eigenvalue. A complication in the sandwich construction is due to the fact that the displacement field is continuous but has a slope discontinuity at the face-sheet/core interfaces, which necessitates imposing ‘internal’ boundary conditions at the face-sheet/core interfaces, as opposed to the traditional two-end-point boundary value problems. Second, the structure is considered a shell and shell theory results are generated with and without accounting for the transverse shear effect. Two transverse shear correction approaches are employed, one based only on the core, and the other based on an effective shear modulus that includes the face-sheets. Third, finite element results are generated by use of the ABAQUS finite element code. In this part, two types of elements are used: a shear deformable shell element and a solid 3D (brick) element. The results from all these three different approaches are compared.     

Influences of elastic foundations and shear deformations on the buckling behavior of functionally graded material truncated conical shells under axial compression

This article presents an investigation on the buckling of functionally graded (FG) truncated conical shells under an axial load resting on elastic foundations within the shear deformation theory (SDT). The governing equations are solved using the Galerkin method, and the closed-form solution of the axial buckling load for FG conical shells on elastic foundations within the SDT is obtained. Various numerical examples are presented and discussed to verify the accuracy of the closed-form solution in predicting dimensionless buckling loads for FG conical shells on the Winkler–Pasternak elastic foundations within the SDT.     

Experimental and numerical investigation of thickness effect on ductile fracture toughness of steel alloy sheets

Effect of thickness on ductile fracture toughness of plates made of steel alloy GOST 08Ch22N6T is investigated experimentally. Multiple specimen tests for determining fracture toughness have been conducted using compact tension (CT) specimens with thicknesses of 1.25, 1.64 and 4.06 mm according to standard test method ASTM E813. The results show the significant effect of thickness on fracture toughness. It is observed that in low thickness, J_c increases with the thickness increase until it reaches a maximum; however, further increase in the thickness causes the J_c-value to decrease. Two-dimensional finite element analysis is also performed to reproduce the experimental results. The comparison shows a very good agreement.     

Experimental investigations on buckling of cylindrical shells under axial compression and transverse shear

This paper presents experimental studies on buckling of cylindrical shell models under axial and transverse shear loads. Tests are carried out using an experimental facility specially designed, fabricated and installed, with provision forin-situ measurement of the initial geometric imperfections. The shell models are made by rolling and seam welding process and hence are expected to have imperfections more or less of a kind similar to that of real shell structures. The present work thus differs from most of the earlier investigations. The measured maximum imperfections δ_max are of the order of ±3t (t = thickness). The buckling loads obtained experimentally are compared with the numerical buckling values obtained through finite element method (FEM). In the case of axial buckling, the imperfect geometry is obtained in four ways and in the case of transverse shear buckling, the FE modelling of imperfect geometry is done in two ways. The initial geometric imperfections affect the load carrying capacity. The load reduction is considerable in the case of axial compression and is marginal in the case of transverse shear buckling. Comparisons between experimental buckling loads under axial compression, reveal that the extent of imperfection, rather than its maximum value, in a specimen influences the failure load. Buckling tests under transverse shear are conducted with and without axial constraints. While differences in experimental loads are seen to exist between the two conditions, the numerical values are almost equal. The buckling modes are different, and the experimentally observed and numerically predicted values are in complete disagreement.     

高聚物熔体锥形收敛流场分布的影响因素数值分析

在入口收敛流基本方程基础上,通过建立锥形入口结构和有限元网格模型,运用数值仿真方法,采用Cross本构方程和壁面无滑移模型,速度采用二次插值、压力采用线性插值和黏度牛顿迭代的有限元计算方法,对影响广义等温流动熔体在口模入口和出口区域的压力、速度和剪切速率分布的熔体材料、工艺参数和口模形状等因素进行了数值分析。研究结果表明,压力分布与熔体黏度、流动指数、松弛时间、入口流率和流道压缩比等有直接关系,而法向速度和剪切速率仅受入口流率的影响较大。通过对多个因素量化分析表明,压力分布随着熔体黏度、入口流率和流道压缩比的增大而增大,而随着流动指数和松弛时间的增大而减小,法向速度和剪切速率随着入口流率增大而增大;这些影响因素使得口模出口处压力、法向速度和剪切速率均不为零,从而引发离模膨胀等问题。     

Buckling behavior of stiffened composite panels with variable thickness skin under compression

In this paper, the effect of the skin configuration on the buckling behavior of stiffened composite panels subjected to uniaxial compression was numerically and experimentally investigated. P-version finite element models containing all the structural details were used to predict the buckling load and buckling mode of stiffened composite panels. The upper and lower ends of the panel were fixed by potting a tin bismuth alloy with melting temperature around 70?°C to get an uniformly loading condition in the test. The alloy could be easily recycled by heating and reutilized later for potting the other test specimens.