Buckling Properties of Water-Drop-Shaped Pressure Hulls with Various Shape Indices Under Hydrostatic External Pressure

The water-drop-shaped pressure hull has a good streamline,which has good application prospect in the underwater observatory.Therefore,this study conducted analytical,experimental and numerical investigation of the buckling properties of water-drop-shaped pressure hulls under hydrostatic pressure.A water-drop experiment was conducted to design water-drop-shaped pressure hulls with various shape indices.The critical loads for the water-drop-shaped pressure hulls were resolved by using Mushtari’s formula.Several numerical simulations including linear buckling analysis and nonlinear buckling analysis including eigenmode imperfections were performed.The results indicated that the critical loads resolved by Mushtari's formula were in good agreement with the linear buckling loads from the numerical simulations.This formula can be extended to estimate the buckling capacity of water-drop-shaped pressure hulls.In addition,three groups of pressure hulls were fabricated by using stereolithography,a rapid prototyping technique.Subsequently,three groups of the pressure hulls were subjected to ultrasonic measurements,optical scanning,hydrostatic testing and numerical analysis.The experimental results were consistent with the numerical results.The results indicate that the sharp end of the water-drop-shaped pressure hulls exhibited instability compared with the blunt end.This paper provides a new solution to the limitations of experimental studies on the water-drop-shaped pressure hulls as well as a new configuration and evaluation method for underwater observatories.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fbers

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years.Bamboo fibers are renowned for their good mechanical properties,abundance,and short cycle growth.As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications,this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite(BFRC)beams on the elastic foundation.Three different functionally graded(FG)layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness.The elastic properties of the composite are determined with the law of mixture.Employing Hamilton’s principle,the governing equations of motion are obtained.The generalized differential quadrature method(GDQM)is then applied to the equations to obtain the results.The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions,elastic foundation stiffness values,and boundary conditions(BCs)and slenderness ratio of the beam change.Furthermore,a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials,demonstrating the significant enhancements in both vibration and buckling responses,with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-◇fiber distribution.Eventually,the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite(CNTRC)beams found in the literature,indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams.

Buckling Optimization of Curved Grid Stiffeners through the Level Set Based Density Method

Stiffened structures have great potential for improvingmechanical performance,and the study of their stability is of great interest.In this paper,the optimization of the critical buckling load factor for curved grid stiffeners is solved by using the level set based density method,where the shape and cross section(including thickness and width)of the stiffeners can be optimized simultaneously.The grid stiffeners are a combination ofmany single stiffenerswhich are projected by the corresponding level set functions.The thickness and width of each stiffener are designed to be independent variables in the projection applied to each level set function.Besides,the path of each single stiffener is described by the zero iso-contour of the level set function.All the single stiffeners are combined together by using the p-norm method to obtain the stiffener grid.The proposed method is validated by several numerical examples to optimize the critical buckling load factor.

Non-contact wide-field viewing system-assisted scleral buckling surgery for retinal detachment in silicone oilfilled eyes

AIM:To evaluate scleral buckling(SB)surgery using a noncontact wide-field viewing system and 23-gauge intraocular illumination for the treatment of rhegmatogenous retinal detachment in silicone oil(SO)-filled eyes.METHODS:Totally 9 patients(9 eyes)with retinal detachment in SO-filled eyes were retrospectively analyzed.All patients underwent non-contact wide-field viewing system-assisted buckling surgery with 23-gauge intraocular illumination.SO was removed at an appropriate time based on recovery.The patients were followed up for at least 3mo after SO removal.Retinal reattachment,complications,visual acuity and intraocular pressure(IOP)before and after surgery were observed.RESULTS:Patients were followed up for a mean of 8.22mo(3-22mo)after SO removal.All patients had retinal reattachment.At the final follow-up,visual acuity showed improvement for 8 patients,and no change for 1 patient.The IOP was high in 3 patients before surgery,but it stabilized after treatment;it was not affected in the other patients.None of the patients had infections,hemorrhage,anterior ischemia,or any other complication.CONCLUSION:This new non-contact wide-field viewing system-assisted SB surgery with 23-gauge intraocular illumination is effective and safe for retinal detachment in SO-filled eyes.

Fault Diagnosis for Buckling Friction Components in Wet Multi-Disc Clutches Using IHHT

The wet multi-disc clutches are extensively used in various transmission systems,withone of the most prevalent failure modes being the buckling deformation of friction components.Animproved Hilbert-Huang transform method(IHHT)is proposed to address the limitations of tradi-tional time-domain vibration analyses,such as low accuracy and mode mixing.This paper first clas-sifies the buckling degree of the friction components.Next,wavelet packet transform(WPT)isapplied to the vibration signals of different buckling plates to partition them into distinct fre-quency bands.Then,the instantaneous features are extracted by empirical mode decomposition(EMD)and Hilbert transform(HT)to discarding extraneous intrinsic mode function(IMF)com-ponents.Comparative analyses of Hilbert spectral entropy and time-domain features confirm theenhanced precision of IHHT under specific classifiers,which is better than traditional methods.

Efficacy of scleral buckling for the treatment of rhegmatogenous retinal detachment using a novel foldable capsular buckle

●AIM:To evaluate the effectiveness and safety of scleral buckling for the treatment of rhegmatogenous retinal detachment(RRD)using a novel foldable capsular buckle(FCB).●METHODS:This was a series of case observation studies.Eighteen patients(18 eyes)who visited our ophthalmology department between August 2020 and August 2022 and were treated for RRD with scleral buckling using FCB were included.The procedure was similar to conventional scleral buckling,while a balloon-like FCB was placed onto the retinal break with balanced salt solution filling for a broad,external indentation instead of the silicone buckle.The retinal reattachment rate,best corrected visual acuity(BCVA),intraocular pressure(IOP),refractive dioptre and astigmatism degree,and complications were evaluated and recorded.●RESULTS:There were 7 males and 11 females aged 19-58y.The average time course of RRD was 12d,ranging from 7-20d.The retinal break was located in the superior quadrants in 8 eyes and in the inferior quadrants in 10 eyes,with macula-off detachments in 12 eyes.The patients were followed-up for at least 6mo.The final retinal reattachment rate was 100%.The BCVA was significantly improved compared with the baseline(P<0.05).There was no significant change in refractive dioptre or astigmatism degree at each follow-up(all P>0.05).Three patients had transiently high IOPs within one week after surgery.Mild diplopia occurred in 5 patients after surgery and then disappeared after the balloon fluid was removed.●CONCLUSION:The success rate of FCB scleral buckling for RRD is satisfactory.This procedure can be expected to be applied in new,uncomplicated cases of RRD.

Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio

This paper proposes a three-dimensional(3D)Maltese cross metamaterial with negative Poisson’s ratio(NPR)and negative thermal expansion(NTE)adopted as the core layers in sandwich plates,and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial.First,the NPR and NTE of the metamaterial are derived analytically based on energy conservation.The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method(FEM).Subsequently,the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton’s principle with the consideration of the von Kármán nonlinearity.The differential quadrature(DQ)FEM(DQFEM)is utilized to obtain the numerical solutions.It is shown that NPR and NTE can enhance the global stiffness of sandwich structures.The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress,natural frequency,and critical buckling load.

Theoretical and Numerical Studies on the Coupling Deformation of Global Lateral Buckling and Walking of Submarine Pipeline

Buckling initiation devices/techniques,including sleepers,distributed buoyancy,snake lay,and residual curvature method(RCM),have recently been widely applied in engineering.These initiated buckles may induce a long pipeline to transform into multiple short pipeline segments,which promote the occurrence of pipeline walking.Thus,a pipeline,which is designed to buckle laterally,may laterally and axially displace over time when subjected to repeated heating and cooling cycles.This study aims to reveal the coupling mechanism of pipeline walking and global lateral buckling.First,an analytic solution is proposed to estimate the walking of pipeline segments between two adjacent buckles.Then,the sensitivity of this method to heating and cooling cycles is analyzed.Results show the applicability of the proposed walking analytical solution of buckling pipelines.Subsequently,an influence analysis of walking on global buckling,including the capacity of buckling initiation,buckling amplitude,buckling mode,and failure assessment of the buckling pipeline,is performed.The results reveal that the effect of walking on the buckling axial force is negligible.However,pipeline walking will aggravate the asymmetry of the pipeline buckling and the failure parameters of the pipeline during the post-buckling.

Numerical Study on Lateral Buckling Mode of Pipelines Laid on A Sleeper

Because non-buried submarine pipelines under cyclic thermal loading are prone to global buckling,sleepers are commonly laid along the pipeline route to induce a series of relatively small and controllable lateral buckling.A finite element model which can simulate the transformation of pipeline laid on a sleeper from vertical buckling to lateral buckling is established in this work.The parameters of sleeper affecting pipeline buckling modes are analysed,and a new kind of sleeper is proposed aimed at avoiding antisymmetric buckling.Results show that the lateral trigger force can avoid antisymmetric lateral buckling when acting between 1℃and 13℃before the critical buckling temperature.The range increases slightly with increasing trigger force.Compared with an ordinary sleeper,the proposed new sleeper with slider can reduce the critical buckling temperature by 25%,which significantly improves the success rate of sleepers.

Analytical determination of non-local parameter value to investigate the axial buckling of nanoshells affected by the passing nanofluids and their velocities considering various modified cylindrical shell theories

We analytically determine the nonlocal parameter value to achieve a more accurate axial-buckling response of carbon nanoshells conveying nanofluids. To this end, the four plates/shells' classical theories of Love, Fl ¨ugge, Donnell, and Sanders are generalized using Eringen's nonlocal elasticity theory. By combining these theories in cylindrical coordinates,a modified motion equation is presented to investigate the buckling behavior of the nanofluid-nanostructure-interaction problem. Herein, in addition to the small-scale effect of the structure and the passing fluid on the critical buckling strain,we discuss the effects of nanoflow velocity, fluid density(nano-liquid/nano-gas), half-wave numbers, aspect ratio, and nanoshell flexural rigidity. The analytical approach is used to discretize and solve the obtained relations to study the mentioned cases.

Research on the Critical Buckling Pressure of Bucket Foundations with Inner Compartments for Offshore Wind Turbines

In the process of suction penetration of bucket foundations with inner compartments for offshore wind turbines,most researches focus on soil seepage failure and soil plugs,while the buckling of foundations is rarely investigated.Therefore,theoretical calculation methods for critical buckling pressures of the skirt and bulkheads of the bucket foundation are first presented according to the stability theory of a cylindrical shell and the small deflection theory of a thin plate,respectively.Furthermore,two types of models with and without considering the skirt-soil interaction are developed for the calculation of critical buckling pressure of the bucket foundation.Taking a practical project as an example,theoretical and numerical methods are used to obtain the critical buckling pressures of a bucket foundation.In this work,the theoretical method and the finite element model considering the skirt-soil interaction for calculating the critical buckling pressure of bucket foundations are firstly proposed.The results can help to optimize the design process of offshore wind turbine foundations and improve the safety of offshore wind power systems.

Buckling morphology of glassy nematic films with staggered director field

The photo-induced buckling of axially periodic glassy nematic films with alternating stripped director domains is explored by the F¨oppl-von K′arm′an plate theory along with a modified kinetics approach.The effects of domain widths on the critical light intensity as well as the buckling morphology are examined numerically.It is found that in most cases the buckled film forms regularly aligned dimples and protrusions,but shows large scale bending perpendicular to the periodic axis if the widths of the stripes are nearly the same.In addition,change in light intensity is shown to alter the wavenumber of the buckling pattern.These results are expected helpful to the design of shape-shifting structures with glassy nematic films.

Experimental Study and Fragility Analysis of Effective-Length Factors in Column Buckling

The design of columns relies heavily on the basis of Leonhard Euler’s Theory of Elastic Buckling.However,to increase the accuracy in determining the maximum critical load a column can withstand before buckling,a constant was introduced.This dimensionless coefficient is K,also known as the effective-length factor.This constant is often found in building design codes and varies in value depending on the type of column support that is applied.This paper presents experimental and analytical studies on the determination of the effective-length factor in the buckling stability of columns with partially-fixed support conditions.To this end,the accurate K value of the columns tested by the Instron Testing Machine(ITM)at California State University,Northridge’s(CSUN’s)Mechanics Laboratory is determined.The ITM is used in studying the buckling of columns where the supports are neither pinned nor fixed,and the material cross-section rather rests upon the machine while loading is applied axially.Several column specimens were tested and the experimental data were analyzed in order to estimation of the accurate effective-length factor.The calculations from the tested results as well as the conducted probabilistic analysis shed light on how a fragility curve may aid in predicting the effective-length value of future tests.

Lateral buckling of non-trenched high temperature pipelines with pipelay imperfections

An analysis method for the buckling process of a pipe section with a random pipelay imperfection is proposed. Four basic lateral modes, acquired by finite-element （FE） eigenvalue buckling analysis, are combined to provide the needed grid configurations for describing a real pipelay imperfection and an arc-length algorithm is used to analyze the snap-through process of the shell-element-grid model under nonlinear frictional boundary conditions. This paper also presents evaluation methods for the lateral buckling of two types of pipe-in-pipe systems that are used in the offshore oil and gas industry. For evaluating the buckling and postbuckling of compliant pipe-in-pipe systems FE analyses were carried out to judge the occurrence of the system buckling and furthermore to check postbuckling stresses induced in the buckles. The calculated results of the modified Riks algorithm indicate that only when high temperature would not trigger an abrupt short-wavelength buckle and when no yielding has been induced in the unavoidable long-wavelength buckles, the thermal stability and safety of compliant pipe-in-pipe systems can be proved. In the non-compliant pipe-in-pipe systems, firstly small-amplitude buckles of the carrier pipe may occur in the annulus between carrier pipe and casing pipe and the contact forces between the spacers and the casing pipe may drive the buckle of the pipe-in-pipe systems on the seabed. Based on the classical analytical solution of pipe buckling, four potential buckling modes corresponding to finite- element models are developed to evaluate the stability and the postbuckling strength of such pipe-in-pipe systems.

DYNAMIC BUCKLING OF DOUBLE-WALLED CARBON NANOTUBES UNDER STEP AXIAL LOAD

An approximate method is presented in this paper for studying the dynamic buckling of double-walled carbon nanotubes （DWNTs） under step axial load. The analysis is based on the continuum mechanics model, which takes into account the van der Waals interaction between the outer and inner nanotubes. A buckling condition is derived, from which the critical buckling load and associated buckling mode can be determined. As examples, numerical results are worked out for DWNTs under fixed boundary conditions. It is shown that, due to the effect of van der Waals forces, the critical buckling load of a DWNT is enhanced when inserting an inner tube into a single-walled one. The paper indicates that the critical buckling load of DWNTs for dynamic buckling is higher than that for static buckling. The effect of the radii is also examined. In addition, some of the results are compared with the previous ones.

Structural Integrity Assessment of Offshore Jackets Considering Proper Modeling of Buckling in Tubular Members-a Case Study of Resalat Jacket

In the present research,results of buckling analysis of 384 finite element models,verified using three different test results obtained from three separate experimental investigations,were used to study the effects of five parameters such as D/t,L/D,imperfection,mesh size and mesh size ratio.Moreover,proposed equations by offshore structural standards concerning global and local buckling capacity of tubular members including former API RP 2A WSD and recent API RP 2A LRFD,ISO 19902,and NORSOK N-004 have been compared to FE and experimental results.One of the most crucial parts in the estimation of the capacity curve of offshore jacket structures is the correct modeling of compressive members to properly investigate the interaction of global and local buckling which leads to the correct estimation of performance levels and ductility.Achievement of the proper compressive behavior of tubular members validated by experimental data is the main purpose of this paper.Modeling of compressive braces of offshore jacket platforms by 3D shell or solid elements can consider buckling modes and deformations due to local buckling.ABAQUS FE software is selected for FE modeling.The scope of action of each of elastic buckling,plastic buckling,and compressive yielding for various L/r ratios is described.Furthermore,the most affected part of each parameter on the buckling capacity curve is specified.The pushover results of the Resalat Jacket with proper versus improper modeling of compressive members have been compared as a case study.According to the results,applying improper mesh size for compressive members can under-predict the ductility by 33%and under-estimate the lateral loading capacity by up to 8%.Regarding elastic stiffness and post-buckling strength,the mesh size ratio is introduced as the most effective parameter.Besides,imperfection is significantly the most important parameter in terms of critical buckling load.

Buckling Performances of Spherical Caps Under Uniform External Pressure

This study aims to experimentally and numerically examine the buckling performances of stainless steel spherical caps under uniform external pressure.Three laboratory-scale caps were fabricated,measured,and tested.The buckling behaviors of these caps were investigated through experiments and three numerical methods,namely,nonlinear Riks algorithm,nonlinear bifurcation,and linear elastic analysis.The buckling of equal-radius caps was numerically analyzed with different methods to identify their applicability under different wall thicknesses.The results obtained from the nonlinear Riks algorithm are in good agreement with the experimental results,which means the nonlinear Riks algorithm can accurately predict the buckling performances of spherical caps,including the magnitude of critical buckling loads and the deformation of post-buckling modes.The nonlinear bifurcation algorithm is only suitable for predicting the buckling loads of ultra-thin or large-span caps,and the linear buckling method is inappropriate for predicting the buckling of metal spherical caps.

POSTBUCKLING OF PRESSURE-LOADED SHEAR DEFORMABLE LAMINATED CYLINDRICAL PANELS

A postbuckling analysis is presented for a shear deformable laminated cylindrical panel of finite length subjected to lateral pressure. The governing equations are based on Reddy's higher order shear deformation shell theory with von Krmn_Donnell_type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical panels under lateral pressure. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, cross_ply laminated cylindrical panels. The effects played by transverse shear deformation, panel geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.