This study focused on the buckling characteristics of egg-shaped shells with single crack and double cracks under axial pressure.First,the geometric parameters of the egg-shaped shell were designed,and a numerical mod...This study focused on the buckling characteristics of egg-shaped shells with single crack and double cracks under axial pressure.First,the geometric parameters of the egg-shaped shell were designed,and a numerical model of the egg-shaped shell was established.Then,the initial crack was introduced into the equatorial weld of the egg-shaped shell,and the effects of the crack on the buckling characteristics under different wall thicknesses were explored,as were the effects of the single crack direction,double crack angle and spacing on the buckling characteristics.Finally,crack-free,single crack and double crack egg-shaped shells were fabricated from Q235 steel.The buckling loads and failure modes of the three egg-shaped shells were obtained via axial compression experiments.The numerical critical buckling loads and buckling modes were compared with the experimental results to verify the accuracy of the numerical model.The results of this study are valuable for the design of egg-shaped shells under axial loading.展开更多
Steel cylindrical shells are widely used in engineering structures due to their high strength-to-weight ratio,but they are vulnerable to buckling under axial loads.To address this limitation,fiber-reinforced polymer(F...Steel cylindrical shells are widely used in engineering structures due to their high strength-to-weight ratio,but they are vulnerable to buckling under axial loads.To address this limitation,fiber-reinforced polymer(FRP)composites have emerged as promising materials for structural reinforcement.This study investigates the buckling behavior of steel cylindrical shells reinforced with inner and outer layers of polymer composite materials under axial compression.Using analytical and numerical modeling methods,the critical buckling loads for different reinforcement options were evaluated.Two-sided glass fiber reinforced plastic(GFRP)or carbon fiber reinforced plastic(CFRP)coatings,as well as combined coatings with layers of different composites,were considered.GFRP+CFRPIn the calculations,the coatings were treated as homogeneous orthotropic materials with equivalent averaged elastic characteristics.The numerical analysis revealed that CFRP reinforcement achieved the highest increase in buckling load,with improvements ranging from 9.84%to 47.29%,depending on the composite thickness and steel shell thickness.GFRP reinforcement,while beneficial,demonstrated a lower effectiveness,with buckling load increases between 5.89%and 19.30%.The hybrid reinforcement provided an optimal balance,improving buckling resistance by GFRP+CFRP6.94%to 43.95%.Statistical analysis further identified composite type and thickness as the most significant factors affecting buckling performance.The findings suggest that CFRP is the preferred reinforcement material,especially when applied to thin-walled cylindrical shells,while hybrid reinforcements can be effectively utilized for structures requiring a balance between stiffness and ductility.These insights provide a foundation for optimizing FRP reinforcement strategies to enhance the structural integrity of steel shells in engineering applications.展开更多
The stiffness properties of variable stiffness(VS) composite plates can be controlled by manipulating the variation in the fiber angle, thereby significantly improving their buckling properties. Nonlinear fiber paths ...The stiffness properties of variable stiffness(VS) composite plates can be controlled by manipulating the variation in the fiber angle, thereby significantly improving their buckling properties. Nonlinear fiber paths have attracted attention in the field of composites due to their large design space. The major challenge in adopting nonlinear fiber paths is obtaining a fiber path function within the design space that is easily computable and efficiently yields the highest buckling load of a VS plate. In this investigation, an innovative nonlinear function was proposed to describe the fiber orientation by integrating a center fiber angle into the conventional linear function. The parameters of the nonlinear function can directly represent the fiber angles at a fixed position. This novel approach has promising potential for improving the optimal efficiency of fiber paths because the linear and nonlinear functions are simplified with two identical path parameters. Furthermore, a multilevel optimization method was developed by combining finite element analysis(FEA) with an adaptive radial basis function(RBF) surrogate model, and it was found that the number of FEA cases could be reduced by iteratively inheriting training points. The integration of this nonlinear function with a surrogate model is a significant advancement in the structural optimization of composites. Subsequently, the optimal linear and nonlinear fiber paths were computed to maximize the buckling load of VS plates. The FEA results show that the computational efficiency was greatly improved by the proposed nonlinear function and optimization method. The buckling resistance could be enhanced by the nonlinear fiber path, and the reinforcement mechanism was the redistribution and reduction of in-plane compressive stress.展开更多
AIM:To report the refractive and surgical outcomes of scleral buckling(SB)with or without pars plana vitrectomy(PPV)in patients with pseudophakic rhegmatogenous retinal detachment(PRRD).METHODS:A consecutive case seri...AIM:To report the refractive and surgical outcomes of scleral buckling(SB)with or without pars plana vitrectomy(PPV)in patients with pseudophakic rhegmatogenous retinal detachment(PRRD).METHODS:A consecutive case series of patients with pseudophakia who underwent retinal detachment(RD)surgery was enrolled.The SB procedures were selected to initially treat primary pseudophakic PRRDs and SB-PPV for more complex cases,according to preoperative findings.Eyes with anterior chamber intraocular lens,proliferative vitreoretinopathy anterior to equator,previous invasive glaucoma surgery,severe degenerative myopia or macular hole,and<6mo follow-up were excluded from outcomes analysis.The primary clinical outcome measures were the single surgery anatomic success(SSAS)and final surgery anatomic success(FSAS)rates.Secondary outcome measures were postoperative visual acuity and refractive error.RESULTS:A total of 81 consecutive patients(81 eyes)were enrolled for analysis,comprising 66(81%)men and 15(19%)women with a mean age of 58y(range,33-86y)and the mean final follow-up period was 21.0±19.6mo.A total of 62 PRRDs(n=62;76.5%)were repaired with an initial SB,and 19 PRRDs(n=19;23.5%)were repaired with a combined SB-PPV.The SSAS and FSAS rates were 92.6%(75/81)and 100%(81/81),respectively.All initial failures had retinal reattachment after the secondary PPV.The mean final postoperative best-corrected visual acuity(BCVA)was 0.42±0.33 logMAR(visual acuity 20/55)and final mean refractive error was-1.48±1.40 diopters.The patients who underwent initially SB-PPV had a significantly longer duration of RD and a higher giant retinal tear rate(P<0.05)preoperatively.SSAS was 56/62(90.3%)and 19/19(100%),and the mean postoperative refractive error was-1.30±1.32 D and-1.53±1.38 D for the patients in the SB and SB-PPV groups,respectively.There was no statistically significant difference for those who had SSAS and postoperative refractive errors between the 2 groups.The postoperative BCVAs of the patients with SSAS were not significantly better in the SB group(median,20/40)than in the SB-PPV group(median 20/50).In the SB group,patients with macula-on had better visual acuity postoperatively than patients with macula-off(P=0.000).CONCLUSION:The initial surgical procedures of SB with or without PPV according to the preoperative findings achieve a high reattachment rate and an acceptable refractive error for primary pseudophakic RRD management.展开更多
This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies...This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies,we develop a new framework incorporating yield stress limits either as constraints or objectives alongside previously established local and global buckling constraints.This approach significantly refines the optimization process,ensuring that the resulting designs meet mechanical performance criteria and adhere to critical material yield constraints.First,we establish local density-dependent von Mises yield surfaces based on local yield estimates from homogenization-based analysis to predict the local yield limits of the homogenized materials.Then,these local yield-based load factors are combined with local and global buckling criteria to obtain topology optimized designs that consider yield and buckling failure on all levels.This integration is crucial for the practical application of optimized structures in real-world scenarios,where material yield and stability behavior critically influence structural integrity and durability.Numerical examples demonstrate how optimized designs depend on the stiffness to yield ratio of the considered building material.Despite the foundational assumption of the separation of scales,the de-homogenized structures,even at relatively coarse length scales,exhibit a remarkably high degree of agreement with the corresponding homogenized predictions.展开更多
In this paper,a type of reinforcing structure for composite shell with single and through hole is presented.The experimental tests for the composite shells without hole,with single hole and reinforced structure,with t...In this paper,a type of reinforcing structure for composite shell with single and through hole is presented.The experimental tests for the composite shells without hole,with single hole and reinforced structure,with through hole and reinforced structure subjected to hydrostatic pressure were carried out by the designed experimental test system.The mechanical responses of the composite shells under hydrostatic pressure are obtained by the high-speed camera and strain measurement.The results show that the entire deformation process of the shell can be divided into three:uniform compression,"buckling mode formation"and buckling.The"buckling mode formation"process is captured and reported for the first time.For the composite shell with single hole,the proposed reinforcing structure has a significant reinforcement effect on the shell and the buckling capacity of the shell is not weaker than the complete composite shell.For the composite shell with through hole,sealing effect can be achieved by the proposed reinforcing structure,but the buckling capacity of the shell after reinforcement can only reach 77%of the original buckling capacity.展开更多
Buckling failure in submarine cables presents a prevalent challenge in ocean engineering.This work aims to explore the buckling behavior of umbilical cables with damaged sheaths subjected to compression and bending cy...Buckling failure in submarine cables presents a prevalent challenge in ocean engineering.This work aims to explore the buckling behavior of umbilical cables with damaged sheaths subjected to compression and bending cyclic loads.A finite element model is devised,incorporating a singular armor wire,a rigid core,and a damaged sheath.To scrutinize the buckling progression and corresponding deformation,axial compression and bending cyclic loads are introduced.The observations reveal that a reduction in axial compression results in a larger number of cycles before buckling ensues and progressively shifts the buckling position toward the extrados and fixed end.Decreasing the bending radius precipitates a reduction in the buckling cycle number and minimizes the deformation in the armor wire.Furthermore,an empirical model is presented to predict the occurrence of birdcage buckling,providing a means to anticipate buckling events and to estimate the requisite number of cycles leading to buckling.展开更多
When subjected to sustained high temperatures,the structure of the continuous China railway track system(CRTS)II railway track is susceptible to internal axial pressure,leading to joint damage and the potential for up...When subjected to sustained high temperatures,the structure of the continuous China railway track system(CRTS)II railway track is susceptible to internal axial pressure,leading to joint damage and the potential for upwarp buckling of the track slab.This study employs model testing to derive the upwarp buckling deformation curve of the track slab under conditions of joint damage.An analytical expression for the upwarp buckling equilibrium path of the track slab is derived through the application of the energy principle.Validation of the outcomes is performed by the comparison with experimental data.The effects of initial upwarp amplitude,initial upwarp curve type,elastic modulus,thickness,and gravity load on the upwarp buckling response of the track slab were investigated.The results show that:1)The upwarp deformation of the track slab in the narrow joint damage state is concentrated in a minor range on both sides of the joint,forming an inverted‘V’shape with concave ends.2)The joint damage can significantly reduce the upwarp buckling critical temperature rise of the track slab.3)The magnitude of the initial upwarp amplitude dictates the buckling mode of the track slab,while the initial upwarp curve predominantly influences the upwarp buckling critical temperature rise.Notably,an initial upwarp amplitude below 6.5 mm ensures the buckling resistance for up to a 60℃temperature rise.4)The increases in elastic modulus,gravity load,and track slab thickness can increase the upwarp buckling critical temperature rise.As the initial upwarp amplitude increases,the influence of these factors on the upwarp buckling critical temperature rise of the track slab gradually diminishes.展开更多
The buckling behavior of stiffened panels is significantly influenced by material and geometric defects,making it a critical factor in ensuring structural integrity and safety.These panels are widely used in mechanica...The buckling behavior of stiffened panels is significantly influenced by material and geometric defects,making it a critical factor in ensuring structural integrity and safety.These panels are widely used in mechanical,aerospace,marine,and civil engineering applications due to their ability to enhance bending stiffness with minimal additional weight.Under high loads or stress concentrations,localized structural failures can initiate global buckling in stiffened panels.This study investigates how such defects affect the critical buckling load,stiffness,and thickness of stiffened panels.Two finite element analyses were conducted:a linear analysis to identify the initial buckling mode and a nonlinear analysis using the Riks algorithm in Abaqus CAE,incorporating localized imperfections.The simulations show that material and geometric defects can reduce buckling resistance depending on their severity.展开更多
This study investigates the dynamical behavior of two parallel fluid-conveying pipes by developing a non-planar dynamical model of the two pipes coupled with an intermediate spring. A systematic analysis is conducted ...This study investigates the dynamical behavior of two parallel fluid-conveying pipes by developing a non-planar dynamical model of the two pipes coupled with an intermediate spring. A systematic analysis is conducted to evaluate the effects of spring parameters on the non-planar vibration characteristics and buckling behaviors of the coupled system. The nonlinear governing equations are derived with Hamilton's principle,subsequently discretized through Galerkin's method, and finally numerically solved by the Runge-Kutta algorithm. Based on the linearized equations, an eigenvalue analysis is performed to obtain the coupled frequencies, modal shapes, and critical flow velocities for buckling instability. Quantitative assessments further elucidate the effects of the spring position and stiffness coefficient on the coupled frequencies and critical flow velocities.Nonlinear dynamic analyses reveal the evolution of buckling patterns and bifurcation behaviors between the lateral displacements of the two pipes and the flow velocity. Numerical results indicate that the intermediate spring increases the susceptibility to buckling instability in the out-of-plane direction compared with the in-plane direction. Furthermore, synchronized lateral displacements emerge in both pipes when the flow velocity of one pipe exceeds the critical threshold. This work is expected to provide a theoretical foundation for the stability assessment and vibration analysis in coupled fluid-conveying pipe systems.展开更多
Magneto-active soft materials,composed of hard-magnetic particles embedded in polymeric matrices,have found widespread applications in soft robotics,active metamaterials,and shape-morphing structures across various le...Magneto-active soft materials,composed of hard-magnetic particles embedded in polymeric matrices,have found widespread applications in soft robotics,active metamaterials,and shape-morphing structures across various length scales due to their ability to undergo reversible,untethered,and rapid deformation in response to magnetic actuation.At small scales,surface effects play a crucial role in the mechanical behavior of these soft materials.In this paper,we theoretically investigate the influence of surface effects on the buckling instability and large deformation of magneto-active soft beams under a uniform magnetic field.The theoretical model is derived according to the principle of minimum potential energy and numerically solved with the finite difference method.By employing the developed theoretical model,parametric studies are performed to explore how surface effects influence the buckling instability and large deformation of magneto-active soft cantilever beams with varying geometric parameters under different uniform magnetic fields.Our results reveal that the influence of surface effects on the mechanical behavior of magneto-active soft beams depends not only on the geometric parameters but also on the magnetic field strength.Specifically,when the magnetic field strength is relatively small,surface effects reduce the deformation of magneto-active soft beams,particularly for beams with smaller thicknesses and larger length-to-thickness ratios.However,when the magnetic field strength is sufficiently large,and the beam's deformation becomes saturated,surface effects have little influence on the deformation.This work uncovers the role of surface effects in the mechanical behavior of magnetoactive soft materials,which could provide guidelines for the design and optimization of small-scale magnetic-active soft material-based applications.展开更多
This paper investigates the development and performance of a new higher-order geometric stiffness matrix that more closely approximates the theoretically derived stiffness coefficients.Factors that influence the accur...This paper investigates the development and performance of a new higher-order geometric stiffness matrix that more closely approximates the theoretically derived stiffness coefficients.Factors that influence the accuracy of the solution are studied using two columns,two braced frames,and one unbraced frame.Discussion is provided when the new geometric stiffness matrix can be used to improve the buckling load analysis results and when it may provide only nominal additional benefit.展开更多
The elastic properties of membranes are typically characterized by a few phenomenological parameters,including bending and Gaussian curvature moduli measuring the membrane rigidity against its deformation and topologi...The elastic properties of membranes are typically characterized by a few phenomenological parameters,including bending and Gaussian curvature moduli measuring the membrane rigidity against its deformation and topological change,as well as spontaneous curvature arising from the asymmetry between the two leaflets in the lipid bilayers.Though tether-based and fluctuationbased experiments are commonly utilized to measure the bending modulus,measuring the Gaussian curvature modulus and the spontaneous curvature of the membrane is considered to be much more difficult.In this paper,we study the buckling process of a circular membrane with nonzero spontaneous curvature under compressive stresses.It is found that when the stress exceeds a critical value,the circular membrane will transform from a spherical cap to a buckled shape,with its buckling degree enhanced with the increase of stress until its base is constricted to almost zero.As the stress-strain relationship of the buckled membrane strongly depends on the Gaussian curvature modulus and the spontaneous curvature,we therefore propose a method to determine the Gaussian curvature modulus and the spontaneous curvature simultaneously by measuring its stress-strain relationship during a buckling process.展开更多
This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated al...This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated along both the radial and circumferential directions.By transforming the proposed integral constitutive equations into the equivalent differential forms,complemented by the corresponding constitutive boundary conditions(CBCs),a well-posed mathematical formulation is established for analyzing the axisymmetric bending and buckling of annular/circular functionally graded(FG)sandwich nanoplates.The boundary conditions at the inner edge of a solid nanoplate are derived by L'H?spital's rule.The numerical solution is obtained by the generalized differential quadrature method(GDQM).The accuracy of the proposed model is validated through comparison with the data from the existing literature.A parameter study is conducted to demonstrate the effects of FG sandwich parameters,size parameters,and nonlocal gradient parameters.展开更多
Currently,experimental research on variable stiffness design mainly focuses on laminates.To ensure adaptability in practical application,it is imperative to conduct a systematic study on stiffened variable stiffness s...Currently,experimental research on variable stiffness design mainly focuses on laminates.To ensure adaptability in practical application,it is imperative to conduct a systematic study on stiffened variable stiffness structures,including design,manufacture,experiment,and simulation.Based on the minimum curvature radius and process schemes,two types of T-stiffened panels were designed and manufactured.Uniaxial compression tests have been carried out and the results indicate that the buckling load of variable stiffness specimens is increased by 26.0%,while the failure load is decreased by 19.6%.The influence mechanism of variable stiffness design on the buckling and failure behavior of T-stiffened panels was explicated by numerical analysis.The primary reason for the reduced strength is the significantly increased load bearing ratio of stiffeners.As experimental investigations of stiffened variable stiffness structures are very rare,this study can be considered a reference for future work.展开更多
In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)an...In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.展开更多
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.MET...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.展开更多
●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...●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.展开更多
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 buc...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.展开更多
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 linea...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.52271277)the Natural Science Foundation of Jiangsu Province(Grant No.BK20211343)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.SJCX23_2150).
文摘This study focused on the buckling characteristics of egg-shaped shells with single crack and double cracks under axial pressure.First,the geometric parameters of the egg-shaped shell were designed,and a numerical model of the egg-shaped shell was established.Then,the initial crack was introduced into the equatorial weld of the egg-shaped shell,and the effects of the crack on the buckling characteristics under different wall thicknesses were explored,as were the effects of the single crack direction,double crack angle and spacing on the buckling characteristics.Finally,crack-free,single crack and double crack egg-shaped shells were fabricated from Q235 steel.The buckling loads and failure modes of the three egg-shaped shells were obtained via axial compression experiments.The numerical critical buckling loads and buckling modes were compared with the experimental results to verify the accuracy of the numerical model.The results of this study are valuable for the design of egg-shaped shells under axial loading.
文摘Steel cylindrical shells are widely used in engineering structures due to their high strength-to-weight ratio,but they are vulnerable to buckling under axial loads.To address this limitation,fiber-reinforced polymer(FRP)composites have emerged as promising materials for structural reinforcement.This study investigates the buckling behavior of steel cylindrical shells reinforced with inner and outer layers of polymer composite materials under axial compression.Using analytical and numerical modeling methods,the critical buckling loads for different reinforcement options were evaluated.Two-sided glass fiber reinforced plastic(GFRP)or carbon fiber reinforced plastic(CFRP)coatings,as well as combined coatings with layers of different composites,were considered.GFRP+CFRPIn the calculations,the coatings were treated as homogeneous orthotropic materials with equivalent averaged elastic characteristics.The numerical analysis revealed that CFRP reinforcement achieved the highest increase in buckling load,with improvements ranging from 9.84%to 47.29%,depending on the composite thickness and steel shell thickness.GFRP reinforcement,while beneficial,demonstrated a lower effectiveness,with buckling load increases between 5.89%and 19.30%.The hybrid reinforcement provided an optimal balance,improving buckling resistance by GFRP+CFRP6.94%to 43.95%.Statistical analysis further identified composite type and thickness as the most significant factors affecting buckling performance.The findings suggest that CFRP is the preferred reinforcement material,especially when applied to thin-walled cylindrical shells,while hybrid reinforcements can be effectively utilized for structures requiring a balance between stiffness and ductility.These insights provide a foundation for optimizing FRP reinforcement strategies to enhance the structural integrity of steel shells in engineering applications.
基金supported by the National Natural Science Foundation of China (No. 52305026)the China Postdoctoral Science Foundation (No. 2023M741941)。
文摘The stiffness properties of variable stiffness(VS) composite plates can be controlled by manipulating the variation in the fiber angle, thereby significantly improving their buckling properties. Nonlinear fiber paths have attracted attention in the field of composites due to their large design space. The major challenge in adopting nonlinear fiber paths is obtaining a fiber path function within the design space that is easily computable and efficiently yields the highest buckling load of a VS plate. In this investigation, an innovative nonlinear function was proposed to describe the fiber orientation by integrating a center fiber angle into the conventional linear function. The parameters of the nonlinear function can directly represent the fiber angles at a fixed position. This novel approach has promising potential for improving the optimal efficiency of fiber paths because the linear and nonlinear functions are simplified with two identical path parameters. Furthermore, a multilevel optimization method was developed by combining finite element analysis(FEA) with an adaptive radial basis function(RBF) surrogate model, and it was found that the number of FEA cases could be reduced by iteratively inheriting training points. The integration of this nonlinear function with a surrogate model is a significant advancement in the structural optimization of composites. Subsequently, the optimal linear and nonlinear fiber paths were computed to maximize the buckling load of VS plates. The FEA results show that the computational efficiency was greatly improved by the proposed nonlinear function and optimization method. The buckling resistance could be enhanced by the nonlinear fiber path, and the reinforcement mechanism was the redistribution and reduction of in-plane compressive stress.
文摘AIM:To report the refractive and surgical outcomes of scleral buckling(SB)with or without pars plana vitrectomy(PPV)in patients with pseudophakic rhegmatogenous retinal detachment(PRRD).METHODS:A consecutive case series of patients with pseudophakia who underwent retinal detachment(RD)surgery was enrolled.The SB procedures were selected to initially treat primary pseudophakic PRRDs and SB-PPV for more complex cases,according to preoperative findings.Eyes with anterior chamber intraocular lens,proliferative vitreoretinopathy anterior to equator,previous invasive glaucoma surgery,severe degenerative myopia or macular hole,and<6mo follow-up were excluded from outcomes analysis.The primary clinical outcome measures were the single surgery anatomic success(SSAS)and final surgery anatomic success(FSAS)rates.Secondary outcome measures were postoperative visual acuity and refractive error.RESULTS:A total of 81 consecutive patients(81 eyes)were enrolled for analysis,comprising 66(81%)men and 15(19%)women with a mean age of 58y(range,33-86y)and the mean final follow-up period was 21.0±19.6mo.A total of 62 PRRDs(n=62;76.5%)were repaired with an initial SB,and 19 PRRDs(n=19;23.5%)were repaired with a combined SB-PPV.The SSAS and FSAS rates were 92.6%(75/81)and 100%(81/81),respectively.All initial failures had retinal reattachment after the secondary PPV.The mean final postoperative best-corrected visual acuity(BCVA)was 0.42±0.33 logMAR(visual acuity 20/55)and final mean refractive error was-1.48±1.40 diopters.The patients who underwent initially SB-PPV had a significantly longer duration of RD and a higher giant retinal tear rate(P<0.05)preoperatively.SSAS was 56/62(90.3%)and 19/19(100%),and the mean postoperative refractive error was-1.30±1.32 D and-1.53±1.38 D for the patients in the SB and SB-PPV groups,respectively.There was no statistically significant difference for those who had SSAS and postoperative refractive errors between the 2 groups.The postoperative BCVAs of the patients with SSAS were not significantly better in the SB group(median,20/40)than in the SB-PPV group(median 20/50).In the SB group,patients with macula-on had better visual acuity postoperatively than patients with macula-off(P=0.000).CONCLUSION:The initial surgical procedures of SB with or without PPV according to the preoperative findings achieve a high reattachment rate and an acceptable refractive error for primary pseudophakic RRD management.
基金supported by Villum Fonden through the Villum Investigator Project“AMSTRAD”(Grant No.VIL54487).
文摘This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process.Building upon established multiscale methodologies,we develop a new framework incorporating yield stress limits either as constraints or objectives alongside previously established local and global buckling constraints.This approach significantly refines the optimization process,ensuring that the resulting designs meet mechanical performance criteria and adhere to critical material yield constraints.First,we establish local density-dependent von Mises yield surfaces based on local yield estimates from homogenization-based analysis to predict the local yield limits of the homogenized materials.Then,these local yield-based load factors are combined with local and global buckling criteria to obtain topology optimized designs that consider yield and buckling failure on all levels.This integration is crucial for the practical application of optimized structures in real-world scenarios,where material yield and stability behavior critically influence structural integrity and durability.Numerical examples demonstrate how optimized designs depend on the stiffness to yield ratio of the considered building material.Despite the foundational assumption of the separation of scales,the de-homogenized structures,even at relatively coarse length scales,exhibit a remarkably high degree of agreement with the corresponding homogenized predictions.
基金supported by the Ningbo Major Research and Development Plan Project(Grant No.2024Z135)the Natural Science Basic Research Program of Shaanxi Province(Grant No.2024JC-YBMS-322)+1 种基金China Postdoctoral Science Foundation(Grant No.2020M673492)National Natural Science Foundation of China(Grant No.51909219)。
文摘In this paper,a type of reinforcing structure for composite shell with single and through hole is presented.The experimental tests for the composite shells without hole,with single hole and reinforced structure,with through hole and reinforced structure subjected to hydrostatic pressure were carried out by the designed experimental test system.The mechanical responses of the composite shells under hydrostatic pressure are obtained by the high-speed camera and strain measurement.The results show that the entire deformation process of the shell can be divided into three:uniform compression,"buckling mode formation"and buckling.The"buckling mode formation"process is captured and reported for the first time.For the composite shell with single hole,the proposed reinforcing structure has a significant reinforcement effect on the shell and the buckling capacity of the shell is not weaker than the complete composite shell.For the composite shell with through hole,sealing effect can be achieved by the proposed reinforcing structure,but the buckling capacity of the shell after reinforcement can only reach 77%of the original buckling capacity.
基金financially supported by the National Natural Science Foundation of China(Grant No.52471301)the Fujian Province Transportation Science and Technology Project(Grant No.JC202302)the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY24E090003).
文摘Buckling failure in submarine cables presents a prevalent challenge in ocean engineering.This work aims to explore the buckling behavior of umbilical cables with damaged sheaths subjected to compression and bending cyclic loads.A finite element model is devised,incorporating a singular armor wire,a rigid core,and a damaged sheath.To scrutinize the buckling progression and corresponding deformation,axial compression and bending cyclic loads are introduced.The observations reveal that a reduction in axial compression results in a larger number of cycles before buckling ensues and progressively shifts the buckling position toward the extrados and fixed end.Decreasing the bending radius precipitates a reduction in the buckling cycle number and minimizes the deformation in the armor wire.Furthermore,an empirical model is presented to predict the occurrence of birdcage buckling,providing a means to anticipate buckling events and to estimate the requisite number of cycles leading to buckling.
基金supported by the National Natural Science Foundation of China(No.52278459).
文摘When subjected to sustained high temperatures,the structure of the continuous China railway track system(CRTS)II railway track is susceptible to internal axial pressure,leading to joint damage and the potential for upwarp buckling of the track slab.This study employs model testing to derive the upwarp buckling deformation curve of the track slab under conditions of joint damage.An analytical expression for the upwarp buckling equilibrium path of the track slab is derived through the application of the energy principle.Validation of the outcomes is performed by the comparison with experimental data.The effects of initial upwarp amplitude,initial upwarp curve type,elastic modulus,thickness,and gravity load on the upwarp buckling response of the track slab were investigated.The results show that:1)The upwarp deformation of the track slab in the narrow joint damage state is concentrated in a minor range on both sides of the joint,forming an inverted‘V’shape with concave ends.2)The joint damage can significantly reduce the upwarp buckling critical temperature rise of the track slab.3)The magnitude of the initial upwarp amplitude dictates the buckling mode of the track slab,while the initial upwarp curve predominantly influences the upwarp buckling critical temperature rise.Notably,an initial upwarp amplitude below 6.5 mm ensures the buckling resistance for up to a 60℃temperature rise.4)The increases in elastic modulus,gravity load,and track slab thickness can increase the upwarp buckling critical temperature rise.As the initial upwarp amplitude increases,the influence of these factors on the upwarp buckling critical temperature rise of the track slab gradually diminishes.
文摘The buckling behavior of stiffened panels is significantly influenced by material and geometric defects,making it a critical factor in ensuring structural integrity and safety.These panels are widely used in mechanical,aerospace,marine,and civil engineering applications due to their ability to enhance bending stiffness with minimal additional weight.Under high loads or stress concentrations,localized structural failures can initiate global buckling in stiffened panels.This study investigates how such defects affect the critical buckling load,stiffness,and thickness of stiffened panels.Two finite element analyses were conducted:a linear analysis to identify the initial buckling mode and a nonlinear analysis using the Riks algorithm in Abaqus CAE,incorporating localized imperfections.The simulations show that material and geometric defects can reduce buckling resistance depending on their severity.
基金supported by the National Natural Science Foundation of China(Nos.12325201,12272140,and 12322201)。
文摘This study investigates the dynamical behavior of two parallel fluid-conveying pipes by developing a non-planar dynamical model of the two pipes coupled with an intermediate spring. A systematic analysis is conducted to evaluate the effects of spring parameters on the non-planar vibration characteristics and buckling behaviors of the coupled system. The nonlinear governing equations are derived with Hamilton's principle,subsequently discretized through Galerkin's method, and finally numerically solved by the Runge-Kutta algorithm. Based on the linearized equations, an eigenvalue analysis is performed to obtain the coupled frequencies, modal shapes, and critical flow velocities for buckling instability. Quantitative assessments further elucidate the effects of the spring position and stiffness coefficient on the coupled frequencies and critical flow velocities.Nonlinear dynamic analyses reveal the evolution of buckling patterns and bifurcation behaviors between the lateral displacements of the two pipes and the flow velocity. Numerical results indicate that the intermediate spring increases the susceptibility to buckling instability in the out-of-plane direction compared with the in-plane direction. Furthermore, synchronized lateral displacements emerge in both pipes when the flow velocity of one pipe exceeds the critical threshold. This work is expected to provide a theoretical foundation for the stability assessment and vibration analysis in coupled fluid-conveying pipe systems.
基金Project supported by the National Natural Science Foundation of China(Nos.12202009 and12002004)。
文摘Magneto-active soft materials,composed of hard-magnetic particles embedded in polymeric matrices,have found widespread applications in soft robotics,active metamaterials,and shape-morphing structures across various length scales due to their ability to undergo reversible,untethered,and rapid deformation in response to magnetic actuation.At small scales,surface effects play a crucial role in the mechanical behavior of these soft materials.In this paper,we theoretically investigate the influence of surface effects on the buckling instability and large deformation of magneto-active soft beams under a uniform magnetic field.The theoretical model is derived according to the principle of minimum potential energy and numerically solved with the finite difference method.By employing the developed theoretical model,parametric studies are performed to explore how surface effects influence the buckling instability and large deformation of magneto-active soft cantilever beams with varying geometric parameters under different uniform magnetic fields.Our results reveal that the influence of surface effects on the mechanical behavior of magneto-active soft beams depends not only on the geometric parameters but also on the magnetic field strength.Specifically,when the magnetic field strength is relatively small,surface effects reduce the deformation of magneto-active soft beams,particularly for beams with smaller thicknesses and larger length-to-thickness ratios.However,when the magnetic field strength is sufficiently large,and the beam's deformation becomes saturated,surface effects have little influence on the deformation.This work uncovers the role of surface effects in the mechanical behavior of magnetoactive soft materials,which could provide guidelines for the design and optimization of small-scale magnetic-active soft material-based applications.
文摘This paper investigates the development and performance of a new higher-order geometric stiffness matrix that more closely approximates the theoretically derived stiffness coefficients.Factors that influence the accuracy of the solution are studied using two columns,two braced frames,and one unbraced frame.Discussion is provided when the new geometric stiffness matrix can be used to improve the buckling load analysis results and when it may provide only nominal additional benefit.
基金the financial support from the National Natural Science Foundation of China under Grant Nos.12174323 and 12474199Fundamental Research Funds for Central Universities of China under Grant No.20720240144(RM)111 project B16029。
文摘The elastic properties of membranes are typically characterized by a few phenomenological parameters,including bending and Gaussian curvature moduli measuring the membrane rigidity against its deformation and topological change,as well as spontaneous curvature arising from the asymmetry between the two leaflets in the lipid bilayers.Though tether-based and fluctuationbased experiments are commonly utilized to measure the bending modulus,measuring the Gaussian curvature modulus and the spontaneous curvature of the membrane is considered to be much more difficult.In this paper,we study the buckling process of a circular membrane with nonzero spontaneous curvature under compressive stresses.It is found that when the stress exceeds a critical value,the circular membrane will transform from a spherical cap to a buckled shape,with its buckling degree enhanced with the increase of stress until its base is constricted to almost zero.As the stress-strain relationship of the buckled membrane strongly depends on the Gaussian curvature modulus and the spontaneous curvature,we therefore propose a method to determine the Gaussian curvature modulus and the spontaneous curvature simultaneously by measuring its stress-strain relationship during a buckling process.
基金Project supported by the National Natural Science Foundation of China(No.12172169)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘This paper extends the one-dimensional(1D)nonlocal strain gradient integral model(NStraGIM)to the two-dimensional(2D)Kirchhoff axisymmetric nanoplates,based on nonlocal strain gradient integral relations formulated along both the radial and circumferential directions.By transforming the proposed integral constitutive equations into the equivalent differential forms,complemented by the corresponding constitutive boundary conditions(CBCs),a well-posed mathematical formulation is established for analyzing the axisymmetric bending and buckling of annular/circular functionally graded(FG)sandwich nanoplates.The boundary conditions at the inner edge of a solid nanoplate are derived by L'H?spital's rule.The numerical solution is obtained by the generalized differential quadrature method(GDQM).The accuracy of the proposed model is validated through comparison with the data from the existing literature.A parameter study is conducted to demonstrate the effects of FG sandwich parameters,size parameters,and nonlocal gradient parameters.
基金Supported by the National Natural Science Foundation of China(No.11902124).
文摘Currently,experimental research on variable stiffness design mainly focuses on laminates.To ensure adaptability in practical application,it is imperative to conduct a systematic study on stiffened variable stiffness structures,including design,manufacture,experiment,and simulation.Based on the minimum curvature radius and process schemes,two types of T-stiffened panels were designed and manufactured.Uniaxial compression tests have been carried out and the results indicate that the buckling load of variable stiffness specimens is increased by 26.0%,while the failure load is decreased by 19.6%.The influence mechanism of variable stiffness design on the buckling and failure behavior of T-stiffened panels was explicated by numerical analysis.The primary reason for the reduced strength is the significantly increased load bearing ratio of stiffeners.As experimental investigations of stiffened variable stiffness structures are very rare,this study can be considered a reference for future work.
基金Project supported by the National Key Research and Development Program of China(No.2022YFB3207100)Hubei Provincial Strategic Scientist Training Plan(No.2022EJD009)the Fundamental Research Funds for the Central Universities of China(No.2042023kf1041)。
文摘In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.
基金Supported by National Natural Science Foundation of China(No.81700884)Scientific Research Foundation of National Health and Health Commission(No.WKJ-ZJ-2037)+1 种基金Zhejiang Public Welfare Technology Application Project(No.LGF21H120005)Science and Technology Project of Wenzhou(No.Y20190649).
文摘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.
基金Supported by Xuzhou Health Outstanding Talents Project(No.XWJC001)Critical Special Project for Social Development of Xuzhou(No.KC21153)+1 种基金Science and Technology Innovation Project of Xuzhou Municipal Health Commission(No.XWKYHT20230039)Applied Basic Research Project of Xuzhou(No.KC23016).
文摘●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.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52071160 and 52071203)the 333-Key-Industry Talent Project of Jiangsu Scientific Committee(Grant No.JTO 2022-21).
文摘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.
基金Project supported by the National Natural Science Foundation of China (Nos.12072007,12072006,12132001,and 52192632)the Ningbo Natural Science Foundation of Zhejiang Province of China (No.202003N4018)the Defense Industrial Technology Development Program of China (Nos.JCKY2019205A006,JCKY2019203A003,and JCKY2021204A002)。
文摘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.
