Analysis of bending and buckling of pre-twisted beams:A bioinspired study

Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elas- tic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self- weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.

An Inelastic Material Model for Lateral Torsional Buckling and Biaxial Bending of Steel W-Shapes

A new material model for beam elements was developed for use as normalized tangent modulus expressions when performing 3-dimensional second-order inelastic analyses of steel I-section beams.The stiffness matrix of a 14 degree-of-freedom beam element was updated to include the effects of yielding on St.Venant’s torsion and bimoment stiffness at the initial and terminal nodes.A validation study compared the new model’s results with those from published detailed finite element analyses and was found to be in very close agreement.A biaxial end-moment study with two different depth-to-flange-width ratios provided expected and consistent results over a range of moment conditions.

The Buckling Behavior of Boron Nitride Nanotubes under Bending： An Atomistic Study

In this paper, the buckling behavior of zigzag BN （Boron Nitride） nanotubes under bending is studied through molecular dynamics finite element method with Tersoff potential. The tube with namely （15, 0） BN zigzag tube is investigated. The critical bending buckling angle, moment and curvature are studied and examined with respect to the tube length-diameter ratios from 5 to 30. Effects of a SW （Stone-Wales） defect in the middle tube on the bending behavior are also discussed. The results show that the tube length affects significantly the bending behavior of these tubes. All tubes exhibit brittle fracture under bending. The buckling takes place at the middle in the compressive side of these tubes. These results are important information on the buckling behaviors of pristine and Stone-Wales BN nanotubes, which will be useful for their future applications.

Tunable Bending Stiffness, Buckling Force, and Natural Frequency of Nanowires and Nanoplates

This paper aims to obtain the simple closed-form results for the combined effects of surface elasticity, initial stress/ strain, and material Poisson ratio on the bending stiffness, natural frequency and buckling force of nanowires and nano-plates. The results demonstrate that all these properties of nanowires or nanoplates can be designed either very sensitive or not sensitive at all to the amplitude of an applied electric potential;show how much of those properties can be controlled to vary;and thus provide a reliable guide to the measurement of the Young’s modulus of nanowires/nanoplates and to the design of nano-devices, such as nano-sensors or the cantilever of an AFM.

INFLUENCE OF INITIAL IMPERFECTION AND COUPLING BETWEEN BENDING AND EXTENSION ON VIBRATION, BUCKLING AND NONLINEAR DYNAMIC STABILITY OF LAMINATED PLATES

In this paper, the influence of init ial imperfection and coupling between bending and extension on vibration, buckling and nonlinear dynamic stability of laminated plates is studied. The governing e quation is derived. It is a nonlinear modified Mathieu Equation. Numerical solut ions of 5 typical composite materials namely, Glass_epoxy Scotch_1002, Aramid_ep oxy Kevlar_49, Boron_epoxy B4_5505, Graphite_epoxy T300_5208 and AS_3501 are co mputed. Results reveal that the existence of initial imperfection, and also coup ling effect,make the plates much more sensitive to entering parametric resonance with amplitude greater than that of perfect plates. Coupl ing effect for different composite laminates, especially, for that with few laye rs, is different. If coupling effect is neglected, the design of plate structure s for buckling and dynamic stability would unconservatively be for more than 10% .

Cubic Spline Solutions of Nonlinear Bending and Buckling of Circular Plates with Arbitrarily Variable Thickness

The cubic B-splines taken as trial function, the large deflection of a circular plate with arbitrarily variable thickness,as well as the buckling load, have been calculated by the method of point collocation. The support can be elastic. Loads imposed can be polynomial distributed loads, uniformly distributed radial forces or moments along the edge respectively or their combinations. Convergent solutions can still be obtained by this method under the load whose value is in great excess of normal one. Under the action of the uniformly distributed loads, linear solutions of circular plates with linearly or quadratically variable thickness are compared with those obtained by the parameter method. Buckling of a circular plate with identical thickness beyond critical thrust is compared with those obtained by the power series method.

Axisymmetrical Nonlinear Bending and Buckling of a Circular Plate Under Large Load

With the terms of the exact series solution taken as trial functions, the method of point collocation was used to calculate the large deflection of a circular plate. The axisymmetrical bending formulae were developed for the calculation of a circular plate subjected to polynomial distributed loads, a concentrated load at the center, uniform radial forces and moments along the edge or their combinations. The support may be elastic. The buckling load was calculated. Under action of uniformly distributed load, central load or their compound load, solutions were compared with those obtained by other methods. Buckling beyond critical thrust was compared with that calculated by the power series method. The method presented in this paper has advantages of wide convergent range, high precision and short computing time. Moreover, the computing time is nearly independent of the complexity of the loads.

CUBLIC SPLINE SOLUTIONS OF AXISYMMETRICALNONLINEAR BENDING AND BUCKLING OFCIRCULAR SANDWICH PLATES

Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads, uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal.

Buckling Response of Pipe-in-Pipe Systems Subjected to Bending

The buckling response of pipe-in-pipe(PIP)systems subjected to bending is investigated in this paper. A set of parameterized models are established to explore the bending characteristics of the PIP systems through eigenvalue buckling analysis and nonlinear post-buckling analysis. The results show that the length of PIP systems and the height of centralizers are the most significant factors that influence the buckling moment, ultimate bending moment and buckling mode; the other geometric characteristics, such as initial geometric imperfection and friction between centralizers and outer pipes, evidently influence the post-buckling path and ductility of PIPs; the equivalent bending stiffness is dependent on the length and centralizers. Moreover, the range of equivalent bending stiffness is also discussed.

Bending Failure Mode and Prediction Method of the Compressive Strain Capacity of A Submarine Pipeline with Dent Defects

A dent is a common type of defects for submarine pipeline.For submarine pipelines,high hydrostatic pressure and internal pressure are the main loads.Once pipelines bend due to complex subsea conditions,the compression strain capacity may be exceeded.Research into the local buckling failure and accurate prediction of the compressive strain capacity are important.A finite element model of a pipeline with a dent is established.Local buckling failure under a bending moment is investigated,and the compressive strain capacity is calculated.The effects of different parameters on pipeline local buckling are analyzed.The results show that the dent depth,external pressure and internal pressure lead to different local buckling failure modes of the pipeline.A higher internal pressure indicates a larger compressive strain capacity,and the opposite is true for external pressure.When the ratio of external pressure to collapse pressure of intact pipeline is greater than 0.1,the deeper the dent,the greater the compressive strain capacity of the pipeline.And as the ratio is less than 0.1,the opposite is true.On the basis of these results,a regression equation for predicting the compressive strain capacity of a dented submarine pipeline is proposed,which can be referred to during the integrity assessment of a submarine pipeline.

Post-Buckling Behavior of Laminated Composite Cylindrical Shells Subjected to Axial, Bending and Torsion Loads

In present work, post-buckling behavior of imperfect (of eigen form) laminated composite cylindrical shells with different L/D and R/t ratios subjected to axial, bending and torsion loads has been investigated by using an equilibrium path approach in the finite element analysis. The Newton-Raphson approach as well as the arc-length approach is used to ensure the correctness of the equilibrium paths up to the limit point load. Post-buckling behavior of imperfect cylindrical shells with different L/D and R/t ratios of interest is obtained and the theoretical knock-down factors are reported for the considered cylindrical shells.

Experimental,Numerical,and Analytical Studies on the Bending of Mechanically Lined Pipe

Mechanically lined pipe(MLP)is often used for offshore oil and gas transport because of its low cost and corrosion resistance.During installation and operation,the pipe may undergo severe bending deformation,which causes the liner to separate from the outer pipe and buckles,affecting the stability of the whole line.In this paper,the buckling response of MLP subjected to bending is investigated to clarify its bending characteristics by employing both experiments,numerical simulation,as theoretical methods.Two types of MLPs were manufactured with GB 45 carbon steel(SLP)and Al 6061(ALP)used as the outer pipe material,respectively.The hydraulic expansion and bending experiments of small-scale MLPs are conducted.In addition to the ovalized shape of the cross-section for the SLP specimens,the copper liner was found to wrinkle on the compressive side.In contrast,the liner of ALP remains intact without developing any wrinkling and collapse mode.In addition,a dedicated numerical framework and theoretical models were also established.It was found both the manufacturing and bending responses of the MLP can be well reproduced,and the predicted maximum moment and critical curvatures are in good agreement with the experimental results.

Effect of characteristics and distribution of Mg_(17)Al_(12)precipitates on tensile and bending properties of high-Al-containing Mg alloys

This study investigates the effect of characteristics and distribution of Mg_(17)Al_(12)precipitates on the uniaxial tensile and three-point bending properties of extruded Mg alloys containing high Al contents.The extruded Mg–9Al–1Zn–0.3Mn(AZ91)alloy contains lamellar-structured Mg_(17)Al_(12)discontinuous precipitates along the grain boundaries,which are formed via static precipitation during natural air cooling.The extruded Mg–11Al–1Zn–0.3Mn(AZ111)alloy contains spherical Mg_(17)Al_(12)precipitates at the grain boundaries and inside the grains,which are formed via dynamic precipitation during extrusion.Due to inhomogeneous distribution of precipitates,the AZ111 alloy consists of two different precipitate regions:precipitate-rich region with numerous precipitates and finer grains and precipitate-scarce region with a few precipitates and coarser grains.The AZ111 alloy exhibits a higher tensile strength than the AZ91 alloy because its smaller grain size and more abundant precipitates result in stronger grain-boundary hardening and precipitation hardening effects,respectively.However,the tensile elongation of the AZ111 alloy is lower than that of the AZ91 alloy because the weak cohesion between the dynamic precipitates and the matrix facilitates the crack initiation and propagation.During bending,a macrocrack initiates on the outer surface of bending specimen in both alloys.The AZ111 alloy exhibits higher bending yield strength and lower failure bending strain than the AZ91 alloy.The bending specimens of the AZ91 alloy have similar bending formability,whereas those of the AZ111 alloy exhibit considerable differences in bending formability and crack propagation behavior,depending on the distribution and number density of precipitates in the specimen.In bending specimens of the AZ111 alloy,it is found that the failure bending strain(ε_(f,bending))is inversely proportional to the area fraction of precipitates in the outer zone of bending specimen(A_(ppt)),with a relationship ofε_(f,bending)=–0.1A_(ppt)+5.86.

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.

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.

Fabrication of lightweight 3D interpenetrated NiTi@Mg composite with superior bending properties

A NiTi@Mg interpenetrating phase composite with high strength and lightweight was prepared by additive manufacturing(AM)and infiltration technology,and the interface bonding,three-point bending properties and cyclic compressive properties of NiTi@Mg composites were investigated.The results show that the metallurgically bonded interface is formed at the NiTi/Mg interfaces.The bending strength and compressive strength of the NiTi@Mg composite are 2.5 and 1.7 times higher than those of the NiTi scaffold,respectively.During the bending deformation process,a large number of dislocations are observed to accumulate in the soft Mg area at the interface.Furthermore,the finite element model showed that the stress accumulation area,where the bending crack is initiated,is located at the interface of NiTi and Mg.The strengthening mechanism of NiTi@Mg composites is attributed to the twinning strengthening of Mg and heterogeneous structure strengthening.

Cryogenic springback of 2219-W aluminum alloy sheet through V-shaped bending

A V-shaped bending device was established to evaluate the effects of temperature and bending fillet radius on springback behavior of 2219-W aluminum alloy at cryogenic temperatures.The cryogenic springback mechanism was elucidated through mechanical analyses and numerical simulations.The results indicated that the springback angle at cryogenic temperatures was greater than that at room temperature.The springback angle increased further as the temperature returned to ambient conditions,attributed to the combined effects of the “dual enhancement effect” and thermal expansion.Notably,a critical fillet radius made the springback angle zero for 90° V-shaped bending.The critical fillet radius at cryogenic temperatures was smaller than that at room temperature,owing to the influence of temperature variations on the bending moment ratio between the forward bending section at the fillet and the reverse bending section of the straight arm.

Analysis of deformation mechanisms in magnesium single crystals using a dedicated four-point bending tester

In this study,we explored the deformation mechanisms of Mg single crystals using a combination of scanning electron microscopy and electron backscattered diffraction in conjunction with a dedicated four-point bending tester.We prepared two single-crystal samples,oriented along the<1120>and<1010>directions,to assess the mechanisms of deformation when the initial basal slip was suppressed.In the<1120>sample,the primary{1012}twin(T1)was confirmed along the<1120>direction of the sample on the compression side with an increase in bending stress.In the<1010>sample,T1 and the secondary twin(T2)were confirmed to be along the<1120>direction,with an orientation of±60°with respect to the bending stress direction,and their direction matched with(0001)in T1 and T2.This result implies that crystallographically,the basal slip occurs readily.In addition,the<1010>sample showed the double twin in T1 on the compression side and the tertiary twin along the<1010>direction on the tension side.These results demonstrated that the maximum bending stress and displacement changed significantly under the bend loading because the deformation mechanisms were different for these single crystals.Therefore,the correlation between bending behavior and twin orientation was determined,which would be helpful for optimizing the bending properties of Mg-based materials.

Bending strength degradation of a cantilever plate with surface energy due to partial debonding at the clamped boundary

This paper investigates the bending fracture problem of a micro/nanoscale cantilever thin plate with surface energy,where the clamped boundary is partially debonded along the thickness direction.Some fundamental mechanical equations for the bending problem of micro/nanoscale plates are given by the Kirchhoff theory of thin plates,incorporating the Gurtin-Murdoch surface elasticity theory.For two typical cases of constant bending moment and uniform shear force in the debonded segment,the associated problems are reduced to two mixed boundary value problems.By solving the resulting mixed boundary value problems using the Fourier integral transform,a new type of singular integral equation with two Cauchy kernels is obtained for each case,and the exact solutions in terms of the fundamental functions are determined using the PoincareBertrand formula.Asymptotic elastic fields near the debonded tips including the bending moment,effective shear force,and bulk stress components exhibit the oscillatory singularity.The dependence relations among the singular fields,the material constants,and the plate's thickness are analyzed for partially debonded cantilever micro-plates.If surface energy is neglected,these results reduce the bending fracture of a macroscale partially debonded cantilever plate,which has not been previously reported.

A Light and Simplified Branch Bending Method for Young Pear Trees

Aiming at high cost and low efficiency of conventional branch bending method in the modern intensive planting and labor-saving cultivation mode of young pear trees,this paper provides a new branch bending method with wide source of raw materials,cheap price and simple operation,which is also suitable for the management of low-age branches in the process of high grafting and upgrading of traditional big trees.