On the plastic buckling of curved carbon nanotubes

This research,for the first time,predicts theoretically static stability response of a curved carbon nanotube(CCNT)under an elastoplastic behavior with several boundary conditions.The CCNT is exposed to axial compressive loads.The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy.The elastoplastic stress-strain is concerned with Ramberg–Osgood law on the basis of deformation and flow theories of plasticity.To seize the nano-mechanical behavior of the CCNT,the nonlocal strain gradient elasticity theory is taken into account.The obtained differential equations are solved using the Rayleigh–Ritz method based on a new admissible shape function which is able to analyze stability problems.To authorize the solution,some comparisons are illustrated which show a very good agreement with the published works.Conclusively,the best findings confirm that a plastic analysis is crucial in predicting the mechanical strength of CCNTs.

EXPERIMENTAL STUDIES ON DYNAMIC PLASTIC BUCKLING OF CIRCULAR CYLINDRICAL SHELLS UNDER AXIAL IMPACT

In the present paper, experimental studies on dynamic plasticbuckling of circular cylindrical shells under axial impact are carried out. Hopkinson bar and drop hammer apparatus are used for dynamic loading. Three groups of circular cylindrical shells made of copper are tested under axial impact. From the experiments, the first critical velocity corresponding to the axi-symmetric buckling mode and the second critical velocity corresponding to the non-axisymmetric buckling mode are determined. The present results come close to those of second critical velocity given by Wang Ren[4–6]. Two different kinds of non-axisymmetric buckling modes oval-shaped and triangle shaped are founded. The buckling modes under two loading cases, viz. with small mass but high velocity and with large mass and low velocity using Hopkinson bar and drop hammer, are different. Their critical energies are also discussed.

The Influence of Residual Stress on Plastic Buckling of Cylindrical Shells

-This paper adopts approximate formulas for residual stresses caused by cold bending for plates with stress-strain curve form a = K n. A typical distribution of the longitudinal residual stress due to welding is also assumed. The effects of residual stress due to cold bending and welding on plastic buckling of axially compressed cylindrical shells are studied by the finite element method.

Plastic Buckling of Stiffened Torispherical Shell

This paper uses the nonlinear prebuckling consisten theory to analyse the plasticbuckling problem of of stiffned torispherical shell under uniform exlernal pressure. Thebuckling equation and energy expressions of the shell are built. the calculation formulais presented Numerical examples show that method in ths paper has betterprecision and the calculating process is very simple.

PLASTIC BUCKLING OF STIFFENED TORISPHERICAL SHELL

This paper uses the nonlinear prebuckling consisten theory to analyse the plaslicbuckling problem of stiffened torispherical shell under uniform external pressure. Thebuckling equation and energr expressions of the shell are built, the calculalion formulais presented. Numerical examples show that the method in this paper has betterprecision and the calculating process is very simple.

New formula for predicting the plastic buckling pressure of steel torispherical heads under internal pressure

Thin-walled torispherical heads under internal pressure can fail by plastic buckling because of compressive circumferential stresses in the head knuckle.However,existing formulas still have limitations,such as complicated expressions and low accuracy,in determining buckling pressure.In this paper,we propose a new formula for calculating the buckling pressure of torispherical heads based on elastic-plastic analysis and experimental results.First,a finite element(FE)method based on the arc-length method is established to calculate the plastic buckling pressure of torispherical heads,considering the effects of material strain hardening and geometrical nonlinearity.The buckling pressure results calculated by the FE method in this paper have good consistency with those of BOSOR5,which is a program for calculating the elastic-plastic bifurcation buckling pressure based on the finite difference energy method.Second,the effects of geometric parameters,material parameters,and restraint form of head edge on buckling pressure are investigated.Third,a new formula for calculating plastic buckling pressure is developed by fitting the curve of FE results and introducing a reduction factor determined from experimental data.Finally,based on the experimental results,we compare the predictions of the new formula with those of existing formulas.It is shown that the new formula has a higher accuracy than the existing ones.

ON THE POST-BUCKLING ANALYSIS OF PLASTIC STRUCTURES UNDER IMPULSIVE LOADING

An analytical method is suggested to analyze the plastic post-buckling behavior under impulsive loading. The fundamental equation of motion of a cylindrical shell is taken as an example to explain the main concept and procedure. The axial and the radial displacements are decoupled by an approximate scheme, so that only one non-linear equation for the radial buckling displacement is to be solved. By expanding it in terms of an amplitude measure as a time variable, we may get the post-buckling behavior in the form of a series solution. The post-buckling behavior of a rectangular plate used as a special case of cylindrical shell is discussed.

THE IMPACT TORSIONAL BUCKLING FOR THE RIGID PLASTIC CYLINDRICAL SHELL

By using the energy criterion in [3], the impact torsional buckling for the rigid plastic cylindrical shell is studied. The linear dynamic torsional buckling equations for the rigid plastic shell is drived, and the critical impact velocity is given.

THREE-DIMENSIONAL AXISYMMETRIC FLOW IN PERFECTLY PLASTIC METALS

A method is presented for solving the three-dimensional axisymmet- ric field equations for a perfectly plastic material which obeys the von-Mises yield criterion and the Levy-Mises flow law. The method is used for the particular case in which a small axisymmetric perturbed flow is superposed on a uniform flow without flow reversal taking place. The method then leads to solving a fourth order differen- tial equation for the velocity potential. The special case of a thick cylindrical shell under compressive flow is examined. The solution so obtained, being derived from the three dimensional theory, includes a correct treatment of transverse shear distor- tion. A preferred mode of instability is identified having a wave-length in reasonable agreement with that obtained experimentally by other workers.

Experimental and Numerical Research on Deformation Behavior of Thin-Walled and Large Expansion Ratio Guide Vane Liner in Hydroforming Process

Some tube hydroforming process tests and further research work were conducted to manufacture hollow guide vane liners( made of super alloy GH3030).The relative thickness( t0/ OD) of the tubular blank is approximately 0. 01,and the maximum expansion ratio( Dmax/ OD) of the needed part is more than 40%,and the length to diameter ratio of the expansion regionis more than 3. 0. It is very hard to manufacture this kind of ultra-thin-wall,curved axis and large expansion ratio tubular part without fracture and wrinkles. The success of the process is highly dependent on useful wrinkles with appropriate internal pressure and axial feeding. A simplified finite element model and a theoretical model are used for detecting the deformation behavior and forming laws. Further study results demonstrate that the useful wrinkles do not appear at the same time and middle-wrinkles need bigger axial force than tube-end-wrinkles and feeding-wrinkles. The wrinkles can transfer bigger axial force after its wave peak has come into contact with the die inner surface. The thickness thinning rate of the element at the peak is bigger than that at the trough. With the increase of the axial and hoop stress ratio,the critical buckling stress also increases. Microstructure examination results show that the grain size in the maximum thinning zone has been stretched and refined after the large deformation and annealing treatment.The process is feasible and the finished part is qualified.

Mechanical properties of lattice grid composites

An equivalent continuum method only considering the stretching deformation of struts was used to study the in-plane stiffness and strength of planar lattice grid com- posite materials. The initial yield equations of lattices were deduced. Initial yield surfaces were depicted separately in different 3D and 2D stress spaces. The failure envelope is a polyhedron in 3D spaces and a polygon in 2D spaces. Each plane or line of the failure envelope is corresponding to the yield or buckling of a typical bar row. For lattices with more than three bar rows, subsequent yield of the other bar row after initial yield made the lattice achieve greater limit strength. The importance of the buckling strength of the grids was strengthened while the grids were relative sparse. The integration model of the method was used to study the nonlinear mechanical properties of strain hardening grids. It was shown that the integration equation could accurately model the complete stress-strain curves of the grids within small deformations.