Dynamic Buckling of Elasto-Plastic Cylindrical Shells Under Axial Fluid-Solid Impact Load

The dynamic buckling of elasto-plastic cylindrical shells under axial fluid-solid impact is investigated theoretically. A simplified liquid- gas- structure model is given to approximately imitate the problem. The basic equation of the structure is derived from a minimum principle in dynamics of elasto-plastic continua at finite deformation, and the flow theory of plasticity is employed. The liquid is incompressible and the gas is compressed adiabatically. A number of numerical results are presented and the characteristics of the buckling behavior under fluid-solid impact are illustrated.

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory （MCST）, and the nonlocal elasticity theories using the differential quadrature method （DQM） is presented. Main advantages of the MCST over the classical theory （CT） are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Karman assumption, the governing equations of equilibrium for the micro-classical plate consid- ering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen＇s nonlocal parameter, the material length scale parameter, Young＇s modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen＇s nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young＇s modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G12/E2 and vice versa for E1/E2. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.

Dynamic buckling mechanism of pillar rockbursts induced by stress waves

Rockbursts are sudden and violent rock failures that can lead to huge production and equipment losses,injury or death of mining workers.Buckling has been regarded as one of the key mechanisms of rockbursts,which are often induced by dynamic loads from mining excavations,such as drilling and blasting in underground mining.The paper attempts to investigate the dynamic buckling mechanism of pillar rockbursts in underground mining,by considering rockbursts as a dynamic stability problem of underground rock structures.The results include:(1)A new explanation of the“sudden and violent”phenomenon of rockbursts,characterized by exponential growth of the amplitudes of transverse displacement responses,even in the presence of rock damping;(2)Identification of the critical role in inducing rockbursts of dynamic loads that bear frequencies approximately double the natural pillar frequency;(3)The greater influence on rockburst occurrence of the amplitude of dynamic component relative to the static component of loads;and(4)Quantification of the relative effects of stress waveform of dynamic loads on pillar rockbursts,which are in decreasing order if other parameters remain constant:rectangular,sinusoidal,and exponential waveforms.Application examples are provided and limitations of the approach are discussed.This research is motivated by the on-going and ubiquitous occurrence of rockbursts in underground excavations all around the world.In contrast to conventional methods that use rock specimens or rock materials to study rockbursts,this investigation emphasizes the structural effects on rockbursts,which has potential applications in hard rock mining engineering.

Measurement of length-scale and solution of cantilever beam in couple stress elasto-plasticity

Owing to the absence of proper analytical solution of cantilever beams for couple stress/strain gradient elasto-plastic theory, experimental studies of the cantilever beam in the micro-scale are not suitable for the determination of material length-scale. Based on the couple stress elasto-plasticity, an analytical solution of thin cantilever beams is firstly presented, and the solution can be regarded as an extension of the elastic and rigid-plastic solutions of pure bending beam. A comparison with numerical results shows that the current analytical solution is reliable for the case of σ0 〈〈 H 〈〈 E, where σ0 is the initial yield strength, H is the hardening modulus and E is the elastic modulus. Fortunately, the above mentioned condition can be satisfied for many metal materials, and thus the solution can be used to determine the material length-scale of micro-structures in conjunction with the experiment of cantilever beams in the micro-scale.

High-Order Lateral Buckling Analysis of Submarine Pipeline Under Thermal Stress

It is of importance to study and predict the possible buckling of submarine pipeline under thermal stress in pipeline design.Since soil resistance is not strong enough to restrain the large deformation of pipeline,high-order buckling modes occur very easily.Analytical solutions to high-order buckling modes were obtained in this paper.The relationships between buckling temperature and the amplitude or the wavelength of buckling modes were established.Analytical solutions were obtained to predict the occurrence and consequence of in-service buckling of a heated pipeline in an oil field.The effects of temperature difference and properties of subsoil on buckling modes were investigated.The results show that buckling will occur once temperature difference exceeds safe temperature;high-order pipeline buckling occurs very easily;the larger the friction coefficients are,the safer the submarine pipeline will be.

Buckling of un—stiffened cylindrical shell under non—uniform axial compressive stress

This paper provides a review of recent research advances and trends in the area of stability of unstiffened circular cylindrical shells subjected to general non-uniform axial compressive stresses.Only the more important and interesting aspects of the research,judged from a personal viewpoint,are discussed.They can be crudely classified into four categories:(1) shells subjected to non-uniform loads;(2) shells on discrete supports;(3) shells with intended cutouts/holes;and (4) shells with non-uniform settlements.

A STUDY ON THE EFFECT OF RADIAL INERTIA ON THE ELASTO-PLASTIC COMBINED STRESS WAVE PROPAGATION IN THIN-WALLED TUBES

An in-depth analysis of propagation characteristics ofelasto-plastic combined stress waves in circular thin-walled tubeshas been made. In obtaining the simple-wave solution, however, mostresearches have ignored the influence of the circumferential stressrelated to the radial inertial ef- fect in the tubes. In this paperthe incremental elasto-plastic constitutive relations which areconve- nient for dynamic numerical analysis are adopted, and thefinite-difference method is used to study the evolution adpropagation of elasto-plastic combined stress waves in a thin-walledtube with the radial inertial effect of the tube considered. Thecalculation results are compared with those obtained when the radialinertial effect is not considered. The calculation results show thatthe radial inertial effect of a tube has a fairly great influence onthe propagation of elasto-plastic combined stress waves.

Analytic Solution of Elasto-Plastic Stress in Infinite Slope under Uniform Load

According to the Mohr-Coulomb yield criterion, the stress field of the infinite slope is derived under a vertical uniform load q on the top of the slope. It is indicated that elastic and elasto-plastic states would occur in the slope. When q is smaller than the critical load, q(p), the slope is in the elastic state. If q equals q(p), the slope is in the critical state, and the plastic deformation would occur along the critical angle. With the increase of q, the plastic zone would extend, and the slope is in the elasto-plastic State. If q equals limit load, the slope is in the limit equilibrium state. The slope may be divided into three zones. Some charts of the critical angle, the critical and limit load coefficients are presented in this paper.

Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite (CNTRC) face sheets

In this paper,the stresses and buckling behaviors of a thick-walled mi-cro sandwich panel with a flexible foam core and carbon nanotube reinforced composite(CNTRC)face sheets are considered based on the high-order shear deformation theory(HSDT)and the modified couple stress theory(MCST).The governing equations of equi-librium are obtained based on the total potential energy principle.The effects of various parameters such as the aspect ratio,elastic foundation,temperature changes,and volume fraction of the canbon nanotubes(CNTs)on the critical buckling loads,normal stress,shear stress,and deflection of the thick-walled micro cylindrical sandwich panel consider-ing different distributions of CNTs are examined.The results are compared and validated with other studies,and showing an excellent compatibility.CNTs have become very use-ful and common candidates in sandwich structures,and they have been extensively used in many applications including nanotechnology,aerospace,and micro-structures.This paper also extends further applications of reinforced sandwich panels by providing the modified equations and formulae.

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.

THE DYNAMIC BUCKLING PROBLEM CAUSED BY PROPAGATION OF STRESS WAVE IN ELASTIC CYLINDRICAL SHELLS UNDER IMPACT TORQUE

The buckling problem of cylindrical shells has been studied by many mechanic researchers from different points of view. In this paper,an elastic cylindrical shell with semi-infinite length is studied Let its dynamic buckling under impact torque be reduced to a bifurcation problem caused by propagation of foe torsional stress wave. The bifurcation problem is converted to a solution of nonlinear equations,the lateral inertia effect on the dynamic buckling is also discussed.Finally, numerical computation is carried out,from this,some beneficial conclusions are obtained.

Elasto-Plastic FEM Analysis of Residual Stress in Spun Tube

The residual stress distribution of Hastelloy C corrosion-resistant alloy tubes after power spinning was simulated with the elasto-plastic finite element method combining with the element birth and death technique, the influences of spinning parameters on the distribution of the residual stress were investigated in detail, and the formation mechanism of residual stress during tube spinning was discussed. Based on the calculation of the residual stress, the reasons for annealing cracks on the spun tube during interpass heat treatment were explored. The simulation results and the characteristics of annealing cracks show that the circumferential residual tensile stress is a main factor to cause the annealing cracks.

DESIGN OPTIMIZATION FOR TRUSS STRUCTURES UNDER ELASTO-PLASTIC LOADING CONDITION

In this paper, a method for the design optimization of elasto-plastic truss structures is proposed based on parametric variational principles （PVPs）. The optimization aims to find the minimum weight/volume solution under the constraints of allowable node displacements. The design optimization is a formulation of mathematical programming with equilibrium constraints （MPECs）. To overcome the numerical difficulties of the complementary constraints in optimization, an iteration process, comprising a quadratic programming （QP） and an updating process, is employed as the optimization method. Furthermore, the elasto-plastic buckling of truss mem- bers is considered as a constraint in design optimization. A combinational optimization strategy is proposed for the displacement constraints and the buckling constraint, which comprises the method mentioned above and an optimal criterion. Three numerical examples are presented to show the validity of the methods proposed.

THE DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN SUBJECTED TO AXIAL IMPACT BY A RIGID BODY

The dynamic buckling of an elastic-plastic column subjected to axial impact by a rigid body has been discussed in this paper. The whole traveling process of elastic-plastic waves under impact action is analyzed with the characteristics method. The regularity of stress changes in both column ends and the first separating time of a rigid body and column are obtained. By using the energy principle and taking into account the propagation and reflection of stress waves the lateral disturbance equation is derived and the power series solution is given. In addition, the critical buckling condition can be obtained from the stability analysis of the solution. By numerical computation and analysis, the relationship among critical velocity and impact mass, hardening modulus, and buckling time is given.

Dynamic Buckling of Laminated Composite Bars Subjected to Axial Impact

The impact buckling of a laminated composite bar is investigated in case of one of its ends moving due to axial impact compression. The governing equations considering the first- order shear deformation effect are derived by the Hamilton principle and solved by the finite difference method. The critical axial shortness is determined by the B - R cirterion. The given example is used to highlight the influences of initial imperfection, impact velocity, stress wave and coupled stiffness. It is found that the unsymmetrically laminated bar has a quite different dynamic buckling behaviour from that of the symmetrically laminated bar.

Finite element analysis on thermal upheaval buckling of submarine burial pipelines with initial imperfection

In-service hydrocarbons must be transported at high temperature and high pressure to ease the flow and prevent the solidification of the wax fraction. The pipeline containing hot oil will expand longitudinally due to the rise in temperature. If such expansion is resisted, for example by frictional effects over a kilometer or so of pipeline, compressive axial stress will be built up in the pipe-wall. The compressive forces are often so large that they induce vertical buckling of buffed pipelines, which can jeopardize the structural integrity of the pipeline. A typical initial imperfection named continuous support mode of submarine pipeline was studied. Based on this type of initial imperfection, the analytical solution of vertical thermal buckling was introduced and an elastic-plasticity finite element analysis （FEA） was developed. Both the analytical and the finite element methodology were applied to analyze a practice in Bohai Gulf, China. The analyzing results show that upheaval buckling is most likely to build up from the initial imperfection of the pipeline and the buckling temperature depends on the amplitude of initial imperfection. With the same amplitude of initial imperfection, the triggering temperature difference of upheaval buckling increases with covered depth of the pipeline, the soil strength and the friction between the pipeline and subsoil.

Local buckling failure analysis of high-strength pipelines

Pipelines in geological disaster regions typically suffer the risk of local buckling failure because of slender structure and complex load. This paper is meant to reveal the local buckling behavior of buried pipelines with a large diameter and high strength, which are under different conditions, including pure bending and bending combined with internal pressure. Finite element analysis was built according to previous data to study local buckling behavior of pressurized and unpressurized pipes under bending conditions and their differences in local buckling failure modes. In parametric analysis, a series of parameters,including pipe geometrical dimension, pipe material properties and internal pressure, were selected to study their influences on the critical bending moment, critical compressive stress and critical compressive strain of pipes.Especially the hardening exponent of pipe material was introduced to the parameter analysis by using the Ramberg–Osgood constitutive model. Results showed that geometrical dimensions, material and internal pressure can exert similar effects on the critical bending moment and critical compressive stress, which have different, even reverse effects on the critical compressive strain. Based on these analyses, more accurate design models of critical bending moment and critical compressive stress have been proposed for high-strength pipelines under bendingconditions, which provide theoretical methods for highstrength pipeline engineering.

AN EXPERIMENTAL INVESTIGATION OF THE DYNAMIC AXIAL BUCKLING OF CYLINDRICAL SHELLS USING A KOLSKY BAR

Several experiments were performed with a Kolsky Bar(Split Hop- kinson Pressure Bar)device to investigate the dynamic axial buckling of cylindrical shells.The Kolsky Bar is a loading as well as a measuring device which can subject the shells to a fairly good square pulse.An attempt is made to understand the in- teraction between the stress wave and the dynamic buckling of cylindrical shells.It is suggested that the dynamic axial buckling of the shells,elastic or elasto-plastic,is mainly due to the compressive wave rather than the flexural or bending wave.The experimental results seem to support the two critical velocity theory for plastic buck- ling,with V_c1 corresponding to an axisymmetric buckling mode and V_c2 corresponding to a non-svmmetric buckling mode.

Engineering measures for preventing upheaval buckling of buried submarine pipelines

In-service hydrocarbons must be transported at high temperature and high pressure to ease the flow and to prevent the solidification of the wax fraction. The high temperature and high pressure will induce the additional stress in the pipeline, which results in the upheaval buckling of the pipeline. If such expansion is resisted, e.g., by the frictional effects of the foundation soil over a kilometer or of a pipeline, the compressive axial stress will be set up in the pipe-wall. When the stress exceeds the constraint of the foundation soil on the pipeline, suddenly-deforming will occur to release the internal stress, similar to the sudden deformation of the strut due to stability problems. The upheaval buckling may jeopardize the structural integrity of the pipeline. Therefore, effective engineering measures against this phenomenon play an important role in the submarine pipeline design. In terms of the pipeline installation and protection measures commonly used in Bohai Gulf, three engineering measures are investigated in great details. An analytical method is introduced and developed to consider the protection effect of the anti-upheaval buckling of the pipeline. The analysis results show that the amplitude of the initial imperfection has a great effect on the pipeline thermal upheaval buckling. Both trenching and burial and discrete dumping are effective techniques in preventing the pipeline from buckling. The initial imperfection and operation conditions of the pipelines determine the covered depth and the number of layers of the protection measures.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.