A Comparative Study on the Post-Buckling Behavior of Reinforced Thermoplastic Pipes(RTPs)Under External Pressure Considering Progressive Failure

The collapse pressure is a key parameter when RTPs are applied in harsh deep-water environments.To investigate the collapse of RTPs,numerical simulations and hydrostatic pressure tests are conducted.For the numerical simulations,the eigenvalue analysis and Riks analysis are combined,in which the Hashin failure criterion and fracture energy stiffness degradation model are used to simulate the progressive failure of composites,and the“infinite”boundary conditions are applied to eliminate the boundary effects.As for the hydrostatic pressure tests,RTP specimens were placed in a hydrostatic chamber after filled with water.It has been observed that the cross-section of the middle part collapses when it reaches the maximum pressure.The collapse pressure obtained from the numerical simulations agrees well with that in the experiment.Meanwhile,the applicability of NASA SP-8007 formula on the collapse pressure prediction was also discussed.It has a relatively greater difference because of the ignorance of the progressive failure of composites.For the parametric study,it is found that RTPs have much higher first-ply-failure pressure when the winding angles are between 50°and 70°.Besides,the effect of debonding and initial ovality,and the contribution of the liner and coating are also discussed.

POST-BUCKLING ANALYSIS AND STRUCTURE OPTIMIZATION OF INTEGRAL FUSELAGE PANEL SUBJECTED TO AXIAL COMPRESSION LOAD

Build-up panels for the commercial aircraft fuselage subjected to the axial compression load are studied by both experimental and theoretical methods.An integral panel is designed with the same overall size and weight as the build-up structure,and finite element models（FEMs）of these two panels are established.Experimental results of build-up panels agree well with the FEM results with the nonliearity and the large deformation,so FEMs are validated.FEM calculation results of these two panels indicate that the failure mode of the integral panel is different from that of the build-up panel,and the failure load increases by 18.4% up to post-buckling.Furthermore,the integral structure is optimized by using the multi-island genetic algorithm and the sequential quadratic programming.Compared with the initial design,the optimal mass is reduced by 8.7% and the strength is unchanged.

Buckling and post-buckling analyses of size-dependent piezoelectric nanoplates

This paper attempts to investigate the buckling and post-buckling behaviors of piezoelectric nanoplate based on the nonlocal Mindlin plate model and yon Karman geometric nonlinearity. An external electric voltage and a uniform temperature rise are applied on the piezoelectric nanoplate. Both the uniaxial and biaxial mechanical compression forces will be considered in the buckling and post-buckling analysis. By substituting the energy functions into the equation of the minimum total potential energy principle, the governing equations are derived directly, and then discretized through the differential quadrature （DQ） method. The buckling and post-buckling responses of piezoelectric nanoplates are calculated by employing a direct iterative method under different boundary conditions. The numerical results are presented to show the influences of different factors including the nonlocal parameter, electric voltage, and temperature rise on the buckling and post-buckling responses.

THERMAL POST-BUCKLING OF AN ELASTIC BEAMS SUBJECTED TO A TRANSVERSELY NON-UNIFORM TEMPERATURE RISING

Based on the nonlinear geometric theory of axially extensible beams and by using the shooting method, the thermal post-buckling responses of an elastic beams,with immovably simply supported ends and subjected to a transversely non-uniformly distributed temperature rising, were investigated. Especially, the influences of the transverse temperature change on the thermal post-buckling deformations were examined and the corresponding characteristic curves were plotted. The numerical results show that the equilibrium paths of the beam are similar to what of an initially deformed beam because of the thermal bending moment produced in the beam by the transverse temperature change.

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.

AN EXPERIMENTAL STUDY ON POST-BUCKLING BEHAVIOR OF SLENDER COLUMN WITH FIBER REINFORCED COMPOSITE MATERIAL

Equilibrium paths of post-buckling are measured for large slenderness column specimens made of the fiber reinforced composite material. The influence of the initial curvature is investigated experimentally and compared with the result of the initial post-buckling theory. Both the theoretical and experimental results reveal that the column with the initial curvature has stable post-buckling behaviors and is not sensitive to the imperfection in the form of initial curvature. The experimental results show that when the lateral buckling displacement is less than 20 percent of the column length, the experimental results agree with the results from the theory of initial post-buckling quite well, while they agree with the results from the large deflection theory in a quite large range.

BUCKLING AND POST-BUCKLING OF PIEZOELECTRIC PLATES USING FINITE ELEMENT METHOD

The finite element equations considering the geometrical nonlinearity of piezoelectric smart structures are derived based on the total Lagrange method under the assumption of weak coupling between electricity and mechanics. Buckling and post-buckling of piezoelectric-plate with various boundary conditions are investigated. The calculated results show that piezoelectric effects and external voltage can hardly affect the buckling and post-bucking characteristics of piezoelectric-plate under uniaxial pressure while the buckling caused by displacement in-plane has much to do with the electric field.

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.

A Simplified Model for Buckling and Post-Buckling Analysis of Cu Nanobeam Under Compression

Both of Buckling and post-buckling are fundamental problems of geometric nonlinearity in solid mechanics.With the rapid development of nanotechnology in recent years,buckling behaviors in nanobeams receive more attention due to its applications in sensors,actuators,transistors,probes,and resonators in nanoelectromechanical systems(NEMS)and biotechnology.In this work,buckling and post-buckling of copper nanobeam under uniaxial compression are investigated with theoretical analysis and atomistic simulations.Different cross sections are explored for the consideration of surface effects.To avoid complicated high order buckling modes,a stressbased simplified model is proposed to analyze the critical strain for buckling,maximum deflection,and nominal failure strain for post-buckling.Surface effects should be considered regarding critical buckling strain and the maximum post-buckling deflection.The critical strain increases with increasing nanobeam cross section,while themaximumdeflection increases with increasing loading strain but stays nearly the same for different cross sections,and the underlying mechanisms are revealed by our model.The maximum deflection is also influenced by surface effects.The nominal failure strains are captured by our simulations,and they are in good agreement with the simplified model.Our results can be used for helping design strain gauge sensors and nanodevices with self-detecting ability.

Analysis of nonlinear stability and post-buckling for Euler-type beam-column structure

Based on the assumption of finite deformation, the Hamilton variational principle is extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation. The corresponding three-dimensional （3D） mathematical model for analyzing the nonlinear mechanical behaviors of structures is established, in which the effects of the rotation inertia and the nonlinearity of material and geometry are considered. As an application, the nonlinear stability and the post-buckling for a linear elastic beam with the equal cross-section located on an elastic foundation are analyzed. One end of the beam is fully fixed, and the other end is partially fixed and subjected to an axial force. A new numerical technique is proposed to calculate the trivial solution, bifurcation points, and bifurcation solutions by the shooting method and the Newton- Raphson iterative method. The first and second bifurcation points and the corresponding bifurcation solutions are calculated successfully. The effects of the foundation resistances and the inertia moments on the bifurcation points are considered.

VARIATIONAL PRINCIPLES OF PERFORATED THIN PLATES AND FINITE ELEMENT METHOD FOR BUCKLING AND POST-BUCKLING ANALYSIS

On the basis of the general theory of perforated thin plates under large deflections, variational principles with deflection w and stress function F as variables are stated in detail.Based on these princi- ples,finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated,owing to the multiple connexity of the region.

BUCKLING AND POST-BUCKLING OF ANNULAR PLATES UNDER NON-AXISYMMETRIC PLANE EDGE FORCES

On the basis of both the general theory[1,2]and the finite element method[4]of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are studied.

Closed Solution for Initial Post-Buckling Behavior Analysis of a Composite Beam with Shear Deformation Effect

This paper is focused on the post-buckling behavior of the fixed laminated composite beams with effects of axial compression force and the shear deformation.The analytical solutions are established for the original control equations(that is not simplified)by applying the Maclaurin series expansion,Chebyshev polynomials,the harmonic balance method and the Newton’s method.The validity of the present method is verified via comparing the analytical approximate solutions with the numerical ones which are obtained by the shooting method.The present third analytical approximate solutions can give excellent agreement with the numerical solutions for a wide range of the deformation amplitudes.What’s more,the effect of shear deformation on the post-bucking configuration of the sandwich beam is also proposed.It can be found that the shear angle has a great influence on the post-buckling load of composite beams.Therefore,the model simplifying the shear formation term as small quantity is not accurate for the case of sandwich beam with soft core.

BUCKLING AND POST-BUCKLING OF ANNULAR PLATES ON AN ELASTIC FOUNDATION

On the basis of von Karnmnequations, the axisymmetric buckling and post-buckling of annular plates on anelastic foundation is so wematically discussed byusing shooting

POST-BUCKLING AND IMPERFECTION SENSITIVITY OF A COLUMN WITH AN EQUILATERAL TRIANGULAR CROSS-SECTION IN THE PLASTIC RANGE

The asymmetric initial post-buckling corresponding to the lowest bifurcation load and the imperfection sensitivity are analysed in detail for a compressed simply supported column with an equilateral triangular cross-section in the plastic range. The effect of elastic unloading is taken into ao count in the analysis. The asymptotic relations, including high order terms, among the load, the amplitude of imperfection and the amplitude of the bifurcation mode ark realized. The results show that the maximum supported load is very sensitive to imperfection.

An Analysis of the Post-buckling of Laminated Plates of Symmetric Cross-Ply

In this paper, general equations relating to the stability of laminated plates ofsymmetric cross-ply with initial imperfection factors are derived by using thevariational principle. Taking the deflection as the perturbation parameter, theequilibrium path of the post-buckling path of a simply supported rectangular plate isinvestigated with the perturbation method. An approximation expression and a typicalnumerical example are presented to manifest the post-buekling behavior of therectangular plate.

Experimental and numerical studies on buckling and post-buckling behavior of T-stiffened variable stiffness panels

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.

Nonlinear Bifurcation and Post-buckling Analysis of Cylindrical Composite Stiffened Laminates Based on Weak Form Quadrature Element Method

This paper presents a weak form quadrature element formulation in the analysis of nonlinear bifurcation and post-buckling of cylindrical composite stiffened laminates subjected to transverse loads.A total Lagrangian updating scheme is used in combination with arc-length method,and the branch-switching method is adopted to identify the whole post-buckling procedure of the laminates.The formulation of the shell model and beam model are based on the basic concept of Ahmad.The coincidence of discrete nodes and integration points in quadrature element endows it with compactness and conciseness in the nonlinear buckling analysis of the cylindrical stiffened laminates.Several numerical examples are firstly presented to verify the effectiveness and accuracy of present formulation.Parametric studies on the effects of the height-to-breadth ratio,lamination schemes,positions,distribution,number of the stiffeners on the bifurcation and post-buckling behavior are performed.

POST-BUCKLING BEHAVIOR OF A DOUBLE-HINGED ROD UNDER SELF-WEIGHT

Post-buckling phenomena of slender rods have attracted great attention for both theoretical and engineering aspects. In this study, we explored the post-buckling behavior of a slender rod with two hinged ends under its self-weight. We first established the potential energy functional of the system, and then derived the governing differential equations according to the principle of least potential energy. We further addressed the physical meaning of the Lagrange multiplier by analyzing the force equilibrium. A computer code of shooting method was developed by using the commercial software MathCAD, which has proved efficient in computing the post- buckling configurations of the rod. We finally discussed the buckling of an oil sucker rod adopting our numerical results, which will be beneficial to the engineering design.

Submarine Pipeline Lateral Global Buckling and Buckling Failure Critical State Discussion

Due to high temperature and pressure,unburied or shallow buried submarine pipelines experience lateral global buckling. Excessive bending caused by uncontrolled deformation may threaten the safety of the pipeline system. Thus,the integer of a post-buckling pipeline section should be assessed under design temperature and pressure differences. This study focuses on the post-buckling pipeline safety assessment.First,a series of model tests based on sand obtained from Bohai Gulf were proposed,and soil resistance to pipelines with different embedment are measured. A dynamic soil resistance model with varying pipeline embedment and lateral displacement was established. The influence of embedment on peak soil resistance and residual soil resistance was analyzed. Second,the critical buckling forces of pipelines with different imperfections were analyzed. A"critical force range"was proposed to evaluate whether the pipeline exhibits lateral global buckling or not. Third,the limit state of a post-buckling pipeline in an engineering case was assessed. The assessment was proposed based on both load control condition and displacement control condition. Further comparisons show that pipelines reach their limit state according to load control condition far more quickly than according to displacement control condition.