Narrow Results

This paper primarily refers to the nonlinear instability of functionally graded porous (FGP) egg-shaped subsea pipelines mixed with graphene platelets (GPLs) under pressure and thermal environments. The FGP-GPLs egg-shaped subsea pipeline deflects radially inward since the pipeline is confined tightly and rigidly by the medium (soils/rocks). This deflection may be represented by a refined available displacement formula. The response curves are effectively traced by associating the computational calculus and the thin-walled shell theory. Furthermore, numerical verifications are completed to validate the analytical schemes. It is seen that the numerical curves are closely fitted to the theoretical ones. Moreover, the current study is validated efficiently by other results. Finally, evaluations are conducted on some parameters that affect the instability of the FGP-GPLs subsea pipeline with an egg-shaped profile, including the porosity coefficient, geometric shapes, weight fraction, temperature variations, etc.

In order to study the buckling failure of lining delamination of thin-walled lined composite pipe, a numerical analysis model was established by using bilinear cohesion relationship, the buckling mode and critical load of the composite pipe obtained by linear buckling are taken as reference values, the interlayer initial defects were introduced to carry out the nonlinear buckling analysis on the composite pipe lining structure with thin wall lining. The relative displacement curve and deformation morphology of the relative displacement of the lining with the change of external pressure were obtained, and the results are consistent with the existing test results. Based on this model, the buckling sensitivity of lining pipe was analyzed. The results show that the size of interlayer initial defect is the main factor that affects the critical buckling pressure of liner, but it has little influence on the propagation pressure after buckling; However, the increase of interlayer bonding effect significantly improves the buckling resistance and propagation pressure of lining pipe; The ratio of outer tube wall diameter to thickness and liner thickness have significant effects on the critical buckling pressure of liner. The research results provide a reference for determining the interlayer bonding effect and the optimal design of the minimum thickness of the inner liner.

This paper addresses the nonlinear buckling and post-buckling behavior of an extensible marine elastica pipe conveying fluid. The mathematical model employed in the nonlinear buckling analysis is developed based on the extensible elastica theory and the large strain formulation, so that the high extensibility of the pipe due to large axial strains is tackled thoroughly. The boundary value problem of the model is solved by the shooting method, and the numerical elastica solutions are obtained. For stability examination, the method of adjacent nonlinear equilibrium is exploited. It is revealed that the fundamental mode of nonlinear buckling of the pipe is reached when the pipe experiences either the critical top tension or the critical weight. Postbuckling behavior of the pipe is recognized to be unstable. The investigation is extended to studying various parameters that impinge on the limit states of the pipe. These parameters are the dimensionless quantities that relate to density of pipe material, densities of external and internal fluids, applied top tension, Poisson's ratio, slenderness ratio, vessel offset, seawater depth, current-drag coefficients, current velocity, and internal flow velocity.

This paper presents a numerical technique to determine the full pre-buckling and post-buckling equilibrium path for elastic funicular arches. The formulation includes the effects of shear deformations and geometric nonlinearity due to large deformations. The Timoshenko beam hypothesis is adopted for incorporating shear. Finite strains are considered without approximation. The finite strains are defined in terms of the normal and shear component of the longitudinal stretch. The constitutive relations for the internal actions are based on a hyperelastic constitutive model. Using the differential equilibrium equations and the constitutive laws, the nonlinear buckling behavior of some typical funicular arches are investigated using the trapezoid method with Richardson extrapolation enhancement. The results are validated by using the finite element package ANSYS and solutions available in the literature. Examples include parabolic arches under a uniformly distributed gravity load, a catenary under a distributed load along the arch and a catenary arch under an overburden load. Parametric studies are performed to identify the factors that influence the nonlinear buckling of funicular arches. The axial to shear rigidity ratio is shown to have a significant effect on the buckling load and the buckling mode shape.

Nonlinear buckling analysis for honeycomb auxetic-core sandwich toroidal shell segments with CNT-reinforced face sheets surrounded by elastic foundations under the radial pressure is presented in this study. The basic equation system of shells is established based on the von Kármán–Donnell nonlinear shell theory, combined with Stein and McElman approximation. Meanwhile, the foundation-shell elastic interaction is simulated by the foundation model based on the Pasternak assumption. The Galerkin procedure is utilized to achieve the pre-buckling and post-buckling responses for the shell, from which the radially critical buckling load is determined. Numerical analysis shows the various influences of auxetic-core layer, CNT-reinforced face sheets, and elastic foundation on the pre-buckling and postbuckling behavior of sandwich shells with CNT reinforced face sheets.

Buckling analysis of steel structures can be performed using either linear (LBA) or nonlinear buckling analysis (NLBA). Each method is only effective in particular conditions and improper use might lead to inaccurate predictions. Despite the extensive use of these two methods, there is a lack of research on the accuracy of each method and their limitations regarding the range of application. In this paper, these two methods are evaluated and compared for steel plate girders with a wide range of geometry and the limitations of each method are presented. The numerical modeling of steel plate girders is developed using Abaqus software. The numerical models are verified with the existing experimental results in the literature. An extensive parametric study is conducted using 123 models to investigate the effect of web height, web thickness and beam length on the results. The buckling loads predicted from the numerical models using different analysis methods are compared with those determined based on the AISC 360-16 and EN 1993-1-5 formulations and recommendations are made. Results indicate that while the nonlinear buckling analysis provides accurate predictions of buckling load and mode shape of steel beams, the linear buckling analysis is accurate only for the case of elastic buckling mode without tension field action. A new formulation is proposed to modify the LBA results in order to obtain the advantages of both analysis methods. In addition, based on the NLBA results, a much simple yet accurate equation is proposed to predict the buckling load using plate geometry and material properties instead of the complicated code equations. The accuracy of the proposed equation in comparison with the code equations is also demonstrated for 500 plate girders selected with random geometry.

A new analytical approach to investigate the nonlinear buckling and postbuckling of the sandwich functionally graded circular cylindrical shells reinforced by ring and stringer or spiral stiffeners subjected to external pressure is presented in this paper. By employing the Donnell shell theory, the geometrical nonlinearity in Von Kármán sense and developed Lekhnitskii’s smeared stiffener technique, the governing equations of sandwich functionally graded circular cylindrical shells are derived. Resulting equations are solved by applying the Galerkin method to obtain the explicit expression of critical buckling external pressure load and postbuckling load–deflection curve. Effects of spiral stiffeners, thermal environment, external pressure, and geometrical parameters on nonlinear buckling behavior of sandwich functionally graded circular cylindrical shells are shown in numerical results.

This paper deals with the nonlinear large deflection torsional buckling of functionally graded carbon nanotube (CNT) orthogonally reinforced composite cylindrical shells surrounded by Pasternak’s elastic foundations with the thermal effect. The shell is made by two layers where the polymeric matrix is reinforced by the CNTs in longitudinal and circumferential directions for outer and inner layers, respectively. The stability equation system is obtained by combining the Donnell’s shell theory, von Kármán nonlinearity terms, the circumferential condition in average sense and three-state solution form of deflection. The critical torsional buckling load, postbuckling load-deflection and the load-end shortening expressions are obtained by applying the Galerkin procedure. The effects of temperature change, foundation parameters, geometrical properties and CNT distribution law on the nonlinear behavior of cylindrical shell are numerically predicted. Especially, the effect of orthogonal reinforcement in comparison with longitudinal and circumferential reinforcement on the torsional buckling behavior of shells is observed.

The main purpose of this paper is to analyze the nonlinear post-buckling behavior of three-layer porous sandwich cylindrical shells with shape memory alloy (SMA) wires reinforced outer layers under the mechanical loads. Considering the large deformations, the governing differential equations were extracted and then, using the Ritz energy method and considering the Airy function, the analytical expression for the critical stress of the system was extracted. Three types of porosity distributions were considered in the shell core and the mechanical properties of SMA-reinforced layers were determined using the law of mixtures. After validating the results, the effect of various parameters such as porosity distribution, volume fraction of SMA wires and geometric characteristics on nonlinear buckling loads and post-buckling behavior of these structures has been investigated. According to the results, it can be seen that the difference in critical buckling stress for three different porosity distribution types is significant, which reveals the need to determine the optimal porosity distribution for composite shells reinforced with SMA wires. The results show that the SMA wires increase the equivalent stiffness of the structure and their presence has a significant effect on improving the critical axial stress of the shells. According to the results, for the use of 1% volume fraction of SMA wires, the axial stress of sandwich shells can be increased up to about 51%. Therefore, the use of SMA wires is a good method to increase the load-bearing capacity of this type of structures.

A novel analytical approach for nonlinear thermo-mechanical buckling of higher-order shear deformable porous circular plates and spherical caps with functionally graded material (FGM) face sheets resting on Pasternak elastic foundation is presented in this paper. The circular plates and spherical caps are assumed to be subjected to uniformly distributed external pressure and/or uniformly distributed thermal loads, and the nonlinear higher-order shear deformation theory (HSDT) is used for largely thick plates and caps with the shell-foundation interaction modeled by Pasternak elastic foundation. The caps are assumed to be shallow with clamped boundary conditions. The total potential energy expression of structures is established and the Ritz energy method is used to solve the problem directly from the total potential energy expression. The expressions between external pressure–deflection, thermal load–deflection, and thermo-mechanical combined load–defection can be obtained using the iterative algorithms. The critical buckling loads and postbuckling behavior of plates/caps are investigated numerically. Significant effects of foundation, porosity, structure parameters on the nonlinear thermo-mechanical responses of circular plates and spherical caps are numerically investigated and discussed, and the complex tendencies of postbuckling strength of plates and caps are obtained.

Nonlinear buckling and postbuckling of orthogonal carbon nanotube-reinforced composite (Orthogonal CNTRC) cylindrical shells subjected to axial compression in thermal environments surrounded by elastic foundation are presented in this paper. Two layers of shell are reinforced by carbon nanotube (CNT) in two orthogonal directions (longitudinal and circumferential directions). Based on Donnell’s shell theory with von Karman’s nonlinearity and the Galerkin method, the governing equations are established to obtain the critical buckling loads and postbuckling load-deflection curves. The large effects of CNT volume fraction, temperature change, elastic foundation and geometrical parameters of cylindrical shells on the buckling load and postbuckling behavior of Orthogonal CNTRC cylindrical shells are obtained.