Torsional postbuckling characteristics of functionally graded graphene enhanced laminated truncated conical shell with temperature dependent material properties

Buckling and postbuckling characteristics of laminated graphene-enhanced composite(GEC)truncated conical shells exposed to torsion under temperature conditions using finite element method(FEM)simulation are presented in this study.In the thickness direction,the GEC layers of the conical shell are ordered in a piece-wise arrangement of functionally graded(FG)distribution,with each layer containing a variable volume fraction for graphene reinforcement.To calculate the properties of temperaturedependent material of GEC layers,the extended Halpin-Tsai micromechanical framework is used.The FEM model is verified via comparing the current results obtained with the theoretical estimates for homogeneous,laminated cylindrical,and conical shells,the FEM model is validated.The computational results show that a piece-wise FG graphene volume fraction distribution can improve the torque of critical buckling and torsional postbuckling strength.Also,the geometric parameters have a critical impact on the stability of the conical shell.However,a temperature rise can reduce the crucial torsional buckling torque as well as the GEC laminated truncated conical shell’s postbuckling strength.

BUCKLING AND POSTBUCKLING OF LAMINATED THIN CYLINDRICAL SHELLS UNDER HYGROTHERMAL ENVIRONMENTS

The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro_to_macro_mechanical analytical model. The material properties of the composite are affected by the variation of temperature and moisture, and are based on a micromechanical model of a laminate. The governing equations are based on the classical laminated shell theory, and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account. A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments, and a singular perturbation technique was employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross_ply laminated cylindrical shells under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, fiber volume fraction, shell geometric parameter, total number of plies, stacking sequences and initial geometric imperfections are studied.

ANALYSIS ON BUCKLING AND POSTBUCKLING OF DELAMINATION IN 3D COMPOSITES

In this paper, the problem of axisymmetric buckling and postbuckling of a circular thin-film delamination bridged by through-thickness fiber tows in 3D composites is presented. An iterativeprocedure based on Taylor’s series expansion is used to generate a family of nondimensionalized post-buckling solutions of the above problem by yon Karman’s nonlinear plate theory. Attention is fo-cused, herein, on the effects of the bridge force of through-thickness fibers on the buckling and post-buckling behavior of the delamination. It is found that fiber bridge not only increases the ability of re-sisting delamination buckling and postbuckling, but also brings on the jump of the delamination deflec-tion mode during the postbuckling phase. Consequently the behavior of the composite structure with de-lamination is greatly improved, such as increasing the residual strength and prolonging the service life.

Postbuckling analysis of functionally graded graphene platelet-reinforced polymer composite cylindrical shells using an analytical solution approach

An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von K′arm′an nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.

Mechanical and thermal postbuckling of FGM thick circular cylindrical shells reinforced by FGM stiffener system using higher-order shear deformation theory

The postbuckling of the eccentrically stiffened circular cylindrical shells made of functionally graded materials(FGMs),subjected to the axial compressive load and external uniform pressure and filled inside by the elastic foundations in the thermal environments,is investigated with an analytical method.The shells are reinforced by FGM stringers and rings.The thermal elements of the shells and stiffeners in the fundamental equations are considered.The equilibrium and nonlinear stability equations in terms of the displacement components for the stiffened shells are derived with the third-order shear deformation theory and Leckhniskii smeared stiffener technique.The closed-form expressions for determining the buckling load and postbuckling load-deflection curves are obtained with the Galerkin method.The effects of the stiffeners,the foundations,the material and dimensional parameters,and the pre-existent axial compressive and thermal load are considered.

Deep postbuckling and nonlinear bending behaviors of nanobeams with nonlocal and strain gradient effects

In this paper, multi-scale modeling for nanobeams with large deflection is conducted in the framework of the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with exact bending curvature. The proposed size-dependent nonlinear beam model incorporates structure-foundation interaction along with two small scale parameters which describe the stiffness-softening and stiffness-hardening size effects of nanomaterials, respectively. By applying Hamilton's principle, the motion equation and the associated boundary condition are derived. A two-step perturbation method is introduced to handle the deep postbuckling and nonlinear bending problems of nanobeams analytically. Afterwards, the influence of geometrical, material, and elastic foundation parameters on the nonlinear mechanical behaviors of nanobeams is discussed. Numerical results show that the stability and precision of the perturbation solutions can be guaranteed, and the two types of size effects become increasingly important as the slenderness ratio increases. Moreover, the in-plane conditions and the high-order nonlinear terms appearing in the bending curvature expression play an important role in the nonlinear behaviors of nanobeams as the maximum deflection increases.

Analytical solution approach for nonlinear buckling and postbuckling analysis of cylindrical nanoshells based on surface elasticity theory

The size-dependent nonlinear buckling and postbuckling characteristics of circular cylindrical nanoshells subjected to the axial compressive load are investigated with an analytical approach. The surface energy effects are taken into account according to the surface elasticity theory of Gurtin and Murdoch. The developed geometrically nonlinear shell model is based on the classical Donnell shell theory and the von K′arm′an's hypothesis. With the numerical results, the effect of the surface stress on the nonlinear buckling and postbuckling behaviors of nanoshells made of Si and Al is studied. Moreover, the influence of the surface residual tension and the radius-to-thickness ratio is illustrated.The results indicate that the surface stress has an important effect on prebuckling and postbuckling characteristics of nanoshells with small sizes.

POSTBUCKLING RESPONSE OF CANTILEVER BEAMS OF NON-LINEAR ELASTIC MATERIAL SUBJECTED TO SUBTANGENTIAL FOLLOWER FORCES

This paper deals with the problem of the postbuckling response of a thin cantilever beam ofnon-linear material, subjected to subtangential follower forces. Based on the well-knownBernoulli-Euler bending moment-curvature relation, the proposed problem is reduced to a specialeigenvalue problem of non-linear differential equation. An approximate solution is achieved byusing a simple and very effective technique, which leads to reliable results even in the case of verylarge deflections. The initial postbuckling path depending on the subtangential follower forces inequilibrium is then obtained. Moreover, the individual and coupling effect of the subtangential fol-lower force, the material non-linearity and the beam slenderness ratio on the initial postbucklingpath are also discussed in detail.

POSTBUCKLING OF IMPERFECT STIFFENED CYLINDRICAL SHELLS UNDER COMBINED EXTERNAL PRESSURE AND HEATING

A postbuckling analysis is presented for a stiffened cylindrical shell of finitelength subjected to combined loading of external pressure and uniform temperaturerise. The formulations are based on a boundary layer theory of shell buckling, whichincludes the effects of nonliear prebuckling deformations, nonlinear large deflectonsin the postbuckling range and initial geometrical imperfections of the shell. The"smeared sitffener" approach is adopted for the sitffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbucklingequilibruium paths. Numerical examples cover the performances of perfect and imperfect, stringer and ring stiffened cylindrical shells. Typical resuts are presented in dimensionless graphical form.

APPLICATION OF THE MODIFIED ITERATION METHOD TO NONLINEAR POSTBUCKLING ANALYSIS OF THIN CIRCULAR PLATES

In this paper,the modified iteration method is further generalized to the study ofaxisymmetrical postbuckling of thin circular plates and hereby a new approximate analyticsolution of the problem is obtained.Further utilizations of this method to postbucklinganalyses of plates of more complicated structure are expected.

KRMN-TYPE EQUATIONS FOR A HIGHER-ORDER SHEARDEFORMATION PLATE THEORY AND ITS USE IN THE THERMAL POSTBUCKLING ANALYSIS

篕arman-type nonlinear large deflection equations are derived occnrding to theReddy’s higher-order shear deformation plate theory and used in the thermal postbuckling analysis The effects of initial geometric imperfections of the plate areincluded in the present study which also includes th thermal effects.Simply supported,symmetric cross-ply laminated plates subjected to uniform or nomuniform parabolictemperature distribution are considered. The analysis uses a mixed GalerkinGolerkinperlurbation technique to determine thermal buckling louds and postbucklingequilibrium paths.The effects played by transverse shear deformation plate aspeclraio, total number of plies thermal load ratio and initial geometric imperfections arealso studied.

Postbuckling Analysis for Offshore Pipelines with Residual Stresses

Based on the finite displacement theory of elastic shells, the postbuckling behaviour of submarine pipelines with residual stresses is investigated by using a new finite element formula. The corresponding complementary energy functional is first constructed, and then a geometrical stiffness matrix suitable for the postbuckling of a cylindrical shell is derived. In this matrix the effects of initial stresses and harmonic coupling terms have been considered. The formulation presented in this paper can be used to solve a significant class of problems in the analysis of elastic shells.

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION(III)──LARGE DEFLECTION AND POSTBUCKLING OF SHALLOW SHELLS

篒n this paper, exact solutions of large deflection of multilayer sandwich shallow shellsunder transverse forces and different boundary conditions are presented. Exact results ofpostbuckling of multilayer sandwich plates, shallow cylindrical shells and nonlineardeflection of general shallow shells such as spherical shells under inplane edge forcesare also obtained by the same procedure.

BUCKLING AND POSTBUCKLING OF STIFFENED CYLINDRICAL SHELLS UNDER AXIAL COMPRESSION

Buckling and postbuckling behaviors of perfect and imperfect,stringer andorthotropically stiffened cylindrical shells have been studied under axial compression.Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref.[1],a theoretical analysis is presented.The effects of material properties of stiffeners andskin,which are made of different materials,on the buckling load and postbuckling behaviorof stiffened cylindrical shells have also been discussed.

ELASTO-PLASTIC ANALYSIS FOR THE BUCKLING AND POSTBUCKLING OF RECTANGULAR PLATES UNDER UNIAXIAL COMPRESSION

Full-range analysis for the buckling and postbuckling of rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as itsperturbation parameter.In this paper the effects of initial geometric imperfection on the postbuckling behaviorof plates have been discussed.It is seen that the effect of initial imperfection on the inelasticpostbuckling of plates is sensitive.By comparison,it is found that the theoretical results ofthis paper are in good agreement with experiments.

BUCKLING AND POSTBUCKLING BEHAVIOR OF ANTISYMMETRICALLY ANGLE-PLY LAMINATED COMPOSITE PLATES

The buckling and postbuckling behaviors of perfect and imperfect antisymmetricallyangle-ply laminated composite plates under uniaxial compression have been studied byperturbation technique which takes deflection as its perturbation parameter.In this paper,the effects of in-plane boundary conditions,angles,total number oflayers and initial geometric imperfection on the postbuckling behavior of laminated plateshave been discussed.

ULTIMATE STRENGTH OF POSTBUCKLING FORSIMPLY SUPPORTED RECTANGULAR COMPOSITE THIN PLATES UNDER COMPRESSION

It is proved that the ultimate strength of postbuckling for simply supported rectangular composite thin plates under compression is far higher than their buckling stress through the tests of 283 rectangular composite thin laminates in this paper. The ultimate strength of the composite thin plates is studied using large-deflection theory and small-deflection theory of thin plates. According to the failure criterion of the composites ultimate strength is found finally. It is in accordance with the experimental values,for the plates having 45 degrees off-axial, and for longitudinal and latitudinal plates. when β< 0.11, the theoretical values are higher. The coefficientC given in this paper may be referred to in product designing.

AN ITERATION ALGORITHM FOR SOLVING POSTBUCKLING EQUILIBRIUM PATH OF SIMPLY-SUPPORTED RECTANGULAR PLATES UNDER BIAXIAL COMPRESSION

In this paper,on the basis of von Kárman large deflection equations and itsdouble trigonometric series solution,we present a simple,fast and effective iterationalgorithm for solving simply-supported rectangular plate subjected to biaxial compression.

ELASTO-PLASTIC DYNAMIC BUCKLING AND POSTBUCKLING OF SQUARE PLATES UNDER SOLID-FLUID SLAMMING

The elasto-plastic dynamic buckling and postbuckling phenomena ofsquare plates subjected to in-plane solid-fluid slamming are investigated.According tothe plate’s response,the critical criteria for dynamic buckling,dynamic plasticity andplasti(?)collapse are defined,and the corresponding critical impulses are presented.Meanwhile,dynamic buckling modes and collapse models are observed.The effects ofdifferent boundary conditions and loading histories on the properties of buckling andpostbuckling are discussed.

POSTBUCKLING BEHAViOR OF RECTANGULAR MODERATELY THICK PLATES AND SANDWICH PLATES

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