Thermoelastic stability analysis of imperfect functionally graded cylindrical shells

Postbuckling behavior of a 3D braided composite cylindrical panel under axial compression is investigated. The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on Reddy's higher order shear deformation shell theory with a von Kármán-Donnell type of kinematic nonlinearity and including thermal effects. A boundary layer theory of shell buckling is utilized to study postbuckling of panels. The results reveal that the temperature changes, the fiber volume fraction, in-plane boundary conditions, as well as initial geometric imperfections have a significant effect on the buckling and postbuckling behavior of braided composite cylindrical panels.

This paper presents an analytical approach to postbuckling behaviors of functionally graded multilayer nanocomposite plates reinforced by a low content of graphene platelets (GPLs) using the first order shear deformation theory, stress function and von Karman-type nonlinear kinematics and include the effect of an initial geometric imperfection. The weight fraction of GPL nano fillers is assumed to be constant in each individual GPL-reinforced composite (GPLRC). The modified Halpin-Tsai micromechanics model that takes into account the GPL geometry effect is adopted to estimate the effective Young’s modulus of GPLRC layers. The plate is assumed to resting on Pasternak foundation model and subjected to mechanical and thermal loads. The results show the influences of the GPL distribution pattern, weight fraction, geometry, elastic foundations, mechanical and temperature loads on the postbuckling behaviors of FG multilayer GPLRC plates.
 Keywords: Postbuckling; Graphene nanocomposite plate; First order shear deformation plate theory.
 References
 [1] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A. Firsov, Electric filed effect in atomically thin carbon films, Science 306 (2004) 666–669. http://doi.org/ 10.1126/science.1102896.[2] K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Two-dimensional atomic crystals, Proceedings of the National Academy of Sciences of the United States of America 102 (2005) 10451–10453. https://doi.org/10.1073/pnas.0502848102.[3] C.D. Reddy, S. Rajendran, K.M. Liew, Equilibrium configuration and continuum elastic properties of finite sized graphene, Nanotechnology 17 (2006) 864-870. https://doi. org/10.1088/0957-4484/17/3/042.[4] C. Lee, X.D. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (2008) 385–388. http://doi.org/10.1126/ science.1157996.[5] F. Scarpa, S. Adhikari, A.S. Phani, Effective elastic mechanical properties of single layer graphene sheets, Nanotechnology 20 (2009) 065709. https://doi.org/10.1088/0957-4484/20/6/ 065709.[6] Y.X. Xu, W.J. Hong, H. Bai, C. Li, G.Q. Shi, Strong and ductile poly(vinylalcohol)/graphene oxide composite films with a layered structure, Carbon 47 (2009) 3538–3543. https://doi.org/ 10.1016/j.carbon.2009.08.022.[7] J.R. Potts, D.R. Dreyer, C.W. Bielawski, R.S. Ruoff, Graphene-based polymer nanocomposites, Polymer 52 (2011) 5-25. https://doi.org/10.1016/j .polymer.2010.11.042.[8] T.K. Das, S. Prusty, Graphene-based polymer composites and their applications, Polymer-Plastics Technology and Engineering 52 (2013) 319-331. https://doi.org/10.1080/03602559.2012. 751410.[9] M. Song, J. Yang, S. Kitipornchai, W. Zhud, Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates, International Journal of Mechanical Sciences 131–132 (2017) 345–355. https://doi.org/10.1016/j.ijmecsci.2017.07.017.[10] H.S. Shen, Y. Xiang, F. Lin, D. Hui, Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments, Composites Part B 119 (2017) 67-78. https://doi.org/10.1016/j.compositesb.2017. 03.020.[11] H. Wu, S. Kitipornchai, J. Yang, Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates, Materials and Design 132 (2017) 430–441. https://doi.org/10. 1016/j.matdes.2017.07.025.[12] J. Yang, H. Wu, S. Kitipornchai, Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams, Composite Structures 161 (2017) 111–118. https://doi.org/10.1016/j.compstruct.2016.11.048.[13] H.S. Shen, Y. Xiang, Y. Fan, Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical panels under axial compression in thermal environments, International Journal of Mechanical Sciences 135 (2018) 398–409. https://doi.org/10.1016/j.ijme csci.2017.11.031.[14] M.D. Rasool, B. Kamran, Stability analysis of multifunctional smart sandwich plates with graphene nanocomposite and porous layers, International Journal of Mechanical Sciences 167 (2019) 105283. https://doi.org/10.1016/j.ijmecs ci.2019.105283.[15] J.J. Mao, W. Zhang, Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces, Composite Structures 216 (2019) 392–405. https://doi.org/10.1016/j. compstruct.2019.02.095.[16] P.H. Cong, N.D. Duc, New approach to investigate nonlinear dynamic response and vibration of functionally graded multilayer graphene nanocomposite plate on viscoelastic Pasternak medium in thermal environment, Acta Mechanica 229 (2018) 651-3670. https://doi.org/ 10.1007/s00707-018-2178-3.[17] N.D. Duc, N.D. Lam, T.Q. Quan, P.M. Quang, N.V. Quyen, Nonlinear post-buckling and vibration of 2D penta-graphene composite plates, Acta Mechanica (2019), https://doi.org/10. 1007/s00707-019-02546-0.[18] N.D. Duc, P.T. Lam, N.V. Quyen, V.D. Quang, Nonlinear Dynamic Response and Vibration of 2D Penta-graphene Composite Plates Resting on Elastic Foundation in Thermal Environments, VNU Journal of Science: Mathematics-Physics 35(3) (2019) 13-29. https:// doi.org/10.25073/2588-1124/vnumap. 4371.[19] J.N. Reddy, Mechanics of laminated composite plates and shells; theory and analysis, Boca Raton: CRC Press, 2004.[20] H.S. Shen, A two-step perturbation method in nonlinear analysis of beams, plates and shells, John Wiley & Sons Inc., 2013.

Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments

In this paper, the nonlinear post-buckling analysis of imperfect two-dimensional quasicrystal cylindrical shells is performed. The nonlinear governing equations are established by considering initial geometric imperfection, higher-order shear deformation theory and phonon-phason fields coupling effect. The load-shortening curves and buckling modes are obtained by the Galerkin’s method. Numerical results are compared with the existing results and excellent agreements are obtained. Effects of geometrical parameters, initial imperfection and phonon-phason fields coupling effect on the critical load and imperfection sensitivity of two-dimensional quasicrystal cylindrical shells are discussed in detail.

Concrete-filled steel tubes subjected to axial compression: Life-cycle based performance

Stability analysis of a cylindrical shell with axially symmetric defects under axial compression based on the reduction stiffness method

Experimental and numerical investigations on buckling behaviours of axially compressed cylindrical–conical–cylindrical shells at elevated temperature

This paper presents the comparison of reliability technique that employ Fourier series representations of random axisymmetric imperfections in axially compressed cylindrical shells with evaluations prescribed by ASME Section VIII, Division 2. The ultimate goal of the reliability type technique is to predict the buckling load associated with the axially compressed cylindrical shell. The representation of initial geometrical imperfections in the cylindrical shell requires the determination of appropriate Fourier coefficients. The buckling of cylindrical shells in any type of loading is sensitive to the form and amplitude of geometric imperfections present in the structure. Initial geometric imperfections have significant effect on the load carrying capacity of axisymmetrical cylindrical shells. Many deterministic and probabilistic techniques are there to predict shell behavior during buckling. Fourier decomposition is used to interpret imperfections as structural features can be easily related to the different components of imperfections. The mean vector and the variance-covariance matrix of Fourier coefficients are calculated from the simulated shell profiles. Recommendations for further use of Fourier coefficients through simulation by Monte Carlo Method are laid down. Large number of shells thus created can be used to calculate buckling stress for each shell. The probability of the ultimate buckling stress exceeding a predefined threshold stress can be calculated.

ABSTRACTSteel products which have various characteristic (e.g. high ductility, high yield stress, low yield stress and high weldability) are used as main structures by diversification of demanded application, and technology for steel manufacturing has developed. Because steel square tubular member is processed by cold‐forming and welding in the process of manufacturing, residual stress will exist in the products. Moreover, due to the cold‐forming process, geometrical initial imperfection, i.e., global and local, will exist. These initial imperfection are still remained even so the technology for steel manufacturing is developed. However, effect of the initial imperfection on elasto‐plastic behaviour of square hollow section columns under compressive axial force with bending moment is not clarified. In this paper, firstly, the effect of individual initial imperfection (e.g. initial global imperfection, initial local imperfection or residual stress) on elasto‐plastic performance is investigated independently; comparison between the experimental results are shown. It is shown that initial local imperfection has a significant impact on elasto‐plastic performance. Secondly, the effect of composite initial imperfections is investigated. The amplitude of the local imperfection is the most influential initial imperfection on the deformation capacity of the column, and the deformation capacity decreased with an increase of the amplitude of local imperfection. Validation of the numerical simulation were also performed and recommend values of imperfections are shown.

This paper presents an analytical approach to analyze the nonlinear stability of thin closed circular cylindrical shells under axial compression with material properties varying smoothly along the thickness in the power and exponential distribution laws. Equilibrium and compatibility equations are obtained by using Donnel shell theory taking into account the geometrical nonlinearity in von Karman and initial geometrical imperfection. Equations to find the critical load and the load-deflection curve are established by Galerkin's method. Effects of buckling modes, of imperfection, of dimensional parameters and of volume fraction indexes to buckling loads and postbuckling load-deflection curves of cylindrical shells are investigated. In case of perfect cylindrical shell, the present results coincide with the ones of the paper [13] which were solved by Ritz energy method.

Thin-walled cylindrical shells are key load-carrying components for aerospace structures. Axial compression is the most common load for cylindrical shells; however, critical buckling loads obtained experimentally are significantly lower than the theoretical values, owing to the presence of initial geometric imperfections (GIs). Previous studies often determined only the knockdown factor through the statistics of experimental data; it is an approximate lower limit of the load-carrying capacity and cannot accurately predict the buckling mode in real time. In this paper, an image-driven framework for the intelligent prediction of buckling load and mode based on measured GIs is proposed. First, through measured samples and the random field method, the GI data pool is obtained. Subsequently, two convolutional neural network (CNN) models are trained to predict the buckling load and mode for cylindrical shells, respectively. The active learning strategy is adopted to discern beneficial sample sets and enhance the prediction accuracy and training speed of the CNN models. A numerical example demonstrates that the proposed framework can effectively predict the buckling behavior of cylindrical shells with GIs. Furthermore, using the proposed prediction framework, it was observed that a common feature of unfavorable GIs is a large fluctuation in magnitude along the axial direction.

The initial geometric imperfection is recognized as substantially influential on the buckling behaviour and ultimate strength of stiffened plated structures. Conventionally, the initial geometric imperfection is defined in a deterministic manner, such as a hungry-horse mode, ARE mode or critical buckling mode with characteristic magnitudes. However, due to the uncertainty in manufacturing and in-service effects, the initial geometric imperfection should be better described as a random field. This paper aims to assess the effects of the stochastic nature of geometric imperfection on the ultimate strength of stiffened panel in compression. A probabilistically-based imperfection model developed by spectral representation method is applied to an orthogonally stiffened panel. A Monte-Carlo Simulation enhanced by a Latin-Hypercube Scheme (LHS) is utilized to sample the initial geometric imperfection. A series of nonlinear finite element analyses are completed to calculate the ultimate compressive strength of the case study model. With reference to the deterministic representations, the impact of the stochastic imperfection model is discussed. The present work may provide useful insights for the reliability-based ship structural assessment regarding the uncertainty due to geometric imperfection.

Effect of stiffeners on nonlinear buckling of cylindrical shells with functionally graded coatings under torsional load

The effect of non-uniformity of axial loading on the buckling behaviour of shells with random imperfections

Loading conditions constrained wrinkling behaviors of thin-walled sheet/tube parts during metal forming