Elsevier

Thin-Walled Structures

Volume 95, October 2015, Pages 170-182
Thin-Walled Structures

On nonlinear thermal buckling analysis of cylindrical shells

https://doi.org/10.1016/j.tws.2015.06.013Get rights and content

Highlights

  • A nonlinear semi-analytical finite element method according to continuum-based approach is developed for cylindrical shells under thermal buckling.

  • The several applied comparisons between two approaches ‘continuum-based approach and classical approach’ survey their results.

  • A method is proposed to implement the initial geometric imperfection of the cylinder by transformation of structure due to deformation gradients.

  • The nonlinear buckling paths are not very sensitive to the length of cylindrical shells however; these buckling paths are greatly affected by the radius of them.

Abstract

In this article, the nonlinear buckling behavior of imperfect cylinders made of isotropic, composite and functionally graded materials is studied. A continuum-based semi-analytical finite element formulation is introduced to study the nonlinear behavior of cylinders under thermal loads. A method is proposed to implement the initial geometric imperfection of the cylinder by transformation of structure due to deformation gradients. The influences of geometrical parameters, different materials and imperfection factors are investigated on pre- and post-buckling paths. A comparison is made between the classical von Kármán-based and continuum-based approaches to ensure the validation of the results and to study the applicability of the von-Kármán approximation.

Introduction

There are a broad range of problems within practical and engineering applications possessing nonlinear nature. Theoretical analysis of such problems demands adopting reliable numerical methods. The finite element method (FEM), which commonly is used to tackle complex engineering problems, is recognized as one of the most capable numerical methods in the literature [1], [2], [3], [4], [5]. Under certain circumstance such a versatile numerical method may be combined with analytical methods to enhance both accuracy and efficiency of the underlying numerical investigation. Patel et al. [6], [7], [8], [9], [10] employed the semi-analytical finite element formulation to investigate nonlinear buckling of laminated composite shells under mechanical and thermal loadings. Hong and Teng [11] presented a semi-analytical finite element formulation for the nonlinear analysis of shells. They studied the post-buckling response of shells by the semi-analytical formulation [12]. They also used the semi-analytical formulation for determining the imperfection sensitivity effect on the buckling load and post-buckling path of thin shells [13]. In series studies [14], [15], [16], [17], [18], Eslami et al. discussed the buckling of beams, plates and shells made of composites and functionally graded materials (FGMs). They investigated the critical buckling point and pre- and post-buckling paths of a variety of structures and materials under thermal and mechanical loads.

Most of the previous studies have employed the classical von Kármán-type approximation to investigate the nonlinear buckling of cylinders. In this paper, a new semi-analytical finite element formulation is presented to describe the nonlinear thermal buckling behavior of cylindrical shells made of different materials utilizing a continuum-based approach. This discussion accounts the effects of geometrical parameters, imperfection and material properties to determine bifurcation point and pre- and post-buckling paths. The applicability of von-Kármán approximation is also explored.

Section snippets

Semi-analytical finite element

The semi-analytical finite element method can be acknowledged as a reliable alternative to the full FEM where the buckling behavior of cylindrical shells is studied. In this paper, the first order shear deformation theory (FSDT) and the Fourier series are employed to avoid meshing in the radial and circumferential directions, respectively. So, the buckling behavior can be predicted using such a one dimensional (1D) finite element formulation by meshing the cylinder in the axial direction. The

Results and discussion

Two introduced approaches are utilized to predict the pre- and post-buckling behaviors of isotropic, composite and FG imperfect cylindrical shells. The boundary conditions are clamped-clamped (C–C) as immovable at two ends:u00=u0ci=u0si=v00=v0ci=v0si=w00=w0ci=w0si=βs0=βsci=βssi=βθ0=βθci=βθsi=0

The material properties of cylinder are explained in Table 1.

In Table 1, the material properties with subscripts L, T are associated with composite material properties in the longitudinal and transverse

Conclusion

A continuum-based approach, including the fully nonlinear kinematic and equilibrium equations, was introduced in which the geometric imperfection of cylinder was modeled by transformation of structure due to deformation gradients. This approach was employed to determine the nonlinear thermal buckling behavior of imperfect cylindrical shells. The classical approach based on the von-Kármán shell theory was also adopted to verify the results of the continuum-based approach for various materials

References (28)

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