On nonlinear thermal buckling analysis of cylindrical shells
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:
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)
- et al.
Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells
Compos. Struct.
(2005) - et al.
Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical-cylindrical shells
Int. J. Solids Struct.
(2006) - et al.
Postbuckling characteristics of angle-ply laminated truncated circular conical shells
Commun. Nonlinear Sci. Numer. Simul.
(2008) - et al.
Postbuckling of angle-ply laminated cylindrical shells with meridional curvature
Thin-Walled Struct.
(2009) - et al.
Non-linear analysis of shells of revolution under arbitrary loads
Comput. Struct.
(2002) - et al.
Postbuckling analysis of elastic shells of revolution considering mode switching and interaction
Int. J. Solids Struct.
(2006) - et al.
Imperfection sensitivity and postbuckling analysis of elastic shells of revolution
Thin-Walled Struct.
(2008) - et al.
Thermal buckling of imperfect functionally graded plates
Int. J. Solids Struct.
(2006) - et al.
Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation
Compos. Struct.
(2011) - et al.
Determination of travel directions in path-following methods
Math. Comput. Model.
(1995)
A fast incremental/iterative solution procedure that handles “snap-through”
Comput. Struct.
Physical interpretation and generalization of Marguerre's shallow shell theory
Int. J. Eng. Sci.
Static and dynamic buckling of large thin shells
Nucl. Eng. Des.
Finite strip analysis of laminated plates with general initial imperfection under end shortening
Eng. Struct.
Cited by (28)
Thermal-mechanical buckling analysis and optimization of the stringer stiffened cylinder using smeared stiffener based reduced-order models
2023, Computers and Mathematics with ApplicationsImperfection sensitivity study of the thermal–mechanical buckling of laminated composite cylinders using a novel reduced-order modeling method
2023, Thin-Walled StructuresCitation Excerpt :Wadee et al. [24] developed analytical expressions based on energy methods to define the elastic stability of steel struts with externally anchored prestressed cables, and pre-buckling and post-buckling equilibrium paths of both the perfect and the imperfect systems were calculated. Various methods, such as analytical methods (Galerkin [6,14], Ritz [8], and perturbation techniques [4,11,16,25]), semi-analytical methods [9] and classical finite element methods [26,27], have been used to study the thermal–mechanical buckling problems of laminated composite cylinders under axial compression. Analytical methods are only applicable for structures with a regular geometry and simple boundary conditions.
On buckling of oil storage tanks under nearby explosions and fire
2022, Above Ground Storage Tank Oil Spills: Applications and Case StudiesCircumferential crack modeling of thin cylindrical shells in modal deformation
2021, European Journal of Mechanics, A/SolidsNonlinear thermoelastic analysis of shell structures: solid-shell modelling and high-performing continuation method
2021, Composite StructuresCitation Excerpt :Additionally, the optimisation of the structural response of laminated plates based on thermal buckling analyses has been investigated in several works [24–27]. Finally, the post-buckling behaviour is considered for composite plates [28], cylinders [29] and Variable Angle Tow (VAT) stiffened plates [30] by using semi-analytical and Ritz methods. If from one side such strategies provide high efficiency within a specific context, on the other hand they are not easily applied to full-scale structures characterised by general geometries.
Analytical study on thermal buckling of cylindrical shells with non-uniform thickness
2021, International Journal of Pressure Vessels and Piping