Hybrid layerwise-differential quadrature transient dynamic analysis of functionally graded axisymmetric cylindrical shells subjected to dynamic pressure
Highlights
► Dynamic analysis of FG cylindrical shells subjected to internal dynamic pressure. ► In first method, DQM is used to discretize equations in both spatial and time domains. ► In second approach, Newmark′s time integration scheme is implemented in time domain. ► Considerable less computational efforts of approaches compared to finite element method.
Introduction
Functionally gradient structures are a new class of composites that have a continuous and smooth variation of material properties from one surface to the other. Despite the fact that anisotropic laminated composites often suffer from stress concentrations near material and geometric discontinuities, the gradation in material properties of FG structures reduces thermal and residual stresses [1]. Most of functionally graded materials (FGMs) are made of ceramic and metal. Ceramic material provides a high temperature resistance due to its low thermal conductivity, and metal constituent largely improves load-bearing capacity. Recently, FG shells are widely used in many engineering applications such as aerospace, marine and automobile structures which are mostly subjected to vibration and dynamic loadings. Hence, it is of a great importance to understand the dynamic behavior of FG shells for the design of aforementioned structures.
Over the past decade, research on FG shells focused mainly on static deformation and vibrational response of these structures. However, due to their evident key role in practical applications, the study on dynamic behavior of FG cylindrical shells has recently attracted the attention of many researchers [2]. Awaji and Sivakuman [3] studied thermo-mechanical behavior of a FG hollow circular cylinder subjected to mechanical loads and linearly increasing temperature. Sofiyev and Schnack [4] investigated the stability of cylindrical thin FG shells under torsional loading varied as a linear function of time. Wang et al. [5] investigated transient temperature and associated thermal stresses in FGMs using finite element/finite difference (FE/FD) methods. Zhu et al. [6] developed a three-dimensional (3D) theoretical model for analyzing the dynamic stability behavior of FG piezoelectric circular cylindrical shells subjected to a combined loading of periodic axial compression and electric field in the radial direction. Bahtui and Eslami [7] studied coupled thermoelastic response of a FG cylindrical shell under thermal shock load using higher-order shear deformation theory. Santos et al. [8], presented a semi-analytical finite element model for functionally graded cylindrical shells subjected to transient thermal shock loading, by using the three-dimensional linear elasticity theory.
Guo and Noda [9] studied the thermal stresses of a thin FG cylindrical shell due to a thermal shock. Peng and Li [10], considered transient response of temperature and thermal stresses in a FG hollow cylinder. Hosseini and Shahabian [11] and Shahabian and Hosseini [12], investigated reliability and safety evaluation of dynamic stresses for FG thick hollow cylinder subjected to sudden unloading due to mechanical shock loading.
Due to the complexity encounters in dynamic analysis of FG shells, exact solution is not available. Thus, a precised theory is needed to fully account the dynamic response compared to the 3D elasticity theory. It was also observed that when the shell structure becomes thicker, the tendency of thickness vibration becomes more important [13]. Displacement-based layerwise theories assume a separate displacement field within each subdivision. Therefore, layerwise theory improves the displacement field compared to equivalent single-layer theories. Besides, the computational cost is reduced with respect to 3D elasticity theory. For FGMs, Tahani and Mirzababaee [14] used a layerwise theory to analytically predict displacements and stresses in FG composite plates in cylindrical bending subjected to thermomechanical loadings.
Besides the precision, the computation cost is another critical parameter in modeling. Differential quadrature (DQ) is a numerical technique that is used since 1988. Bert and Malik [15], [16] presented a review of the early developments in DQM. Malekzadeh and his co-workers [17], [18], [19], [20], [21] demonstrated that using DQM for solving the governing equations for different mechanical problems leads to highly accurate results with less computations.
To the best of authors’ knowledge, there is no published paper on the analysis of FG shells by using the mixed layerwise DQM. In this paper, the transient dynamic behavior of FGM hollow cylindrical shells subjected to internal dynamic loading is investigated by DQM. The layerwise theory is used to improve the displacement field and, therefore, also strains and stresses with minimum computational cost. Both DQM and Newmark’s time integration scheme are comparatively employed to solve the developed DQM discretized governing equations in the time domain. The accuracy, convergence and versatility of the algorithm are proved via different examples for both thin and thick shells. Also, the effects of geometrical parameters and different boundary conditions are demonstrated.
Section snippets
Mathematical modeling
Consider a FG hollow circular cylindrical shell with varying material properties in the thickness direction. The thickness, length, inner radius and outer radius of the shell are denoted by h, l, rin and rout respectively, as shown in Fig. 1. A cylindrical coordinate system (r, θ, z) is used to label the material point of the shell referring to the radial, circumferential and axial directions and u, v and w denote the corresponding displacement components.
Numerical results
In this section, numerical results are presented for the transient dynamic response of FG circular cylindrical shells under internal or external dynamic pressure. Two solution methods are used: (1) DQM for both spatial coordinates and time domain (LWDQ) and (2) spatial DQ discretized form of the equations and Newmark’s time integration scheme in the time domain (LWDQN).
As a first step, the correctness and accuracy of the present method are demonstrated. Due to lack of solutions similar to the
Conclusions
A layerwise-differential quadrature method is developed for transient dynamic response of functionally graded cylindrical shells subjected to dynamic pressure. Both DQM and Newmark’s integration scheme are separately employed to discretize the DQ governing equations of motion in the time domain. It is found that both the approaches present a fast rate of convergence and yield accurate results when compared with the solutions of ANSYS software. In comparison with the finite element simulations
References (21)
- et al.
Recent research advances on the dynamic analysis of composite shells: 2000–2009
Compos Struct
(2010) - et al.
The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading
Eng Struct
(2004) - et al.
Thermal shock resistance of functionally graded materials
Acta Mater
(2004) - et al.
Dynamic stability of functionally graded piezoelectric circular cylindrical shells
Mater Lett
(2005) - et al.
Coupled thermoelasticity of functionally graded cylindrical shells
Mech Res Commun
(2007) - et al.
A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials under thermal shock
Compos Struct
(2008) - et al.
Reliability of stress field in Al–Al2O3 functionally graded thick hollow cylinder subjected to sudden unloading, considering uncertain mechanical properties
Mater Des
(2010) - et al.
Stochastic dynamic analysis of a functionally graded thick hollow cylinder with uncertain material properties subjected to shock loading
Mater Des
(2010) - et al.
Free-vibration analysis of thin/thick laminated structures by layer-wise shell models
Comput Struct
(2000) - et al.
Non-linear analysis of functionally graded plates in cylindrical bending under thermomechanical loadings based on a layerwise theory
Eur J Mech A/Solids
(2009)
Cited by (41)
Analytical and numerical analysis of functionally graded (FGM) axisymmetric cylinders under thermo-mechanical loadings
2022, Materials Today CommunicationsLarge displacement transient analysis of FGM super-elliptic shells using GDQ method
2019, Thin-Walled Structures