Hybrid layerwise-differential quadrature transient dynamic analysis of functionally graded axisymmetric cylindrical shells subjected to dynamic pressure

Abstract

In this paper, two computationally efficient and accurate solution methods for transient dynamic analysis of functionally graded (FG) cylindrical shells subjected to internal dynamic pressure are presented. In order to accurately account for the thickness effects, the layerwise theory is employed to approximate the displacement components in the radial direction. In the first solution method, differential quadrature method (DQM) is implemented to discretize the resulting equations in the both spatial and time domains. In the second approach, DQM is applied to discretize equations in the axial direction while Newmark’s time integration scheme is used to solve the problem in the time domain. The fast convergence rate of the methods is demonstrated and their accuracy is verified by comparing the results with those obtained using ANSYS and also with available exact solution of a particular problem. Considerable less computational efforts of the proposed approaches with respect to the finite element method is observed. Furthermore, comparative studies are performed between two approaches in different cases and it is found that the two techniques give very close results. The effects of geometrical parameters and boundary conditions on the transient behavior of shells are also investigated.

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.