Free vibration analysis and design optimization of SMA/Graphite/Epoxy composite shells in thermal environments

Composite shells, which are being widely used in engineering applications, are often under thermal loads. Thermal loads usually bring thermal stresses in the structure which can significantly affect its static and dynamic behaviors. One of the possible solutions for this matter is embedding Shape Memory Alloy (SMA) wires into the structure. In the present study, thermal buckling and free vibration of laminated composite cylindrical shells reinforced by SMA wires are analyzed. Brinson model is implemented to predict the thermo-mechanical behavior of SMA wires. The natural frequencies and buckling temperatures of the structure are obtained by employing Generalized Differential Quadrature (GDQ) method. GDQ is a powerful numerical approach which can solve partial differential equations. A comparative study is carried out to show the accuracy and efficiency of the applied numerical method for both free vibration and buckling analysis of composite shells in thermal environment. A parametric study is also provided to indicate the effects of like SMA volume fraction, dependency of material properties on temperature, lay-up orientation, and pre-strain of SMA wires on the natural frequency and buckling of Shape Memory Alloy Hybrid Composite (SMAHC) cylindrical shells. Results represent the fact that SMAs can play a significant role in thermal vibration of composite shells. The second goal of present work is optimization of SMAHC cylindrical shells in order to maximize the fundamental frequency parameter at a certain temperature. To this end, an eight-layer composite shell with four SMA-reinforced layers is considered for optimization. The primary optimization variables are the values of SMA angles in the four layers. Since the optimization process is complicated and time consuming, Genetic Algorithm (GA) is performed to obtain the orientations of SMA layers to maximize the first natural frequency of structure. The optimization results show that using an optimum stacking sequence for SMAHC shells can increase the fundamental frequency of the structure by a considerable amount

Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns

The main purpose of this study is to compare the methods of differential quadrature (DQ) and harmonic differential quadrature (HDQ). For this purpose, DQ and HDQ methods are presented for buckling, bending, and free vibration analysis of thin isotropic plates and columns. Plates of different shapes such as rectangular, circular, square, skew, trapezoidal, annular, and sectorial plate subjected to different boundary conditions are selected to demonstrate the accuracy of the method. Four different support conditions are taken into consideration for columns. Numerical results are presented to illustrate the method and demonstrate its efficiency. It is emphasized that the HDQ method gives more accurate results and needs less grid points than the DQ method. (C) 2003 Elsevier Ltd. All rights reserved

Discrete Singular Convolution for Free Vibration Analysis of Anisotropic Rectangular Plates

The focus in this study is on the application of the discrete singular convolution (DSC) method to the differential equation, which governs the free vibration of anisotropic plates, Regularized Shannon\u27s delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the present study, free vibration analysis of rectangular composite plates via discrete singular convolution has been presented. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The obtained results are compared with those of other numerical methods available in the literature. Numerical calculations showed that accurate results can be achieved

Vibration of FG porous three-layered beams equipped by agglomerated nanocomposite patches resting on Vlasov's foundation

Equipped sandwich beams (ESBs) are one of the highly demanded structures by the different industries due to their high stiffness to weight ratio. In the present study, the vibrational behavior of a novel ESB is evaluated, analytically. The whole ESB is composed of three layers including functionally graded porous core (FGPC) and two same agglomerated carbon nanofiller reinforced composite (ACNFRC) face sheets. Both nanocomposite layers are constituted from poly(methyl methacrylate) (PMMA) as matrix and CNFs which serve as reinforcing phase. In addition, the effect of agglomeration is considered in nanocomposites, and its tremendous influence on the normalized frequency is depicted in figure and table formats. For the sake of layers properties estimation, power-law and Eshelby–Mori–Tanaka's (EMT)'s approach are hired for, respectively, FGPC and ACNFRCs. Besides this, Hamilton's principle in conjunction with multi-displacement fields and Fourier series analytical method are cooperated tightly to derive motion equations and solve them mathematically. The evaluation of the impacts of various variables as, different displacement fields, thermal environment, CNFs agglomeration, and Vlasov's substrate parameters can be considered as the novelties of this paper. It is revealed that in the context of agglomeration, a higher number of clusters with a lower volume fraction of CNFs inside them can provide higher magnitudes of normalized frequency and consequently rigidity. This work can be assumed as a reference for further future examinations in such a broad context

On the generalized model of shell structures with functional cross-sections

In the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic, and any non-geometric structure with functional cross-section, can be modeled mechanically with only one partial differential equation system. The obtained equations have been solved by applying SAPM semi-analytical solution method. In order to present a comprehensive research, dynamic nonlinear analysis is considered. The variation of material properties through the thickness has been assumed as functionally graded and its effect on the strength of the shell structure with the functional cross-section has been investigated. The numerical results have been compared with available papers and also with FEM results for some structures that there is no paper available for validation. Different types of shell structures have been studied in terms of cross-sectional shape and properties. Finally, the effects of some important factors on the results such as boundary conditions, nonlinear analysis, dynamic analysis, and rotation of the structure around its central axis have been conducted thoroughly. This study and its original governing equations can be considered as a comprehensive reference for mechanical analysis of various shell structures with functional cross-sectional shape

On the non-linear dynamics of torus-shaped and cylindrical shell structures

In this study, the non-linear dynamic analysis of torus-shaped and cylindrical shell-like structures has been studied. The applied material is assumed as the functionally graded material (FGM). The structures are considered to be used for important machines such as wind turbines. The effects of some environmental factors on the analysis like temperature and humidity have been considered. The strain field has been calculated in general form and in continue the dynamic governing equations of torus structure have been derived based on the first-order shear deformation theory. The rotation around two independent axes in the torus coordinate system is considered and time-dependent equations are solved using SAPM semi-analytical method. The stresses and deformations generated in the torus and cylindrical shaped structures are plotted. The rotation of structures has been attended due to some transportation purposes. The effect of internal pressures as well as rotational speed at torus and cylindrical structures has been investigated in several numerical diagrams. The results are presented in the form of graphs that consider the rotational effects, loading, thermal and humid (hygro-thermal) environments, and size of the structures. This research can provide scientific perspectives to researchers who will examine the dynamic analysis of torus and cylindrical shaped structures