On the Vibration Characteristics of Graphene Platelet Reinforced Composite Super-elliptical Plates via Chebyshev-Ritz Method

An analytical-numerical solution of the spatial problem of elasticity theory for a composite in the form of a layer with two longitudinal endless continuous cylindrical inclusions is proposed. Homogeneous, isotropic materials of the layer and inclusions differ from each other in the modulus of elasticity and Poisson's ratio. Normal stresses are set on the upper and lower boundaries of the layer. The object of study is the stress state of such a composite. The problem is the lack of a high-precision method for calculating multiply connected bodies of this type. The solution of the problem is based on the generalized Fourier method for the Lame equations in various coordinate systems. The problem is reduced to an infinite system of linear algebraic equations, which is solved by the reduction method. In a numerical study, the stress state was obtained inside the composite bodies, within their conjugations, and on the isthmus between inclusions. It has been established that extreme stresses sρ=–0.9306 MPa, sf=–0.5595 MPa, tρf=–0.315 MPa occur on the mating face. Analysis of the stress state indicates the need to take into account the normal stresses on the mating surface. This is due to the presence of a binder, which may differ in physical characteristics from the main components of the composite. The results have logical physical correctness and, in simplified versions, are fully consistent with the results of similar problems from other approved sources. In the work, the transition formulas in the basic solutions between different coordinate systems, the conjugation conditions for different bodies, and the strict fulfillment of the equilibrium conditions for given boundary functions are simultaneously applied. This made it possible to obtain a high-precision solution of a new problem in the theory of elasticity for a layer with cylindrical inclusions and given only stresses on the boundary surfaces. The proposed method of calculation can be applied in the design of structures made of fibrous composites in the aircraft industry and construction.

/pdf/solution-of-the-problem-of-the-theory-of-elasticity-and-4bza6pui.pdf

Solution of the problem of the theory of elasticity and analysis of the stress state of a fibrous composite layer under the action of transverse compressive forces

The article presents the study of the stress state of a two-layer composite with a cylindrical cavity located parallel to the surfaces of the layers. Displacements are set on the cavity and the upper and lower boundaries of the upper and lower layers, respectively. The three-dimensional elasticity solution has been obtained by the analytical-numerical generalized Fourier method with respect to the system of Lame equations in local cylindrical coordinates associated with cavity and Cartesian coordinates associated with boundaries of the layers. The infinite systems of linear algebraic equations resulting from satisfying the boundary conditions are solved by the reduction method. As a result, displacements and stresses have been obtained at various points of the elastic body. We have compared the stress-strain state of a two-layer structure with a cylindrical cavity located in either of the layers. The analysis included various geometrical parameters and boundary functions; the results obtained were compared with a single-layer holed structure.

http://jsm.iau-arak.ac.ir/article_683397_73be0aed7947461a12bf4aeca8e2b1dd.pdf

Investigation of Stress State of the Layered Composite with a Longitudinal Cylindrical Cavity

In this work, a nonlinear investigation of non-homogeneous varying thickness circular plates resting on elastic foundations under the influence of the magnetic fieldis investigated. The non-homogeneity of the circular plates’ material is presumed to occur due to linear and parabolic changes in Young’s modulus likewise the density along the radial direction in a unique manner. The geometric Von Karman equations are used in modelling the governing differential equations. The transverse deflection is approximated using an assumed single term mode shape while the central deflection in form of Duffing’s equation is obtained using the Galerkin method.  Subsequently, the semi-analytical solutions are provided using the Optimal Homotopy Asymptotic Method (OHAM), the analytical solutions are used for parametric investigation. The results in this work are in good harmony with past results in the literature. From the results, it is realized that the nonlinear frequency of the circular plate increases with an increase in the linear elastic foundation. Also, the results showed that clamped edge and simply supported edge condition produced the same hardening nonlinearity. However, varying taper and non-homogeneity lower the nonlinear frequency ratio. Also, maximum deflection occurs when excitation force is zero, and attenuation of deflection is observed due to the presence of a magnetic field, varying thickness, homogeneity, and elastic foundation. It is anticipated that the discoveries from this research will boost the design of structures subjected to vibration.

http://jsm.iau-arak.ac.ir/article_683918_4e9b2864aa8cebfd9b181c2cc6ce9e3e.pdf

Nonlinear Investigation of Magnetic Influence on Dynamic Behaviour of Non-Homogeneous Varying Thickness Circular Plates Resting on Elastic Foundations

The bending analysis of moderately thick elliptic plates weakened by an eccentric circular hole has been investigated in this article. The nonlinear governing equations have been presented by considering the von-Karman assumptions and the first-order shear deformation theory in cylindrical coordinates system. Semi-analytical polynomial method (SAPM) which had been presented by the author before has been used. By applying SAPM method, the nonlinear partial differential equations have been transformed to the nonlinear algebraic equations system. Then, the nonlinear algebraic equations have been solved by using Newton–Raphson method. The obtained results of this study have been compared with the results of other references and the accuracy of the results has been shown. The effect of some important parameters on the results such as the location of the circular hole, the ratio of major to minor radiuses of elliptical plate, the size of circular hole and boundary conditions have been studied. It is concluded that applying the presented method is very convenient and efficient. So, it can be used for analyzing the mechanical behavior of elliptical plates, instead of relatively complicated formulations in elliptic coordinates system.

http://jsm.iau-arak.ac.ir/article_544403_3bc6d0710e1f14a64435dfe287fd8a1b.pdf

L Yazdanparast

Papers

New Method for Large Deflection Analysis of an Elliptic Plate Weakened by an Eccentric Circular Hole