Static analysis of functionally graded doubly-curved shells and panels of revolution (original) (raw)
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International Journal of Mechanical Sciences, 2012
The Generalized Differential Quadrature (GDQ) Method is applied to study laminated composite shells and panels of revolution. The mechanical model is based on the so called First-order Shear Deformation Theory (FSDT) deduced from the three-dimensional theory, in order to analyze the above moderately thick structural elements. In order to include the effect of the initial curvature from the beginning of the theory formulation a generalization of the kinematical model is adopted for the Reissner-Mindlin theory. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. The results are obtained taking the two co-ordinates into account, without using the Fourier expansion methodology, as done in semi-analytical methods. After the solution of the fundamental system of equations in terms of displacements and rotations, the generalized strains and stress resultants can be evaluated by applying the Differential Quadrature rule to the generalized displacements themselves. The transverse shear and normal stress profiles through the laminate thickness are reconstructed a posteriori by simply using local three-dimensional equilibrium equations. No preliminary recovery or regularization procedure on the extensional and flexural strain fields is needed when the Differential Quadrature technique is used. By using GDQ procedure through the thickness, the reconstruction procedure needs only to be corrected to properly account for the boundary equilibrium conditions. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained with 3D finite element methods. Stresses of several composite shell panels are evaluated. Very good agreement is observed without using mixed formulations and higher order kinematical models. Various examples of stress profiles for different shell elements are presented to illustrate the validity and the accuracy of GDQ method.
Composite Structures, 2014
Equivalent single layer approach Generalized differential quadrature method a b s t r a c t This study focuses on the static analysis of functionally graded conical shells and panels and extends a previous formulation by the first three authors. A 2D Unconstrained Third order Shear Deformation Theory (UTSDT) is used for the evaluation of tangential and normal stresses in moderately thick functionally graded truncated conical shells and panels subjected to meridian, circumferential and normal uniform loadings. To investigate the behavior of the functionally graded structures at issue, a four parameter power law function is considered. The initial curvature effect is discussed and the role of the parameters in the power law function is shown. The conical shell problem described in terms of seven partial differential equations is solved by using the generalized differential quadrature (GDQ) method. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. The stress recovery is worked out to reconstruct the correct distribution of transverse stress components. Accurate stress profiles for general loading combinations applied at the extreme surfaces are obtained. The influence of the semi vertex angle is pointed out.
Journal of Sound and Vibration, 2009
This paper focuses on the dynamic behavior of functionally graded conical, cylindrical shells and annular plates. The last two structures are obtained as special cases of the conical shell formulation. The first-order shear deformation theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is developed within the theory of linear elasticity, when materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. Two different power-law distributions are considered for the ceramic volume fraction. The homogeneous isotropic material is inferred as a special case of functionally graded materials (FGM). The governing equations of motion, expressed as functions of five kinematic parameters, are discretized by means of the generalized differential quadrature (GDQ) method. The discretization of the system leads to a standard linear eigenvalue problem, where two independent variables are involved without using the Fourier modal expansion methodology. For the homogeneous isotropic special case, numerical solutions are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Nastran, Straus, Pro/Mechanica. Very good agreement is observed. Furthermore, the convergence rate of natural frequencies is shown to be very fast and the stability of the numerical methodology is very good. Different typologies of non-uniform grid point distributions are considered. Finally, for the functionally graded material case numerical results illustrate the influence of the power-law exponent and of the power-law distribution choice on the mechanical behavior of shell structures.
Finite Element Modeling and Analysis of Functionally Graded (FG) Composite Shell Structures
Procedia Engineering, 2012
This article deals with the finite element modeling and analysis of functionally graded (FG) shell structures under different loading such as thermal and mechanical. Free vibration analysis of functionally graded (FG) spherical shell structure has also been presented. In order to study the influences of important parameters on the responses of FG shell structures, different types of shells have been considered. The responses obtained for FG shells are compared with the homogeneous shells of pure ceramic (Al 2 O 3) and pure metal (steel) shells and it has been observed that the responses of the FGM shells are in between the responses of the homogeneous shells. Based on the analysis, some important results are presented and discussed for thick as well as thin shells.
Composite Structures, 2012
ABSTRACT A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded cylindrical shells subjected to mechanical loadings. Eight types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded cylindrical shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.
Static analysis of functionally graded conical shells based on an unconstrained third order theory
. In this paper, the generalized differential quadrature (GDQ) method is applied to study the static behavior of functionally graded conical shells. The Unconstrained third order shear deformation theory (UTSDT) is used to analyze the above mentioned thick structural elements. In order to include the effect of the initial curvature, a generalization of the developed theory has been worked out. The governing equations, written in terms of stress resultants, are expressed as functions of seven kinematic parameters, by using the constitutive and kinematic relationships. The solution is given in terms of generalized displacement components of points lying on the middle surface of the shell. Comparisons among the generalized UTSDT, the third order theory of Reddy and the first order shear deformation theory (FSDT) are presented, in terms of the stresses across the thickness of the shell, and the influence of the parameters of the graded material is presented.
Modeling and Fe Analysis of Functionally Graded (FG) Composite Shell Structures
2020
This manuscript comprises with FG (functionally graded) analysis and finite modeling element shell frameworks under divergent loading like mechanical & thermal. The analysis of free vibration of FG spherical shell framework has also been depicted. In respect to research the impact of significant aspects on FG shell frameworks responses, divergent kinds of shells were deliberated. Here, responses were attained for FG shells were compared to pure ceramic homogeneous shells (AI203) and EN 31 Steel (pure metal) and it is perceived that FGM Shells responses were in between homogenous shells responses. Furthermore, static analysis done on FG shell structure is to determine the circumferential and longitudinal stress, strain and deformation. Furthermore, modal analysis is to be determining the natural frequencies.
Composite Structures, 2013
This paper investigates the static analysis of doubly-curved laminated composite shells and panels. A theoretical formulation of 2D Higher-order Shear Deformation Theory (HSDT) is developed. The middle surface of shells and panels is described by means of the differential geometry tool. The adopted HSDT is based on a generalized nine-parameter kinematic hypothesis suitable to represent, in a unified form, most of the displacement fields already presented in literature. A three-dimensional stress recovery procedure based on the equilibrium equations will be shown. Strains and stresses are corrected after the recovery to satisfy the top and bottom boundary conditions of the laminated composite shell or panel. The numerical problems connected with the static analysis of doubly-curved shells and panels are solved using the Generalized Differential Quadrature (GDQ) technique. All displacements, strains and stresses are worked out and plotted through the thickness of the following six types of laminated shell structures: rectangular and annular plates, cylindrical and spherical panels as well as a catenoidal shell and an elliptic paraboloid. Several lamination schemes, loadings and boundary conditions are considered. The GDQ results are compared with those obtained in literature with semi-analytical methods and the ones computed by using the finite element method.