In this work, the Generalized Differential Quadrature (GDQ) Method is applied to study functionally graded and laminated composite shells and panels of revolution. The mechanical model is based on the so called First-order Shear Deformation Theory (FSDT), in particular on the Toorani-Lakis Theory, deduced from the three-dimensional theory, in order to analyse the above moderately thick structural elements. 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 meridional and the circumferential coordinates into account, without using the Fourier expansion methodology. Complete revolution shells are obtained as special cases of shell panels by satisfying the kinematical and physical compatibility at the common meridian characterized by   0,2 . After the solution of the fundamental system of equations in terms of displacements, the generalized strains and stress resultants can be evaluated by applying the Differential Quadrature rule to the displacements themselves. However, in order to design laminated composite and functionally graded structures properly, accurate stress analyses have to be performed. The determination of accurate values for interlaminar normal and shear stresses is of crucial importance, since they are responsible for the activation and the development of delamination mechanisms. In this work, the transverse shear and normal stress profiles through the laminated thickness are reconstructed a posteriori by simply using local three-dimensional equilibrium. 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 and static equivalence of shear forces. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained using analytical solutions for laminated composite plates. Very good agreement is observed. Examples of shear stress profile for plate and shell elements are presented to illustrate the validity and the accuracy of the GDQ method.
Shear and Normal Stress Recovery for Anisotropic Shells and Panels of Revolution via the GDQ Method
TORNABENE, FRANCESCO
2011
Abstract
In this work, the Generalized Differential Quadrature (GDQ) Method is applied to study functionally graded and laminated composite shells and panels of revolution. The mechanical model is based on the so called First-order Shear Deformation Theory (FSDT), in particular on the Toorani-Lakis Theory, deduced from the three-dimensional theory, in order to analyse the above moderately thick structural elements. 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 meridional and the circumferential coordinates into account, without using the Fourier expansion methodology. Complete revolution shells are obtained as special cases of shell panels by satisfying the kinematical and physical compatibility at the common meridian characterized by 0,2 . After the solution of the fundamental system of equations in terms of displacements, the generalized strains and stress resultants can be evaluated by applying the Differential Quadrature rule to the displacements themselves. However, in order to design laminated composite and functionally graded structures properly, accurate stress analyses have to be performed. The determination of accurate values for interlaminar normal and shear stresses is of crucial importance, since they are responsible for the activation and the development of delamination mechanisms. In this work, the transverse shear and normal stress profiles through the laminated thickness are reconstructed a posteriori by simply using local three-dimensional equilibrium. 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 and static equivalence of shear forces. In order to verify the accuracy of the present method, GDQ results are compared with the ones obtained using analytical solutions for laminated composite plates. Very good agreement is observed. Examples of shear stress profile for plate and shell elements are presented to illustrate the validity and the accuracy of the GDQ method.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
