Based on the Unconstrained Third Order Shear Deformation Theory (UTSDT), this paper focuses on the dynamical behaviour of moderately thick laminated domes and spherical shell panels. A higher order theory, within linear elasticity, is used to analyse the above moderately thick structural elements. This theory allows the presence of a finite transverse shear strain on the top and bottom surfaces of shells, releasing in this manner the additional constraint that must be imposed in the TSDT of Reddy [1]. The UTSDT involves seven displacement functions: two in plane displacements, one transverse displacement, two linear rotations and two cubic variations of the in plane displacements (higher order rotations)[2]. The governing dynamic equilibrium equations are expressed as functions of seven kinematic parameters, by using the constitutive and kinematic relations. The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of the equations of the system by means of the Generalized Differential Quadrature (GDQ) method leads to a standard linear eigenvalue problem [3]. Shell structures mentioned above are considered within their classical boundary conditions: clamped (C), simply supported (S) and free (F) edge. Numerical solutions will be computed by means of the GDQ Method. Numerical results concerning various types of laminate are considered in order to perform a correct benchmark procedure [4]. The inf uence of the material anisotropy compared to an isotropic one is shown considering the free vibration frequencies of spherical panels and domes. The effect of different grid point distributions on convergence, stability and accuracy of the GDQ procedure is investigated. Numerical results are sensitive to the number of sampling points used, to their distribution and to the boundary conditions. Furthermore, the transverse stresses through the laminate thickness are reconstructed a posteriori by using three dimensional equilibrium equations.
Free vibration of laminated shells via GDQ method using third-order theories / N. Fantuzzi; L. Rossetti; E. Viola. - ELETTRONICO. - (2012), pp. 472-472. (Intervento presentato al convegno International Conference of Mechanics of Nano, Micro and Macro Composite Structures (ICNMMCS2012) (http://paginas.fe.up.pt/~icnmmcs/proceedings.html) tenutosi a Politecnico di Torino nel 18-20 June 2012).
Free vibration of laminated shells via GDQ method using third-order theories
FANTUZZI, NICHOLAS;ROSSETTI, LUIGI;VIOLA, ERASMO
2012
Abstract
Based on the Unconstrained Third Order Shear Deformation Theory (UTSDT), this paper focuses on the dynamical behaviour of moderately thick laminated domes and spherical shell panels. A higher order theory, within linear elasticity, is used to analyse the above moderately thick structural elements. This theory allows the presence of a finite transverse shear strain on the top and bottom surfaces of shells, releasing in this manner the additional constraint that must be imposed in the TSDT of Reddy [1]. The UTSDT involves seven displacement functions: two in plane displacements, one transverse displacement, two linear rotations and two cubic variations of the in plane displacements (higher order rotations)[2]. The governing dynamic equilibrium equations are expressed as functions of seven kinematic parameters, by using the constitutive and kinematic relations. The solution is given in terms of generalized displacement components of the points lying on the middle surface of the shell. The discretization of the equations of the system by means of the Generalized Differential Quadrature (GDQ) method leads to a standard linear eigenvalue problem [3]. Shell structures mentioned above are considered within their classical boundary conditions: clamped (C), simply supported (S) and free (F) edge. Numerical solutions will be computed by means of the GDQ Method. Numerical results concerning various types of laminate are considered in order to perform a correct benchmark procedure [4]. The inf uence of the material anisotropy compared to an isotropic one is shown considering the free vibration frequencies of spherical panels and domes. The effect of different grid point distributions on convergence, stability and accuracy of the GDQ procedure is investigated. Numerical results are sensitive to the number of sampling points used, to their distribution and to the boundary conditions. Furthermore, the transverse stresses through the laminate thickness are reconstructed a posteriori by using three dimensional equilibrium equations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
