Erasmo Viola

Vibration analysis of spherical structural elements using the GDQ method

This paper deals with the dynamical behaviour of hemispherical domes and spherical shell panels. The First-order Shear Deformation Theory (FSDT) is used to analyze the above moderately thick structural elements. The treatment is conducted within the theory of linear elasticity, when the material behaviour is assumed to be homogeneous and isotropic. The governing equations of motion, written in terms of internal resultants, are expressed as functions of five kinematic parameters, by using the constitutive and the congruence relationships. The boundary conditions considered are clamped (C), simply supported (S) and free (F) edge. Numerical solutions have been computed by means of the technique known as the Generalized Differential Quadrature (GDQ) Method. These results, which are based upon the FSDT, are compared with the ones obtained using commercial programs such as Abaqus, Ansys, Femap/Nastran, Straus, Pro/Engineer, which also elaborate a three-dimensional analysis. The effect of different grid point distributions on the convergence, the stability and the accuracy of the GDQ procedure is investigated. The convergence rate of the natural frequencies is shown to be fast and the stability of the numerical methodology is very good. The accuracy of the method is sensitive to the number of sampling points used, to their distribution and to the boundary conditions.

Four-parameter functionally graded cracked plates of arbitrary shape: A GDQFEM solution for free vibrations.

ABSTRACT The dynamic behavior of moderately thick FGM plates with geometric discontinuities and arbitrarily curved boundaries is investigated. The Generalized Differential Quadrature Finite Element Method (GDQFEM) is proposed as a numerical approach. The irregular physical domain in Cartesian coordinates is transformed into a regular domain in natural coordinates. Several types of cracked FGM plates are investigated. It appears that GDQFEM is analogous to the well-known Finite Element Method (FEM). With reference to the proposed technique the governing FSDT equations are solved in their strong form and the connections between the elements are imposed with the inter-element compatibility conditions. The results show excellent agreement with other numerical solutions obtained by FEM.

Detection of crack location using cracked beam element method for structural analysis

The local flexibility introduced by cracks changes the dynamic behavior of the structure and, by examining this change, crack position and magnitude can be identified. In order to model the structure for FEM analysis, a special finite element for a cracked Timoshenko beam is developed. Shape functions for rotational and translational displacements are used to obtain the consistent mass matrix for the cracked beam element. Effect of the crack on the stiffness matrix and consistent mass matrix is investigated. Proposed is a procedure for identifying cracks in structures using modal test data.

Crack propagation in an orthotropic medium

Abstract In this paper, the partial differential equations related to elastodynamic plane problems in an orthotropic medium are reduced by means of composite transformations to a first order elliptic system of the Cauchy-Riemann type. This result justifies the representation of stress and displacement fields in terms of holomorphic functions defined into appropriate complex domains. The above formulation has been used to solve the boundary value problem concerned with the steady state propagation of a finite straight crack in an orthotropic medium. Some asymptotic results are also represented and briefly discussed.

A passive monitoring technique based on dispersion compensation to locate impacts in plate-like structures

A method for impact location in plate-like structures is proposed. The approach is based on guided waves dispersion compensation. Procedures based on dispersion compensation are usually applied to active monitoring techniques, as they require the knowledge of the time of impact to effectively compensate the guided waves dispersive behaviour. Unfortunately, this knowledge is not given in passive monitoring techniques. Despite this limit, the proposed dispersion compensation procedure is useful as it removes in the group delay of the acquired signals the dependence on the travelled distance. By cross-correlating the signals related to the same event acquired by different sensors, the difference in travelled distances can be determined and used to locate the wave source via hyperbolic positioning. The results show that the developed tool could pave he way for a new class of procedures to locate impacts in waveguides.

Biaxial load effects on a crack between dissimilar media

Abstract An analysis of the in-plane biaxial loading of two dissimilar materials with a crack along their common interface is considered. The elastic solution is obtained by the application of the complex variable technique coupled with the principle of superposition. The stress and displacement fields near the tip of the crack are described and the influence of the load parallel to the crack direction is shown. Then a failure criterion is formulated to discuss the debonding along the interface or the brittle fracture of the elastic system. In particular the effect of the non-singular terms on the critical applied tensile stress and on the deviation of the interfacial crack into one of the adjacent media is analyzed.

Analysis of Sandwich Plates by Generalized Differential Quadrature Method

We combine a layer-wise formulation and a generalized differential quadrature technique for predicting the static deformations and free vibration behaviour of sandwich plates. Through numerical experiments, the capability and efficiency of this strong-form technique for static and vibration problems are demonstrated, and the numerical accuracy and convergence are thoughtfully examined.

Crack propagation in an orthotropic medium under general loading

Abstract The elastodynamic response of a finite crack steadily propagating in an orthotropic medium, acted upon at infinity by uniform biaxial and shear loads, is studied. In particular, the effects of varying crack velocity as well as the ratio of shear load to tensile load are described. The action of material orthotropy on various quantities describing the crack propagation characteristics is pointed out.

Inter-laminar stress recovery procedure for doubly-curved, singly-curved, revolution shells with variable radii of curvature and plates using generalized higher-order theories and the local GDQ method

ABSTRACT The stress and strain recovery procedure already applied for solving doubly-curved structures with variable radii of curvature has been considered in this article using an equivalent single layer approach based on a general higher-order formulation, in which the thickness functions of the in-plane displacement parameters are defined independently from the ones through the shell thickness. The theoretical model considers composite structures in such a way that employs the differential geometry for the description of doubly-curved, singly-curved, revolution with variable radii of curvature and degenerate shells. Furthermore, the structures at hand can be laminated composites made of a general stacking sequence of orthotropic generically oriented plies. The governing static equilibrium equations are solved in their strong form using the local generalized differential quadrature (GDQ) method. Moreover the generalized integral quadrature (GIQ) is exploited for the evaluation of the stress resultants of the model under study. Several numerical applications are presented and the local GDQ results are compared with finite element method (FEM) commercial codes.

Graphical User Interface for Guided Acoustic Waves

This paper presents GUIGUW v0.1, a graphical user interface (GUI) for the computation of stress-guided wave dispersive features. The software exploits semianalytical finite-element (SAFE) formulations for the calculation of wave-propagation characteristics. The interface allows for the selection of geometrical, mechanical, and frequency-related parameters for the computation. Isotropic and anisotropic materials with linear elastic and linear viscoelastic rheological behaviors can be considered, and any waveguide cross section can be modeled. For each existing wave, the dispersive results can be represented in terms of wave number, wavelength, phase velocity, group velocity (for undamped waveguides), energy velocity, and attenuation (for damped waveguides). By simply working with the GUI, original results for guided stress waves can be obtained.