J.V. Araújo dos Santos

Development of a numerical model for the damage identification on composite plate structures

This paper deals with a numerical technique for the identification of damage on laminated structures. The numerical model is based on a first-order shear deformation finite element. When the structure undergoes some kind of damage, its stiffness is reduced, changing the dynamic response. By considering the sensitivities of the orthogonality conditions of the mode shapes, an algorithm is formulated, which calculates a damage parameter in each finite element. The damage parameter is directly related to the stiffness reduction of the damaged finite element. Only the mechanical properties of the layers of the undamaged plate and the natural frequencies and mode shapes of the damaged plate are required. The proposed numerical model allows the identification of multiple damage and does not require the knowledge of the probable damaged areas. The algorithm is applied to a laminated rectangular plate and its efficiency is demonstrated through several damage simulations.

A damage identification numerical model based on the sensitivity of orthogonality conditions and least squares techniques

Abstract This paper presents a numerical model for damage identification of composite structures. This model is based on the orthogonality conditions sensitivities of the damaged and undamaged structure mode shapes and relies on a discretisation by finite elements. The damage is directly related to the stiffness reduction of the damaged element. A study on the use of eigenvector sensitivities for damage identification and the influence of measurement errors and noise in the modal data is also presented. This model is applied to a laminated rectangular plate, free in space, and the efficiency of the numerical tools used to solve the defined set of equations is discussed.

FREE VIBRATION AND BUCKLING ANALYSIS OF BEAMS WITH A MODIFIED COUPLE-STRESS THEORY

A model based on a modified couple stress theory for the free vibration and buckling analyses of beams is presented. The model also incorporates the Poissons effect and allows the analysis of Timoshenko beams with any arbitrary end boundary condition. The natural frequencies and buckling loads are computed using the Ritz method. Parametric studies show that, while the natural frequencies and the buckling loads increase monotonically with the increase of the material length scale, they present a minimum in certain values of the Poissons ratio. A study relating the classical elasticity and the couple stress strain energies is also presented. By establishing this relation, explicit formulas to obtain the natural frequencies and buckling loads, in which the couple stress and Poissons effects are accounted for, in terms of the buckling loads of the classical elasticity are found. These formulas, which are valid when the shear strain and stress are zero, allow an expedite computation of natural frequencies and buckling loads of beams with couple stress and Poissons effect.

Vibration of Timoshenko beams using non-classical elasticity theories

This paper presents a comparison among classical elasticity, nonlocal elasticity, and modified couple stress theories for free vibration analysis of Timoshenko beams. A study of the influence of rotary inertia and nonlocal parameters on fundamental and higher natural frequencies is carried out. The nonlocal natural frequencies are found to be lower than the classical ones, while the natural frequencies estimated by the modified couple stress theory are higher. The modified couple stress theory results depend on the beam cross-sectional size while those of the nonlocal theory do not. Convergence of both non-classical theories to the classical theory is observed as the beam global dimension increases.

Effective Elastic Moduli Evaluation of Single Walled Carbon Nanotubes Using Flexural Vibrations

Two new methods for effective elastic moduli evaluation of single walled carbon nanotubes (SWCNT) are presented. These methods rely on the Euler-Bernoulli and the Timoshenko beam theories, the modification of finite elements based on these theories, and an optimization technique. The proposed modification of the standard Euler-Bernoulli and Timoshenko finite elements assumes that the SWCNT diameter is much larger than its thickness. It is shown that the method based on the Timoshenko finite element presents better elastic moduli evaluations of short nanotubes than the ones based on the Euler-Bernoulli finite element.Two new methods for effective elastic moduli evaluation of single walled carbon nanotubes (SWCNT) are presented. These methods rely on the Euler-Bernoulli and the Timoshenko beam theories, the modification of finite elements based on these theories, and an optimization technique. The proposed modification of the standard Euler-Bernoulli and Timoshenko finite elements assumes that the SWCNT diameter is much larger than its thickness. It is shown that the method based on the Timoshenko finite element presents better elastic moduli evaluations of short nanotubes than the ones based on the Euler-Bernoulli finite element.

Nonlocal material properties of single-walled carbon nanotubes

Natural frequencies of single-walled carbon nanotubes (SWCNTs) obtained using a model based on Eringens nonlocal continuum mechanics and the Timoshenko beam theory are compared with those obtained by molecular dynamics simulations. The goal was to determine the values of the material constant, considered here as a nonlocal property, as a function of the length and the diameter of SWCNTs. The present approach has the advantage of eliminating the SWCNT thickness from the computations. A sensitivity analysis of natural frequencies to changes in the nonlocal material constant is also carried out and it shows that the influence of the nonlocal effects decreases with an increase in the SWCNT dimensions. The matching of natural frequencies shows that the nonlocal material constant varies with the natural frequency and the SWCNT length and diameter.Natural frequencies of single-walled carbon nanotubes (SWCNTs) obtained using a model based on Eringens nonlocal continuum mechanics and the Timoshenko beam theory are compared with those obtained by molecular dynamics simulations. The goal was to determine the values of the material constant, considered here as a nonlocal property, as a function of the length and the diameter of SWCNTs. The present approach has the advantage of eliminating the SWCNT thickness from the computations. A sensitivity analysis of natural frequencies to changes in the nonlocal material constant is also carried out and it shows that the influence of the nonlocal effects decreases with an increase in the SWCNT dimensions. The matching of natural frequencies shows that the nonlocal material constant varies with the natural frequency and the SWCNT length and diameter.

Identification of Damage in Composite Structures: A Numerical Model

This article deals with a numerical technique for the identification of damage in composite structures. The laminated structure is modeled by finite elements. When the structure undergoes some kind of damage, its stiffness is reduced, changing the dynamic response. By considering the sensitivities of the orthogonality conditions of the mode shapes, a novel algorithm is formulated, which calculates a damage parameter in each finite element. The damage parameter is related directly to the reduction in stiffness of the damaged finite element. The proposed numerical model allows the identification of multiple damage and does not require a priori knowledge of the probable areas of damage. The algorithm is applied to a laminated rectangular plate and its efficiency is demonstrated through several damage simulations.

Interferometric Techniques in Structural Damage Identification

This paper describes several interferometric techniques and their applications in structural damage identification. With that objective in mind, damaged aluminum beams with clamped-free and free-free boundary conditions are analyzed. Different damages cases are inflicted by creating small cuts perpendicular to the beams longitudinal axis, being the damage, therefore, characterized by the dimensions of these cuts. The out-of-plane displacement field of modal response is measured with an electronic speckle pattern interferometric system. The static and dynamic rotation fields, defined as the spatial derivative of the displacement field, are measured with two different speckle shearography systems. Second and third order spatial derivatives of the displacement field, which are related to the bending moment and shear force, are computed by differentiation techniques. The cuts locations are determined by looking for maximum values and/or perturbations of damage indicators based on bending moments and shear forces. This method is validated by comparing its results with numerical ones, from which the most suitable interferometric technique is chosen.

A damage localisation method based on higher order spatial derivatives of displacement and rotation fields

This paper presents the development of a damage localisation method based on low and higher order spatial derivatives of displacement and rotation fields. The method relies on the Timoshenko beam theory, the Hamiltons principle and the Ritz method, allowing the computation of an approximate analytical solution of natural frequencies, displacement and rotation fields. Since these fields are expressed analytically, through a series expansion, the spatial derivatives are also obtained analytically. Besides the usual curvature difference and damage index, which are based on comparisons of second order spatial derivative of the displacement field of a beam in the undamaged and damaged states, other damage indicators are proposed. These new indicators rely on spatial derivatives of rotation fields. The indicators are applied to the localisation of various cases of damages in beams and a comparison among them is carried out. It is found that, for relatively thick beams, the values of the indicators based on rotation fields spatial derivatives are, in general, lower than those based on displacement fields. It is also observed that these differences are negligible for beams with high length to thickness ratio.

Damage localization in laminated composite plates using double pulse-electronic holographic interferometry

One method for the damage localization of impact damage in laminated composite plates, based on their vibrational characteristics, is presented in this paper. This method uses double pulse-electronic holographic interferometry for mode shapes acquisition and the differences in curvatures. The rotations and curvatures are numerically obtained. The method is applied to a carbon fibre reinforced epoxy rectangular plate, free in space, subjected to two cases of impact damage. It is shown that the method based on curvatures allows for the localization of both cases of damage, which can be undetected by visual, X-ray or C-Scan inspections. The best localizations are achieved by selecting and applying the method to the most changed mode.