Bending analysis of a laminated composite patch considering the free-edge effect using a stress-based equivalent single-layer composite model

The interlaminar stresses of a laminated composite patch, which is made up of reinforcing fibers (carbon/graphite) and epoxy matrix are analyzed using a stress-based equivalent single-layer model under a bending load. The composite patch is frequently used as reinforcement for a metallic adherend of mechanical/aerospace structures (i.e., aluminum alloy, etc) by attaching the film- or paste-type adhesive (i.e., epoxy, BMI, etc). To calculate the adhesive stresses transferred from the substrate, an interlayer model is introduced. The adhesive stresses are obtained by solving the equilibrium equations. The stress fields of the patch are determined by assuming certain stress functions. To satisfy the equilibrium state of the patch, the stress functions are divided into homogeneous and particular parts. The adhesive stresses act as prescribed stress boundary conditions of the laminated composite patch. The stress functions are substituted into a complementary virtual work principle, and from this, two coupled ordinary differential equations are obtained. General eigenvalue problems are derived to solve the coupled governing equations. To demonstrate the validity and efficiency of the proposed method, cross-ply, angle-ply and quasi-isotropic laminated composite patches are studied. From the observations made, the authors found that the stress function-based approach is suitable for solving the stress prescribed boundary value problem with accuracy and efficiency compared to a displacement-based approach such as the finite element method. The proposed method can be used as an efficient tool in the initial design stage of structural components when it is necessary to consider the free-edge effect.     

Static, dynamic, and buckling analysis of partial interaction composite members using Timoshenko's beam theory

The static, dynamic, and buckling behavior of partial interaction composite members is investigated in this paper by taking into account for the influences of rotary inertia and shear deformations. The governing differential equations obtained are very comprehensive, covering and extending the current models for the problems that are based on Euler–Bernoulli beam theory. The analytical solutions of the deflection are then found for the beam with uniformly distributing load under common boundary conditions. The free vibration and buckling behavior are also studied and the analytical expressions of the frequencies of the simply supported beam are obtained explicitly, as are the buckling loads. For other boundary conditions, the eigen-equations are transcendental and thus some numerical examples are presented to demonstrate the effects of the shear deformation and rotary inertia on the resonant frequencies and buckling loads.     

An analysis of turbulent flow around a NACA4412 airfoil by using a segregated finite element method

A turbulent flow around a NACA4412 airfoil is simulated by a segregated finite element method based on the SIMPLE algorithm and the low Reynolds numberk-ω turbulence model. The originalk-ω model and a modified version of thek-ω, model (shear stress transport model) are adopted, for which grid independent solutions are obtained, respectively. From the present numerical experiment, it has been shown that the segregated finite element method with thek-ω turbulence model can predict the turbulent flow leading to separation satisfactorily with apparently reduced memories compared with the mixed integrated formulation. It is also recommended that for the analysis of external flows a modifiedk-ω model should be used instead of the originalk-ω model, which combines the features of both the standardk-ε model and the originalk-ω model.     

Microstructural analysis of a FeAl/quasicrystal-based composite prepared using a focused ion beam miller

A composite consisting of a brittle multiphase matrix containing both an Al-based quasicrystalline phase (ψ) and an ordered body centred cubic phase (β) and a relatively ductile ordered body centred cubic intermetallic FeAl phase has been developed as an abrasive wear-resistant coating material. It is applied as a 500 μm thick layer onto stainless steel substrates through plasma spray processing. The microstructure of such materials can be readily examined by optical and scanning electron microscopy, but the inherent difficulty of preparing transmission electron microscope (TEM) samples has inhibited higher resolution studies. However, the relatively recent development of the focused ion beam (FIB) miller as a tool in materials science provides a method ideal for the preparation of TEM specimens of these materials. In this study a coating consisting of a mixture of an Al–Cu–Fe based quasicrystal and FeAl+Cr was deposited on to a 304 stainless steel substrate. TEM specimens were prepared using a FIB and subjected to detailed microstructural characterization. The structure consisted of elongated bands of a FeAl phase about 100 nm in width and several micrometres in length, which enclosed more equiaxed regions about 1 μm in diameter that consisted of fine mixtures of quasicrystal and two Al-Fe-Cu phases isostructurally related to FeAl.     

A study on stress analysis of orthotropic composite cylindrical shells with a circular or an elliptical cutout

The stress analysis on orthotropic composite cylindrical shells with one circular or one elliptical cutout subjected to an axial force is carried out by using an analytical and experimental method. The composite cylindrical shell governing equation of the Donnell's type is applied to this study and all results are presented by the stress concentration factor. The stress concentra-tion factor is defined as the ratio of the stress on the region around a cutout to the nominal stress of the shell. The stress concentration factor is classified into the circumferential stress concen-tration factors and the radial stress concentration factors due to the cylindrical coordinate of which the origin is the center of a cutout. The considered loading condition is only axial tension loading condition. In this study, thus, the maximum stress is induced on perpendicular region against axial direction, on the coordinate. Various cutout sizes are expressed using the radius ratio,, which is the radius of a cutout over one of the cylindrical shell. Experimental results are obtained using strain gages, which are attached around a cutout of the cylindrical shell. As the result from this study, the stress concentration around a cutout can be predicted by using the analytical method for an orthotropic composite cylindrical shell having a circular or an elliptical cutout.     

Vibration analysis of delaminated composite beams and plates using a higher-order finite element

In order to analyze the vibration response of delaminated composite plates of moderate thickness, a FEM model based on a simple higher-order plate theory, which can satisfy the zero transverse shear strain condition on the top and bottom surfaces of plates, has been proposed in this paper. To set up a C⁰-type FEM model, two artificial variables have been introduced in the displacement field to avoid the higher-order derivatives in the higher-order plate theory. The corresponding constraint conditions from the two artificial variables have been enforced effectively through the penalty function method using the reduced integration scheme within the element area. Furthermore, the implementation of displacement continuity conditions at the delamination front has been described using the present FEM theory. Various examples studied in many previous researches have been employed to verify the justification, accuracy and efficiency of the present FEM model. The influences of delamination on the vibration characteristic of composite laminates have been investigated. Especially the variation of ‘curvature of vibration mode’ (i.e., the second-order differential of deflections in vibration mode) caused by delamination has been studied in detail to provide valuable information for the possible identification of delamination. Furthermore, two approaches have been investigated to detect a delamination in laminates by employing this information.     

Probabilistic uncertainty analysis of an FRF of a structure using a Gaussian process emulator

This paper introduces methods for probabilistic uncertainty analysis of a frequency response function (FRF) of a structure obtained via a finite element (FE) model. The methods are applicable to computationally expensive FE models, making use of a Bayesian metamodel known as an emulator. The emulator produces fast predictions of the FE model output, but also accounts for the additional uncertainty induced by only having a limited number of model evaluations. Two approaches to the probabilistic uncertainty analysis of FRFs are developed. The first considers the uncertainty in the response at discrete frequencies, giving pointwise uncertainty intervals. The second considers the uncertainty in an entire FRF across a frequency range, giving an uncertainty envelope function. The methods are demonstrated and compared to alternative approaches in a practical case study.