Radial basis functions based on differential quadrature method for the free vibration analysis of laminated composite arbitrarily shaped plates

The conventional strong form collocation approach known as Differential Quadrature (DQ) method has been applied in the past to a vast type of engineering problems. It is well-known that its application is strictly limited to regular regions where derivatives are approximated along mesh lines. Generally, its accuracy increases when the number of collocation points is large and the method tends to be stable. However, for some numerical problems several points are needed in order to obtain an accurate solution. Changing the basis functions another numerical technique was developed called Radial Basis Functions (RBFs) method, which has the advantage of approximating derivatives using irregular point distributions and the basis functions depend on the mutual radial distance of the grid points. In order to extend the idea of DQ method to a general case a Radial Basis Function based on Differential Quadrature (RBF-DQ) method has been recently developed. This method merges the advantages of both techniques. Furthermore, this work proposes the application of RBF-DQ when a domain decomposition technique is considered. In this way it will be shown that, using some kind of basis functions the number of grid points per element can be reduced compared to other classical approaches. Furthermore, once the shape parameter is fixed for one case, it is not needed to calculate it again for other applications.     

Microporomechanical behavior of perfectly straight unidirectional fiber assembly: Theoretical and experimental

The theory of poromechanics, most often used for macroscopically isotropic granular material, is applied to unidirectional fiber assemblies. When the deformation of the constituting fibers of those assemblies is taken into account during undrained forced compression, the Biot coefficients are expected to be lower than one. In the case of transversely isotropic materials, two independent Biot coefficients exist, one according to the fiber length direction and another relative to the plane perpendicular to that direction. The present paper aims at predicting the Biot coefficients for perfectly straight unidirectional (UD) fiber assemblies using micromechanical methods: dilute, Mori–Tanaka and Ponte Castañeda–Willis estimates. An experimental procedure, based on both uniaxial and triaxial material testing machines, is also detailed and applied to rubber fiber assemblies. The theoretical and experimental Biot coefficient results are compared and show a good agreement.     

Prediction of transport properties of wood below the fiber saturation point - A multiscale homogenization approach and its experimental validation. Part II: Steady state moisture diffusion coefficient

In this publication a multiscale homogenization model for moisture transport in wood is developed and validated. The model aims at prediction of macroscopic transport properties of clear wood samples from their microstructure and the physical properties of a few microscale constituents. In the first part of this two-part paper, the theoretical background and fundamentals of the model were presented, and its specification for the estimation of macroscopic thermal conductivities was shown. In this second part the model is applied to steady state moisture diffusion below the fiber saturation point. The model starts on a scale of about 50 μm, where the wood cells form a honeycomb-like structure. In a first homogenization step the effective moisture transport behavior of the cell structure is determined from moisture diffusion properties of the cell walls and the (moist) air in lumens, respectively. Further homogenization steps account for the larger vessels that exist in hardwood species, the annual rings which are a succession of layers with different densities, and finally wood rays, that form pathways in the radial direction throughout the stem. The model validation rests on experiments as in the case of heat conduction: The macroscopic diffusion coefficients predicted by the multiscale homogenization model for tissue-specific composition data (input data set II) are compared to corresponding experimentally determined tissue-specific diffusion coefficients under steady state conditions (experimental data set). As for thermal conductivity, the good agreement of model predictions and test data underlines the suitability of the presented multiscale model.     

Experimental and numerical study of fastener pull-through failure in GFRP laminates

A methodology to design and analyze multi-material bolted joints in hybrid train structures is presented. This methodology enables the prediction of the response of a multi-material bolted joint in a short amount of time and it is suitable to be used for large structures, where the number of bolts can be very high. The method developed is applied to a real industrial case which consists on the connection between the roof and the side of a carbody shell train structure. Experimental tests are performed on a full-size sub-component. The comparison between the experimental data and the numerical results confirms the accuracy of the method.     

Modeling of the thermopiezoelastic behavior of prismatic smart composite structures made of orthotropic materials

Asymptotic homogenization models for prismatic smart composite structures are derived and the effective elastic, piezoelectric, and thermal expansion coefficients are obtained. The actuation coefficients characterize the intrinsic transducer nature of active smart materials that can be used to induce strains and stresses in a coordinated fashion. Examples of such actuators employed with smart composite material systems are derived from piezoelectric, magnetostrictive and some other materials. The constituents of the smart structures are assumed to exhibit orthotropic characteristics. The original problem for the regularly non-homogeneous smart composite structure reduces to a system of three simpler types of problem, called unit cell problems. It is precisely these unit cell problems that enable the determination of the aforementioned coefficients. These effective coefficients are universal in nature and can be used to study a wide variety of boundary value problems associated with a smart structure of a given geometry.     

Theory of fabric-reinforced viscous fluids

Constitutive equation are formulated for flow of fabric-reinforced composite materials which show viscous response at the forming temperature. It is shown that in general the characterization for linear viscous response involves five viscosity coefficients, but this number may be reduced as a result of material symmetry of the fabric. In the case in which the material is a plane sheet, the rheological behaviour is described by a single function of the current angle between the fibre directions. The theory is applied to the analysis of the ‘picture-frame’ experiment, and it is shown that this experiment provides a method of measuring the response function. The effect of symmetry of the fabric architecture is considered, and it is found that for some fabric symmetries the theory allows the possibility of different responses to in-plane shearing in different shearing directions, as has been observed in picture-frame experiments. The general theory for nonlinear viscosity is also formulated, and specialized to the analysis of plane sheets, and in particular to the case of a power law fluid. In this case also, it is shown that the material can be characterized by a single response function of the rate-of deformation and the angle between the fibre directions.     

Intercalation of Ru(II) tris (1,10-phenanthroline) complex in α- and γ-zirconium dihydrogen phosphate. Synthesis, thermal behaviour and X-ray characterization

Layered inorganic systems such as ion-exchangers (α- and γ-zirconium dihydrogen phosphate) already used as hosts for larger cations, were studied for the intercalation of Ru(II) tris (1,10-phenanthroline) complex into these host matrices. The uptake of the complex occurs using the batch method; the colour of the materials changes from white to brilliant orange; the highest ion uptake is obtained in the case of the γ-phase. The materials obtained are thermally stable up to ∼350 °C and the complex decomposition occurs in two (α-phase) or three (γ-phase) steps. The complex decomposition is complete at ∼700 °C and at 550 °C (respectively for α- and γ-Ru(II) materials). As can be seen from the X-ray patterns, the Ru(II) materials are still layered and show a new phase with an increase in the interlayer distance with respect to the starting materials. The hydrogen form is always present in the case of the α-materials; whereas, in the case of the γ-materials, it is present when ≤0.12 moles of the complex/mole of exchanger are inserted. Microanalysis measurements confirm the fact that the Ru(II) complex is not modified when exchanged.     

Efficient structural computations with parameters uncertainty for composite applications

The aim of this paper is to propose a methodology in order to take into account the influence of uncertain data in structural calculations. To attain this goal, an approximation of the responses as a function of the uncertain data response called surface method (RSM) is proposed. In order to decrease the number of identification points necessary for the RSM, a progressive strategy is proposed. Error indicators are also used in order to increase the confidence. This strategy is applied to a laminate plate subjected to bending tests. The results are compared to Monte-Carlo simulations (considered as a reference). The method proposed in the present work permits to estimate correctly the whole response and is very simple to use (pre- and post-processing). This method is applied to asses the robustness of the point-stress method used to predict the rupture of perforated plates.     

Analysis of effective properties of electroelastic composites using the self-consistent and asymptotic homogenization methods

The problem of the calculation of overall properties of a binary electroelastic fibre-reinforced composite is studied here, whose constituents are an elastic matrix and piezoelectric fibres that have transversely isotropic properties. Randomly positioned fibres as well as periodic distributed fibres are considered. The former case is dealt with by means of the self-consistent method and the latter one by asymptotic homogenization. Closed-form expressions are given for two variants of the self-consistent method, one in explicit form (effective field) and the other implicitly (effective medium). The former agree with the Mori-Tanaka equations. The equations derived using the asymptotic homogenization method are also explicit. It is shown that the three sets of effective coefficients satisfy analytically Schulgasser’s universal relations; the Milgrom-Shtrikman determinant is also explicitly satisfied by the effective field method variant. Overall properties are computed as a function of the fibre concentration. It is generally found that the properties calculated using the effective field self-consistent and homogenization methods are very close to each other for at least concentrations up to or near 0.3. In many cases the agreement is beyond that. Also the case when the constituents have either the same or opposite poling directions can be studied with the exact formulae. The antiplane strain related properties display interesting larger effects with opposite polings.     

Hygroscopic strain measurement by fibre Bragg gratings sensors in organic matrix composites – Application to monitoring of a composite structure

This study is devoted to the identification of the moisture expansion coefficients of composite materials by means of a novel measurement technique. This method is based on the insertion of Fibre Bragg Grating (FBG) sensors between composite layers. The sensor enables to measure the hygroscopic strain induced by moisture diffusion in the plane of the laminated composite. Experimental results from immersed samples, varying both the direction of measurement and the fibre volume fraction are given according to the water uptake, and leading to the characterisation of moisture expansion coefficient.     

Lifting line theory for wing-in-ground effect in proximity to a free surface

Although it has some limitations in applications, the classical Prandtl lifting line theory remains a standard methodology for evaluating lifting problems in free space. It is of theoretical interest in revealing lifting mechanisms. It is therefore, interesting to generalize the classical lifting line theory to cases more general than just the free space problem. In this article, we present the Prandtl lifting line theory for wing-in-ground effect (WIG) near a free surface. While, the fundamental methodology being similar to the classical lifting line theory, it turns out that the difficulty lies in finding the three-dimensional Green’s function for the system of horseshoe vortices operating over the deformable free surface. Linear free surface boundary conditions are applied to deal with the two-dimensional lifting problem solved by the singularity distribution method and the three-dimensional correction found by placing a system of horseshoe vortices on the wing. This approach was validated against published data. Excellent agreement is found among results obtained from this study, experiments and numerical simulations. Extensive numerical examples are carried out to show the features of lift coefficients in the vicinity of a free surface. As expected, the free surface can be represented by a rigid wall for the case of high velocity. Finally, the free surface effect on WIG is discussed.     

Study of the dynamic formation of transmission gratings recorded in photopolymers and holographic polymer-dispersed liquid crystals

Local and nonlocal models for the diffusion of photopolymers are applied to the dynamic formation of transmission gratings recorded in photopolymers and holographic polymer-dispersed liquid crystals (H-PDLCs). We retrieve the main parameters of H-PDLCs (refractive-index modulation and diffusion coefficient) by combining a solution of the one-dimensional diffusion equation and the rigorous coupled-wave theory applied to transmission gratings. The rigorous coupled-wave theory method provides us with information on higher harmonics of the refractive profile (not only on the first harmonic as when the classical Kogelnik theory is applied). Measurements concerning the second harmonic validate the modeling.     

Material characterization of laminated composite materials using a three-point-bending technique

A three-point-bending technique is presented for identifying the elastic constants of laminated composite materials. In the proposed technique, three strains in the axial, lateral, and 45° directions on the bottom surface at the mid-span of a symmetric angle-ply beam subjected to three-point-bending testing are measured for elastic constants identification. The narrow beam theory together with the trial elastic constants is used to predict the theoretical strains of the beam. The theoretical and experimental strains of the beams are then used in a stochastic optimization method to identify the elastic constants of the beam. The accuracy and applications of the proposed technique are demonstrated by means of a number of examples on the elastic constants identification of graphite/epoxy (Gr/ep) or glass/epoxy (Gl/ep) laminated composite materials. The effects of specimen aspect ratio and thickness on the accuracy of the proposed method are investigated.     

Interaction of free-surface waves with a floating dock

A new method to describe the interaction of waves with a rigid or flexible dock, with zero draft, is derived. By means of Green's theorem an integral equation along the platform for either the velocity potential or the deflection is obtained. In the two-dimensional case this equation is solved by means of a superposition of exponential functions. With a specific choice of the Green function the integration with respect to the space coordinate can be carried out analytically. The integration left is the integration in the k-plane that occurs in the chosen Green function. Subsequently the contour of this integral is modified in the complex plane. This results at first in a dispersion relation for the phase functions in the expansion. Then the set of algebraic equations for the amplitude coefficients follows from the same singularity analysis in the complex plane. These equations are very simple and easy to solve. In contrast to the classical approach of eigen-mode expansions, there is no need to split the problem in a symmetric and antisymmetric one. An other advantage is that the transmission and reflection coefficients are determined seperately by means of Green's theorem, applied at the free surface in the far field. The method is first explained for the semi-infinite rigid dock, followed by the rigid strip, the moving strip and the flexible moving platform. In the appendix it is explained how to derive a set of algebraic equations in the case when the incident wave is not perpendicular to the strip.     

Selection of the best calibration sample subset for multivariate regression

This paper discusses a methodology for selecting the minimum number of calibration samples in principal component regression (PCR) analysis. The method uses only the instrumental responses of a large set of samples to select the optimal subset, which is then submitted to chemical analysis and calibration. The subset is selected to provide a low variance of the regression coefficients. The methodology has been applied to UV-visible spectroscopy data to determine Ca(2+) in water and near-IR spectroscopy data to determine moisture in corn. In both cases, the regression models developed with a reduced number of samples provided accurate results. As far as precision is concerned, a similar root-mean-squared error of cross-validation (RMSECV) is found when comparing the new methodology with the results of the regression models that use the complete set of calibration samples and PCR. The number of analyzed samples in the calibration set can be reduced by up to 50%, which represents a considerable reduction in costs.     

A modification of the rigid finite element method and its application to the J-lay problem

This article presents the Rigid Finite Element Method (RFEM), which allows us to take into account the flexibility of a system. Beam-like structures are analyzed, in which large deformations occur. The RFEM has been developed many years ago and successfully applied to practical engineering problems. The main difference between this method and the classical Finite Element Method (FEM) is the element deformation during analysis. In RFEM, the finite elements generated in a discretization process are treated as nondeformable bodies, whilst in FEM the elements are deformable; in RFEM, flexible, mass-less elements with properly chosen coefficients are introduced. A modification of the stiffness coefficients used in RFEM is proposed and explained in the article. It is shown how these new coefficients applied in RFEM lead to the same energy of deformation as in the case when the system is discretized by the classical FEM. This means that the energy of deformation is identical to that obtained in FEM, which leads to identical deformations of the elements. It is of particular importance that the RFEM is a much simpler method, faster in calculations and easier to learn and interpret. Furthermore, the generation of the inertia and stiffness matrices is much faster than in FEM. Another advantage is relatively easy implementation for multicore processor architecture. The calculation examples investigated cover some practical problems related to the offshore pipe laying process. The J-lay method is simulated by the use of the author??s own computer model based on a modified RFEM. The model takes into account wave and sea current loads, hydrodynamic forces and material nonlinearity (plastic strains can develop during large deformation). The simulation results are compared with those obtained from the commercial package ANSYS.     

Complex-Valued Wavelet Lifting and Applications

Signals with irregular sampling structures arise naturally in many fields. In applications such as spectral decomposition and nonparametric regression, classical methods often assume a regular sampling pattern, thus cannot be applied without prior data processing. This work proposes new complex-valued analysis techniques based on the wavelet lifting scheme that removes “one coefficient at a time.” Our proposed lifting transform can be applied directly to irregularly sampled data and is able to adapt to the signal(s)’ characteristics. As our new lifting scheme produces complex-valued wavelet coefficients, it provides an alternative to the Fourier transform for irregular designs, allowing phase or directional information to be represented. We discuss applications in bivariate time series analysis, where the complex-valued lifting construction allows for coherence and phase quantification. We also demonstrate the potential of this flexible methodology over real-valued analysis in the nonparametric regression context. Supplementary materials for this article are available online.     

Measurement of resistance curves in the longitudinal failure of composites using digital image correlation

This paper presents a new methodology to measure the crack resistance curves associated with fiber-dominated failure modes in polymer–matrix composites. The crack resistance curves not only characterize the fracture toughness of the material, but are also the basis for the identification of the parameters of the softening laws used in the numerical simulation of fracture in composite materials. The proposed method is based on the identification of the crack tip location using Digital Image Correlation and the calculation of the J-integral directly from the test data using a simple expression derived for cross-ply composite laminates. It is shown that the results obtained using the proposed methodology yield crack resistance curves similar to those obtained using Finite Element based methods for compact tension carbon–epoxy specimens. However, it is also shown that, while the Digital Image Correlation based technique mitigates the problems resulting from Finite Element based data reduction schemes applied to compact compression tests, the delamination that accompanies the propagation of a kink-band renders compact compression test specimens unsuitable to measure resistance curves associated with fiber kinking.     

Multiscale Modeling of Crystalline Energetic Materials.

The large discrepancy in length and time scales at which characteristic processes of energetic materials are of relevance pose a major challenge for current simulation techniques. We present a systematic study of crystalline energetic materials of different sensitivity and analyze their properties at different theoretical levels. Information like equilibrium structures, vibrational frequencies, conformational rearrangement and mechanical properties like stiffness and elastic properties can be calculated within the density functional theory (DFT) using different levels of approximations. Dynamical properties are obtained by computations using molecular dynamics at finite temperatures through the use of classical force fields. Effect of defects on structure is studied using classical molecular dynamics methods. Temperature induced reactions at elevated temperatures have been studied using ab initio molecular dynamics method for moderate size crystals of nitroethane. Furthermore, while presenting the state of the art in the study of modeling energetic materials, the current advances in the area as well as the limitations of each methodology are discussed.