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This paper presents a static analysis of functionally graded single and sandwich beams by using an efficient 7DOFs quasi-3D hybrid type theory. The governing equations are derived by employing the principle of virtual works in a weak form and solved by means of the Finite Element Method (FEM). A C1 cubic Hermite interpolation is used for the vertical deflection variables while C0 linear interpolation is employed for the other kinematics variables. Convergence rates are studied in order to validate the finite element technique. Numerical results of the present formulation are compared with analytical and FEM solutions available in the literature. / Revisión por pares

There are many calculation methods for layered structures in scientific literature, but in most cases these calculation methods are complicated and inapplicable for layered structures made of reinforced concrete. Moreover, most of the calculation methods do not estimate the possibility of appearance of the cracks in the internal layers before the cracks in external layer in which the tensile stresses are higher. The internal layers could be made of lightweight concrete type materials (e.g. foamed concrete) which shrinkage deformations are several times higher if compared to the external layers. Therefore, the cracks in the internal layer may appear even before actual loading of the structure. The flexural layered members may have very complex state of stress and strain. Such state of stress and strain should be estimated when designing the effective and reliable building structures. The proposed method for the calculation of carrying capacity and cracking moment of the external layer of flexural layered reinforced concrete structures estimates the cracking of the internal layer, concrete shrinkage deformations and the physical and mechanical properties of used materials.

There are many calculation methods for layered structures in scientific literature, but in most cases these calculation methods are complicated and inapplicable for layered structures made of reinforced concrete. Moreover, most of the calculation methods do not estimate the possibility of appearance of the cracks in the internal layers before the cracks in external layer in which the tensile stresses are higher. The internal layers could be made of lightweight concrete type materials (e.g. foamed concrete) which shrinkage deformations are several times higher if compared to the external layers. Therefore, the cracks in the internal layer may appear even before actual loading of the structure. The flexural layered members may have very complex state of stress and strain. Such state of stress and strain should be estimated when designing the effective and reliable building structures. The proposed method for the calculation of carrying capacity and cracking moment of the external layer of flexural layered reinforced concrete structures estimates the cracking of the internal layer, concrete shrinkage deformations and the physical and mechanical properties of used materials.

Les matériaux magnéto-électro-élastiques (MEE) sont l'association des matériaux piézo-électrique et piézo-magnétique qui présentent un couplage "magnéto-électrique". L'objectif de cette thèse est d'étudier d'une part, le comportement effectif de ces composites et d'autre part, la propagation des ondes planes dans le milieu homogène équivalent. Dans la première partie de la thèse, nous avons modélisé le comportement effectif des composites MEE à partir de la méthode de la moyenne. Nous avons d'abord établi les équations générales, ensuite nous avons traité le cas où chaque phase est supposée isotrope transverse suivant un axe et polarisée suivant la même direction. La loi de comportement obtenue, ainsi que les tenseurs effectifs du milieu homogène équivalent ont été établis. Les propriétés élastiques effectives sont influencées par les propriétés électriques et magnétiques et réciproquement. Nous nous sommes intéressés en particulier à deux types de composites : les stratifiés et les fibres longues. L'influence de la géométrie des constituants ainsi que la proportion des phases sur le comportement effectif ont été étudiées. La deuxième partie du travail a porté sur l'étude de la propagation d'ondes planes dans les stratifiés. En utilisant la méthode d'homogénéisation périodique, nous avons obtenu les équations de la dynamique dans le milieu homogène équivalent. La longueur d'onde considérée est supposée grande devant la périodicité spatiale. Une méthode de résolution numérique a été développée afin d'obtenir les courbes de dispersion. Nous avons obtenu ces courbes en fonction des proportions des phases constitutives. Bien que les trois propriétés: élastique, électrique, magnétique, contribuent au comportement oscillatoire global, l'onde conserve essentiellement une nature élastique. / The objective of this thesis is estimating fundamental properties and studying the propagation of waves in the equivalent homogeneous medium based on the periodic magneto-electro-elastic (MEE) composite. These artificial MEE media are realized by means of combining piezo-electric and piezo-magnetic materials, and featurea direct "magneto-electric" coupling. In the first part, we modeled the effective behavior of these composites applying the averaging method. First, we derived the general equations, then we treated a particular case a uni axial medium comprised of alternating layers of piezo-electric and piezo-magnetic phases and polarized in the direction normal to the surfaces of these layers. The law of behavior was obtained as well as the effective tensors of the equivalent homogeneous medium. The effective elastic properties are influenced by the magnetic and electrical properties and inversely. We were particularly interested in two types of materials: multi-layers (planar symmetry) and long fibers (cylindrical symmetry). The influence of the geometry of these components on the effective behavior was revealed. The second part of the study focuses on the propagation of plane waves in the case of periodic multilayer structures. Using the periodic homogenization method, we obtained the effective tensors and the equations of propagation of elasto-electro-magnetic plane waves. The wavelength is supposed much larger than the spatial period of the investigated structure, hence the quasi-static approximation for the equations of electromagnetic could be used. The chosen method has allowed estimation of the wave frequency as a function of the wave number, the corresponding dispersion curves were plotted for a wide range of proportions of the constituent materials. Although all the three properties, mechanical, electrical and magnetic contribute to the global oscillatory behavior, the wave is essentially elastic.

Recently developed mathematical tools for the modelling of contact problems on thin film structures are adapted to allow the investigation of arbitrarily mixed purely isotropic and transversally isotropic laminate structures. The new tool is applied to model a variety of load problems resulting in the failure of windsurfing boards consisting of a relatively thin laminate shell and a soft polymer foam core. It is shown that local impact and distributed bending loads due to “bad landing” after high jumps or contact with parts of the sailing gear (the so called rig) especially the front part of the boom are leading to the most critical stress distributions resulting in failure. So most of the investigated boards were damaged because the rider (windsurfer) landed flat and thus produced a sudden impact force under his feet (impact defect). Other overloading occurred due to overturning of so called loop movements or the landing of the board exactly on respectively between two waves and this way producing high bending moments. Some of those typical loads are analysed in detail and the stresses occurring in the complex structure of the windsurfing boards are evaluated.

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Layered crystals with magnetic elements as Co and Fe have been studied. In TlCo2Se2, where Co atoms in one sheet are separated by Tl and Se from the next Co sheet, magnetic interaction within and between the sheets have been studied. Samples doped with 4% 57Fe replaced Co, show a magnetic spiral character with hyperfine fields in a flower shape in the ab-plane. The magnetic moment of 0.46 μB per Co atom derived from the average field is in good agreement with the result from neutron diffraction. In TlCu1.73Fe0.27Se2 the easy axis of magnetisation is the c-axis. The magnetic moment calculated from the Mössbauer data and SQUID magnetrometry is 0.97 μB per Fe atom with TC = 55(5) K. Multilayers of different elements have been studied. The effect of vanadium atoms on iron atoms at the interface of FeNi/V multilayers has been determined and the intermixing at the interface has been calculated to be 2-3 monolayers. For FeNi/Co 1/1 monolayer the magnetic hyperfine field (Bhf) is 45° out-of-plane, while for superlattices containing 2 to 5 monolayers it is in the plane. An study on Fe/Co superlattice were done by experimental, theoretical and simulational methods. The Bhf is highest for the Fe at the second layer next to the interface and gets the bulk value in the centre of thicker Fe layers. Studied magnetic nanoparticles coated with a lipid bilayer (magnetoliposomes) are found to have the magnetite structure but being non-stoichiometric as a result of the manufacturing process. The composition was approximately 32% γ-Fe2O3 and 68% Fe3O4. The oxidation evolution and its effect on magnetic properties of Fe clusters were also studied by means of different techniques. The extraction and insertion mechanism of lithium in the cathode material Li2FeSiO4 has been monitored by in situ x-ray diffraction and Mössbauer spectroscopy during the first two cycles. The relative amount of Fe+3/ Fe+2 at each end state was in good agreement with the results obtained from electrochemical measurements. A possible explanation to the observed lowering of the potential plateau from 3.10 to 2.80 V occurring during the first cycle, involves a structural rearrangement process in which some of the Li ions and the Fe ions are interchanged. The behaviour of small amounts of Fe in brass is investigated using Mössbauer spectroscopy. It was shown that a heat treatment can increase the amount of the precipitates of γ-Fe and ~650° C is the optimal treatment for having the highest amount of this phase.

Recently developed mathematical tools for the modelling of contact problems on thin film structures are adapted to allow the investigation of arbitrarily mixed purely isotropic and transversally isotropic laminate structures. The new tool is applied to model a variety of load problems resulting in the failure of windsurfing boards consisting of a relatively thin laminate shell and a soft polymer foam core. It is shown that local impact and distributed bending loads due to “bad landing” after high jumps or contact with parts of the sailing gear (the so called rig) especially the front part of the boom are leading to the most critical stress distributions resulting in failure. So most of the investigated boards were damaged because the rider (windsurfer) landed flat and thus produced a sudden impact force under his feet (impact defect). Other overloading occurred due to overturning of so called loop movements or the landing of the board exactly on respectively between two waves and this way producing high bending moments. Some of those typical loads are analysed in detail and the stresses occurring in the complex structure of the windsurfing boards are evaluated.

The subject of this dissertation is to develop a rigorous transverse-mode integral equation formulation for analyzing TE/TM electromagnetic mode field solutions for dielectric waveguides. The main topics are composed of two related parts. The first part deals with scalar problems. In which we propose a transverse-mode integral-equation formulation for problems such as mode solutions of the ridged microwave waveguides. This same technique also applies to EM waves scattering off the facet of dielectric slab waveguides terminating in free space. For both problems we constructed a specifically chosen basis for the unknown tangential field functions, and we were able to reduce the kernel matrix size by more than one half without noticeable degradation of the field solutions. In the second part of the thesis, we apply a full-vector integral-equation formulation to analyze modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic vector mode field solution is completely determined by the y-component electric and magnetic field functions on the interfaces between slices. These interfacial functions are governed by a system of vector-coupled transverse-mode integral equations (VCTMIE) whose kernels are made of orthonormal sets of both TE-to-y and TM-to-y modes from each slice. Finally, we show the numerical results to present the stable and quick convergence of this method as well as to improve the Gibb¡¦s phenomenon in the recreation of the transverse fields.