Based on the principle of virtual displacements, the incremental equations of motion of a continuous medium are formulated by using the total Lagrangian description. After linearization of the incremental equations of motion, the displacement finite element model is obtained, which is solved iteratively. From this displacement finite element model, four different elements, i.e. degenerated shell element, degenerated curved beam element, 3-D continuum element and solid-shell transition element, are developed for the geometric nonlinear analysis of general shell-type structures, anisotropic as well as isotropic. Compatibility and completeness requirements are stressed in modelling the general shell-type structures in order to assure the convergence of the finite-element analysis. For the transient analysis Newmark scheme is adopted for time discretization. An iterative solution procedure, either Newton-Raphson method or modified Riks/Wempner method, is employed to trace the nonlinear equilibrium path. The latter is also used to perform post-buckling analysis. A variety of numerical examples are presented to demonstrate the validity and efficiency of various elements separately and in combination. The effects of boundary conditions, lamination scheme, transverse shear deformations and geometric nonlinearity on static and transient responses are also investigated. Many of the numerical results of general shell-type structures presented here could serve as references for future investigations. / Ph. D.

The Levy-type analytical solutions in conjunction with the state-space concept are developed for symmetric laminated composite rectangular plates. Combinations of simply-supported, free and clamped boundary conditions are considered. The solutions are obtained for the first-order and higher-order theories in predicting the transverse deflections and stresses. Numerical results are presented for various boundary conditions, aspect ratios, lamination schemes and different loadings. The developments of these theories accomplished in general coordinates allow one to fulfill both the invariance requirements and to derive the relevant equations in any convenient planar systems of coordinates. The dynamic response problems are analyzed in the framework of higher order theories where the effects of transverse normal stress and rotary inertia forces are evaluated. The comparison between the theories as well as previously reported results is reported. / Ph. D. / incomplete_metadata

Directional wave-field decomposition for heterogeneousanisotropic media with in-stantaneous response is establishedfor both the acoustic and the electromagnetic equations. We derive a sufficient condition for ellipticity of thesystem's matrix in the Laplace domain and show that theconstruction of the splitting matrix via a Dunford-Taylorintegral over the resolvent of the non-compact, non-normalsystem's matrix is well de ned. The splitting matrix also hasproperties that make it possible to construct the decompositionwith a generalized eigenvector procedure. The classical way ofobtaining the decomposition is equivalent to solving analgebraic Riccati operator equation. Hence the proceduredescribed above also provides a solution to the algebraicRiccati operator equation. The solution to the wave-field decomposition for theisotropic wave equation is expressed in terms of theDirichlet-to-Neumann map for a plane. The equivalence of thisDirichlet-to-Neumann map is the acoustic admittance, i.e. themapping between the pressure and the particle velocity. Theacoustic admittance, as well as the related impedance aresolutions to algebraic Riccati operator equations and are keyelements in the decomposition. In the electromagnetic case thecorresponding impedance and admittance mappings solve therespective algebraic Riccati operator equations and henceprovide solutions to the decomposition problem. The present research shows that it is advantageous toutilize the freedom implied by the generalized eigenvectorprocedure to obtain the solution to the decomposition problemin more general terms than the admittance/impedancemappings. The time-reversal approach to steer an acoustic wave eld inthe cavity and half space geometries are analyzed from aboundary control perspective. For the cavity it is shown thatwe can steer the field to a desired final configuration, withthe assumption of local energy decay. It is also shown that thetime-reversal algorithm minimizes a least square error forfinite times when the data are obtained by measurements. Forthe half space geometry, the boundary condition is expressedwith help of the wave-field decomposition. In the homogeneousmaterial case, the response of the time-reversal algorithm iscalculated analytically. This procedure uses the one-wayequations together with the decomposition operator.

Estimation of elastic anisotropy, which is usually caused by rock fabrics and mineral orientation, has an important role in exploration seismology and better understanding of crustal seismic reflections. If not properly taken care of during processing steps, it may lead to wrong interpretation or distorted seismic image. In this thesis, a state-of-the-art under the development Laser Doppler Interferometer (LDI) device is used to measure phase velocities on the surface of rock samples from a major deformation zone (Österbybruk Deformation Zone) in the Bergslagen region of eastern Sweden. Then, a general inversion code is deployed to invert measured phase velocities to obtain full elastic stiffness tensors of two samples from the major deformation zone in the study area. At the end, results are used to correct for the anisotropy effects using three dimensionless Tsvankin's parameters and a non-hyperbolic moveout equation. The resulting stacked section shows partial reflection improvement of the deformation zone compared with the isotropic processing section. This suggests that rock anisotropy may also contribute to the generation of reflections from the deformation zones in the study area but requires further investigations.

<p>Directional wave-field decomposition for heterogeneousanisotropic media with in-stantaneous response is establishedfor both the acoustic and the electromagnetic equations.</p><p>We derive a sufficient condition for ellipticity of thesystem's matrix in the Laplace domain and show that theconstruction of the splitting matrix via a Dunford-Taylorintegral over the resolvent of the non-compact, non-normalsystem's matrix is well de ned. The splitting matrix also hasproperties that make it possible to construct the decompositionwith a generalized eigenvector procedure. The classical way ofobtaining the decomposition is equivalent to solving analgebraic Riccati operator equation. Hence the proceduredescribed above also provides a solution to the algebraicRiccati operator equation.</p><p>The solution to the wave-field decomposition for theisotropic wave equation is expressed in terms of theDirichlet-to-Neumann map for a plane. The equivalence of thisDirichlet-to-Neumann map is the acoustic admittance, i.e. themapping between the pressure and the particle velocity. Theacoustic admittance, as well as the related impedance aresolutions to algebraic Riccati operator equations and are keyelements in the decomposition. In the electromagnetic case thecorresponding impedance and admittance mappings solve therespective algebraic Riccati operator equations and henceprovide solutions to the decomposition problem.</p><p>The present research shows that it is advantageous toutilize the freedom implied by the generalized eigenvectorprocedure to obtain the solution to the decomposition problemin more general terms than the admittance/impedancemappings.</p><p>The time-reversal approach to steer an acoustic wave eld inthe cavity and half space geometries are analyzed from aboundary control perspective. For the cavity it is shown thatwe can steer the field to a desired final configuration, withthe assumption of local energy decay. It is also shown that thetime-reversal algorithm minimizes a least square error forfinite times when the data are obtained by measurements. Forthe half space geometry, the boundary condition is expressedwith help of the wave-field decomposition. In the homogeneousmaterial case, the response of the time-reversal algorithm iscalculated analytically. This procedure uses the one-wayequations together with the decomposition operator.</p>

published_or_final_version / Physics / Doctoral / Doctor of Philosophy

Avhandlingen behandlar de teoretiska och praktiska aspekterna av att använda spektrala vinkelupplösta reflektansmätningar för optisk karakterisering av fiberbaserade material såsom papper och kartong. En spektral goniofotometer används för att mäta det reflekterade ljusets vinkelfördelning. En stor del av arbetet utgörs av att utvärdera instrumentets noggrannhet, samt utreda hur de vinkelupplösta mätningarna skall utföras på bästa sätt för att erhålla en så fullständig karakterisering som möjligt. Det reflekterade ljuset består av tre komponenter; ytreflektans, bulkreflektans samt fluorescens. En fullständig karakterisering förutsätter att dessa tre komponenter kan analyseras separat, vilket i detta arbete görs genom nyutvecklade metoder. En metod har utvecklats för separation av ytreflektans och bulkreflektans. Metoden bygger på att analysera hur den totala reflektansen förändras vid ökande absorption i det reflekterande materialet. Absorptionen kontrolleras genom inkjet-tryckning där tryckfärg appliceras på substratet i sådan mängd att bulkreflektansen helt släcks ut. Genom att kombinera mätningar på tryckt och otryckt substrat kan de båda komponenterna separeras. Trots att ytreflektansen från ett matt papper är liten i förhållande till bulkreflektansen, så visar resultaten att den ökar markant med ökande betraktningsvinkel och kan därmed ha stor inverkan på den totala reflektansen. Bidraget från fluorescens kan kvantitativt analyseras genom att kombinera mätningar utförda med respektive utan UV-filter. Vinkelupplösta mätningar och Monte Carlo-simuleringar av fluorescensens vinkelfördelning visar att dess anisotropi är relaterad till det medeldjup vid vilket fluorescensen emitteras. Resultaten förklarar observerade skillnader och motstridigheter i tidigare rapporterade studier kring huruvida fluorescens kan anses vara Lamberskt fördelad. Samtliga goniofotometriska mätningar är utförda med ett kompakt, kommersiellt tillgängligt, dubbelstråleinstrument. För att undersöka instrumentets lämplighet för absoluta reflektansmätningar utförs en analys av dess mätnoggrannhet. Resultaten visar att instrumentets kompakta storlek i kombination med den anisotropa reflektansen från papper introducerar systematiska fel av samma storleksordning som den totala mätnoggrannheten. Dessa fel uppstår på grund av den relativt stora detektorapertur som måste användas vid mätningar av diffus reflektans, vilket är karakteristiskt för papper och kartong. Resultaten visar även att felen är störst vid flacka mätvinklar och för prover med hög grad av anisotropisk reflektans, och en geometrisk korrektionsmetod för denna typ av systematiska fel föreslås. Spektrala och vinkelupplösta mätningar medför per automatik stora mängder mätdata. Genom att använda strålningstransportteori som en matematisk modell för hur ljus sprids i papper kan mätdatat reduceras till en uppsättning beskrivande materialparameterar. Att uppskatta dessa optiska parametrar utifrån vinkelupplösta reflektansmätningar är i sig ett komplicerat problem, vilket dessutom är känsligt för mätfel och val av mätvinklar. Detta inversa problem analyseras i detalj, och speciellt hur valet av mätvinklar kan reduceras utan att försämra förutsättningarna för estimeringen. Simuleringar visar att mätningarna kan begränsas till infallsplanet, eller till och med enbart framåtriktningen, så länge tillräckligt flacka mätvinklar är inkluderade i mätsekvensen. / This thesis is about measuring and modelling light reflected from paper by using goniophotometric measurements. Measuring bidirectional reflectance requires highly accurate instruments, and a large part of the work in this thesis is about establishing the requirements that must be fulfilled to ensure valid data. A spectral goniophotometer is used for measuring the light reflected from paper and methods are developed for analyzing the different components, i.e. the fluorescence, surface reflectance and bulk reflectance, separately. A separation of the surface and bulk reflectance is obtained by inkjet printing and analyzing the total reflectance in the absorption band of the ink. The main principle of the method is to add dye to the paper until the bulk scattered light is completely absorbed. The remaining reflectance is solely surface reflectance, which is subtracted from the total reflectance of the undyed sample to give the bulk reflectance. The results show that although the surface reflectance of a matte paper is small in comparison with the bulk reflectance, it grows rapidly with increasing viewing angle, and can have a large influence on the overall reflectance. A method for quantitative fluorescence measurements is developed, and used for analyzing the angular distribution of the fluoresced light. The long-standing issue whether fluorescence from turbid (or amorphous) media is Lambertian or not, is resolved by using both angle-resolved luminescence measurements and radiative transfer based Monte Carlo simulations. It is concluded that the degree of anisotropy of the fluoresced light is related to the average depth of emission, which in turn depends on factors such as concentration of fluorophores, angle of incident light and the absorption coefficient at the excitation wavelength. All measurements are conducted with a commercially available benchtop sized double-beam spectral goniophotometer designed for laboratory use. To obtain reliable results, its absolute measurement capability is evaluated in terms of measurement accuracy. The results show that the compact size of the instrument, combined with the anisotropic nature of reflectance from paper, can introduce significant systematic errors of the same order as the overall measurement uncertainty. The errors are related to the relatively large detection solid angle that is required when measuring diffusely reflecting materials. Situations where the errors are most severe, oblique viewing angles and samples with high degree of anisotropic scattering, are identified, and a geometrical correction is developed. Estimating optical properties of a material from bidirectional measurements has proved to be a challenging problem and the outcome is highly dependent on both the quality and quantity of the measurements. This problem is analyzed in detail for optically thick turbid media, and the study targets the case when a restricted set of detection angles are available. This is the case when e.g. an unobstructed view of the sample is not possible. Simulations show that the measurements can be restricted to the plane of incidence (in-plane), and even the forward direction only, without any significant reduction in the precision or stability of the estimation, as long as sufficiently oblique angles are included.

Optical filters and thin film optical devices play an important role in Science and Industry. Several significant applications have emerged in optics, microelectronics and computer technology. In this work, we study some aspects of their design and applications. One class of optical fibers, known as Christiansen filters, are based on scattering phenomena in suspensions of solid particles in a liquid medium. Some new scattering filters in the visible and the near UV regions and their performance characteristics are reported here. Feasibility to fabricate such optical filters in solid matrix form is established. Some applications of these scattering filters are discussed. After an introduction to the optics of homogeneous and isotropic thin films, I discuss the general design of anisotropic thin film media and a scheme implemented to calculate their performance. Optical anisotropy, produced by the growth-induced columnar microstructure in thin films and its effects on the performance of optical filters are studied. Large shifts in the peak wavelength of a typical narrow band filter are predicted. Magneto-optical (MO) thin film media of great importance to erasable optical data storage technology are studied. An approximate technique based on a 2 x 2 matrix formalism is developed to calculate the normal incidence performance of these media. To investigate anisotropic effects, to incorporate more than one magnetic film with arbitrary orientations of magnetization, and to study oblique incidence performance, a completely general 4 x 4 matrix technique is implemented in a computer program. Effects of substrate/superstrate birefringence in the read-out signal of MO media are investigated. Several optimizing design criteria, particularly, the effectiveness in employing appropriate metal or dielectric reflector layers are studied. The influence of the plasma edge of metals in enhancing the polar Kerr rotation of MO media is discussed with illustrations. A contour plot of the Kerr rotation and reflectance is developed to help in the design of these media. An explanation is given for the observation of Kerr rotation enhancement near the plasma reflection edge of the reflector layer adjacent to the active MO layer and in general, where the reflectance spectrum shows a steep gradient.

Subduction zone structure and kinematics are topics of ongoing investigation with broadband seismology. Recent advances in experimental observations of mantle materials at high temperatures and pressure, expanded broadband seismic datasets, new seismic analysis methods, and advances in computational modeling are ever increasing our capacity for synthesized investigation of tectonic environments. With the resulting expanded capability for interpretation, the geophysical community is in a position to build more refined and detailed models of subduction zone processes. This study takes part in these advances by refining structural observations of the subducting slab and making new observations of mantle kinematics in a part of the South American subduction zone in Chile and Argentina (between 30 degrees and 36 degrees S). First, I investigate the utility of multiple-event earthquake relocation algorithms for accurate locations using a regional dataset for seismic events in Nevada and then I apply the observations resulting from this study in the determination of new Wadati-Benioff zone seismicity hypocenter locations for the study area in South America. I interpolate new contours of the top of the subducting slab from this seismicity that, when interpreted with focal mechanism solutions for these events, are consistent with its deformation due to slab pull. I use shear wave splitting of teleseismic earthquake waves and s-waves from local earthquakes to characterize mantle strain within the mantle wedge and within and below the subducting slab. From these observations, I conclude that mantle flow in subduction zones is quite responsive to local changes in slab geometry as well as the thermal state of and shear stresses in the mantle wedge.

No description available.