Dissertations / Theses on the topic 'Transverse displacement'

The advantages of Integral Abutment Bridges (IABs) include reduced maintenance costs and increased useful life spans. However, comprehensive and practical analysis tools for design of IABs have not been developed to account for the impacts of thermal displacements on abutment and foundation components, including the components of mechanically stabilized earth (MSE) walls that are often used around the abutment piling. During this research, over 65 three-dimensional numerical analyses were performed to investigate and quantify how different structural and geotechnical bridge components behave during thermal expansion and contraction of the bridge deck. In addition, separate three-dimensional numerical models were developed to evaluate the usefulness of corrugated steel pipes around the abutment piles. The results of this research quantify the influence of design parameter variations on the effects of thermal displacement on system components, and thus provide guidelines for IAB design, where none had existed before. One of the findings is that corrugated steel pipes around abutment piles are not necessary. One of the most important products of this research is an easy-to-use Excel spreadsheet, named IAB v2, that not only quantifies the impact of thermal displacement in the longitudinal direction, but also in the transverse direction when the abutment wall is at a skew angle to the bridge alignment. The spreadsheet accommodates seven different pile sizes, which can be oriented in weak or strong directions, with variable offset of the abutment from the MSE wall and for variable skew angles. The spreadsheet calculates the increment of displacements, forces, moments, and pressures on systems components due to thermal displacement of IABs.<br>Ph. D.

Le travail proposé est le résultat d’une collaboration entre le laboratoire Physique de la matière condensée et nanosciences de Monastir, le laboratoire Laplace de Toulouse et le laboratoire Hubert Curien de Saint-Étienne. Il s’inscrit dans un projet visant à étudier théoriquement la propagation des ondes électromagnétiques dans des dispositifs passifs à base du matériau magnétique anisotrope. La présence d’une couche magnétique dans telle structure a de nombreux avantages : non réciprocité́, performances intéressantes, isolation importante, …Plus précisément, c’est la fabrication des dispositifs non-réciproques tels que les isolateurs et les circulateurs. L’étude théorique d’une telle structure avec plusieurs couches de substrats anisotropes nécessite l’utilisation des logiciels commerciaux. Ces logiciels ont l’avantage de permettre l’étude de structures très complexes, mais ont pour principaux inconvénients leur coût d’achat et capacité́ mémoire nécessaire. C’est pourquoi il est indispensable d’une part de comprendre le comportement des matériaux magnétiques utilisés dans la structure : il s’agit de modéliser le matériau magnétique par un tenseur de perméabilité dépendant de son état d’aimantation. L’objectif de cette thèse est la modélisation électromagnétique par la méthode SDA numérique des structures complexes avec des milieux anisotropes dispersifs. Cette approche, est basé sur le calcul numérique de la fonction de Green spectrale par la méthode de l’opérateur transverse (MOT), sera en mesure d’atteindre un niveau élevé de précision dans la description de l’interaction du signal haute fréquence avec une structure constituée d’un milieu magnétique anisotrope saturé. Les résultats de simulation ont été validés avec d’autres résultats numériques publiés dans la littérature et le logiciel commercial HFSS dans le cas d’une ligne microruban imprimée sur une couche isotrope (diélectrique). Ils ont été numériquement validés avec la littérature pour la même structure mais présence d’un substrat magnétique anisotrope pour différentes directions de polarisation. Ensuite, Ils ont été validés aussi par confrontation avec les résultats expérimentaux pour une ligne coplanaire fabriquée sur un substrat de ferrite-LTCC transversalement aimanté par un champ magnétique statique<br>The work proposed here took place in Hubert Curien Laboratory in collaboration with Laplace Laboratory and Laboratory of Monastir. It is part of a project aiming for the theoretical study of the propagation of the electromagnetic waves inside passive devices fabricated with anisotropic magnetic material. Using a magnetic substrate in such structure has many advantages: non reciprocity, high isolation...More precisely, the fabrication of nonreciprocal de- vice such as isolator and circulator. The numerical study of such structure containing many anisotropic magnetic layers needs to use commercial software. As a principal inconvenience is their purchase cost and their necessary memory capacity. In this case, it is necessary to understand the behavior of the magnetic material used in the structure: it is a question of modeling the magnetic material by a permeability tensor depending on its state of magnetization. The aim of this thesis is the electromagnetic modeling of multilayers structures with complex media using the numerical spectral domain approach. The numerical SDA is based on the numerical computation of the Green’s function with the transverse operator formalism. The numerical results are validated with published numerical data for a microstrip line printed on isotropic or anisotropic magnetic material. They are then compared with an excellent agreement with numerical data provided from software based on the finite elements method (HFSS). For more credibility of our numerical approach, the results of simulation about the complex propagation constant are compared with a good much with measured data for coplanar waveguide fabricated on a low temperature co-fired ceramic (LTCC-ferrite). The validation was done in a large band of frequency from 1 to 12 GHz

Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2017-02-02T16:47:10Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) GEISA GUIMARAES DE ALENCAR.pdf: 2551073 bytes, checksum: 0cec34009ffa04010ce2175cb58b6606 (MD5)<br>Made available in DSpace on 2017-02-02T16:47:10Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) GEISA GUIMARAES DE ALENCAR.pdf: 2551073 bytes, checksum: 0cec34009ffa04010ce2175cb58b6606 (MD5) Previous issue date: 2016-07-12<br>O objetivo deste estudo foi analisar a efetividade da Facilitação Neuromuscular Proprioceptiva (FNP) e da Estabilização Segmentar Vertebral (ESV) na redução da dor, assim como no aumento nas dimensões dos multífidos e transverso do abdome em indivíduos com hérnia de disco lombar. A pesquisa foi do tipo intervencional, comparativo e controlado, aprovada pelo Comitê de Ética em Pesquisa da Universidade Federal de Pernambuco. Participaram indivíduos com idade entre 25 e 50 anos e com hérnia de disco lombar com localização entre L4-L5 e/ou L5-S1, desde que comprovada por ressonância magnética e atestada por um médico. O estudo foi constituído por dois grupos: grupo FNP composto por nove participantes e o grupo de ESV com 12 participantes. Os indivíduos foram submetidos a um exame antropométrico (peso, altura e IMC) e a avaliação da intensidade da dor pela Escala Analógica Visual (EVA) e posteriormente a um exame ultrassonográfico para avaliação do trofismo dos multifidos e do transverso do abdome, através de ultrassom da marca ALOKA 500® e com transdutores de5 MHz e de 7,5 MHz, respectivamente. Cada grupo totalizou 15 atendimentos, sendo realizado por três vezes na semana, com tempo médio de 60 minutos para cada atendimento. No grupo de ESV, a técnica foi executada em três fases: cognitiva, a associativa e a de automatismo. No grupo FNP utilizou-se os padrões: escapular nas diagonais de antero-elevação-póstero-depressão e póstero-elevação-antero-depressão; pélvico na diagonal antero-elevação-póstero-depressão; e de tronco nos movimentos de flexão e extensão, através das técnicas de iniciação rítmica, combinação de isotônicas e reversão dinâmica. Ao final dos 15 atendimentos, todos os instrumentos usados na avaliação foram reutilizados na reavaliação. Nos resultados verificou-se redução da intensidade da dor em todos os participantes, não havendo diferenças entre os grupos após as intervenções (p=0,20), sendo a EVA no final de 1,4 + 1,2 para grupo de ESV e de 2,4 + 2,3 para o grupo FNP. Houve um maior trofismo do transverso do abdome para o grupo ESV (0,9 + 0,1 cm) após a intervenção, quando comparado ao FNP (0,8 + 0,3cm), p=0,02; e uma maior espessura do multífido para o grupo FNP (4,7 + 0,4 cm²) quando comparado ao ESV (3,3 + 0,3 cm), p=0,007. Sendo assim, o estudo mostrou que os dois protocolos são efetivos para a melhora da dor e para o aumento das dimensões dos músculos estabilizadores lombares, porém a ESV se mostrou mais efetiva para o recrutamento do transverso do abdome e a FNP para os multífidos. No entanto, esse resultado precisa ser melhor investigado em relação a persistência a longo prazo.<br>The objective of this study was to analyze the effectiveness of Neuromuscular Facilitation (PNF) and stabilization Segmental Vertebral (ESV) in reducing pain, as well as increasing the size of the multifidus and transversus abdominis in patients with lumbar disc herniation. The research was the interventional type, comparative and controlled, approved by the Ethics Committee of the Federal University of Pernambuco. Participated in individuals aged between 25 and 50 years and with lumbar disc herniation with location between L4-L5 and / or L5-S1, since confirmed by MRI and certified by a doctor. The study consisted of two groups: FNP group of nine participants and the ESV group with 12 participants. The subjects underwent an anthropometric examination (height, weight and BMI) and the assessment of pain intensity by the Visual Analog Scale (VAS) and later to a ultrasonography examination for tropism assessment of the multifidus and transversus abdominis through ultrasound the ALOKA 500® brand and transducers de5 MHz and 7.5 MHz, respectively. Each group totaled 15 sessions, being held three times a week, with an average time of 60 minutes for each service. In the ESV group, the technique was performed in three phases: cognitive, associative and the automatism. In the PNF group standards were used: scapular on the diagonals of anterior-elevation-depression posterolateral and posteromedial high-anterior-depression; pelvic diagonal high-anterior-posterior-depression; and the trunk flexion and extension, through the rhythmic initiation techniques, isotonic and dynamic combination of reversal. At the end of the 15 sessions, all instruments used in the evaluation were reused in the revaluation. These results indicate a reduction in pain intensity for all participants, with no differences between groups after the intervention (p = 0.20), the EVA being at the end of 1.4 + 1.2 for ESV group and 2.4 + 2.3 for the FNP group. There was a higher tropism of the transversus abdominis to the ESV group (0.9 + 0.1 cm) after the intervention compared to the FNP (0.8 + 0.3 cm), p = 0.02; and a thickness greater multifidus for FNP group (4.7 ± 0.4 cm²) compared to ESV (3.3 + 0.3 cm) p = 0.007. Thus, the study showed that the two protocols are effective for improving pain and the increase in the size of the lumbar stabilizer muscles, but the ESV was more effective for the transversus abdominis recruitment and PNF for the multifidus. However, this result must be further investigated with regard to long-term persistence.

FundaÃÃo de Amparo à Pesquisa do Estado do CearÃ<br>Nesta dissertaÃÃo foi estudada a aplicaÃÃo do filtro AcÃstico-Ãptico SintonizÃvel (AOTF), com a ModulaÃÃo de Pulsos por PosiÃÃo (PPM), objetivando implementar, utilizando o mÃtodo de Runge-Kutta de 4a ordem, portas lÃgicas (OR-OU e AND-E) Ãpticas operando com pulsos de luz ultracurtos (2ps). Neste trabalho à investigado o desempenho das portas considerando vÃrios comprimentos do filtro (&#61678; L) que integra a sua estrutura interna, com o intuito de obter o comprimento de filtro mais adequado para uma operaÃÃo satisfatÃria, em regime dispersivo, nÃo linear, sem perdas e com modulaÃÃo de fase cruzada (XPM). Esta investigaÃÃo à realizada em duas situaÃÃes: primeiramente, sÃo considerados filtros com automodulaÃÃo de fase (SPM) e GVD (dispersÃo da velocidade de grupo). Em um segundo momento, as mesmas portas sÃo obtidas com efeitos SPM, XPM e GVD agindo juntos no AOTF. Foi observado que para pulsos do tipo sÃliton, os efeitos da dispersÃo, da nÃo linearidade e da modulaÃÃo de fase cruzada exercem juntos uma forte influÃncia na propagaÃÃo do mesmo, provocando a quebra do pulso na saÃda do dispositivo quando utilizamos um comprimento maior para os filtros. Para dispositivos mais curtos, o pulso chaveado apresentou compressÃes e alargamentos temporais e espectrais, bem comodeslocamentos temporais nos dois modo de propagaÃÃo (TE e TM). ApÃs a escolha de um comprimento de filtro adequado, foi selecionado um deslocamento temporal Ãtimo a ser aplicado nos pulsos de entrada para conseguirmos, na saÃda da porta lÃgica, deslocamentos temporais satisfatÃrios (acertos) na aplicaÃÃo da modulaÃÃo PPM. Em seguida, introduzimos fases em um dos pulsos de entrada (TM), provocando um defasamento entre os pulsos TE e TM, reduzindo ainda mais a margem de erro PPM de operaÃÃo das portas. Finalmente, ao analisarmos as fases aplicadas no pulso TM (0 a 2&#61680;), definirmos o melhor Ãngulo de fase para que as portas operem na regiÃo de acerto da modulaÃÃo PPM.<br>In this dissertation it was studied the application of the Acoustic Optical Tunable Filter (AOTF), with Pulse Position Modulation (PPM), aiming at to implement, using the method of Runge-Kutta of 4a order, logical gates (OR and AND) optical operating with pulses of light ultra shorts (2ps). In this work the acting of the gates is investigated, considering several lengths of the filter ( &#61678; L) that integrates your internal structure, with the intention of obtaining the length of more appropriate filter for a satisfactory operation, in dispersion regime, nonlinear, without losses and with Cross Phase Modulation (XPM). This investigation is accomplished in two situations: firstly, filters are considered with Self Phase Modulation (SPM) and GVD (group-velocity dispersion). In a second moment, the same gates are obtained with effects SPM, XPM and GVD, acting together in AOTF. It was observed that for pulses of the type soliton, the effects of the dispersion, of the nonlinearity and of the cross phase modulation exercise together a strong influences in the propagation of the same, provoking the break of the pulse in the exit of the device when we used a larger length for the filters. For shorter devices, the switched pulse presented temporary and spectral compression and spread, as well as, displacement in the time in the two propagation modes (TE and TM). After the choice of a length of appropriate filter, a great temporary displacement was selected to be applied in the input pulses for us to get, in the exit of the logical gate, satisfactory temporary displacements (successes) in the application of the PPM modulation. Soon after, we introduced phases in one of the entrance pulses (TM), provoking a phase displacement among TE and TM pulses, still reducing more the margin of error PPM of operation of the gates. Finally, to the we analyze the applied phases in the pulse TM (0 to 2&#61680;), we defined the best phase angle for the gates to operate in the success area of the PPM modulation.

碩士<br>國立虎尾科技大學<br>光電與材料科技研究所<br>98<br>Study on the transverse displacement measurement by uses of the critical angle method and a CCD, the technique based on the critical angle method and the use of the image system of CCD is presented. We used an objective with the NA value of 0.7 and the magnification of 100 to enhance the displacement resolution and utilized the critical angle characteristic of a parallelogram prism to improve its image sensitivity. Then, the image from the CCD is resolved and analyzed using a personal computer and the Matlab program to calculated the transverse displacement. It has some advantage, such as, non-contact, non-destructive, non-interfering, and real-time measurement , low cost and sub-micron resolution.

Dispersion has been shown to degrade miscibility in miscible displacements by lowering the concentration of the injected solute at the displacement fronts. Dispersion can also improve oil recovery by increasing sweep efficiency. Either way, dispersion is an important factor in understanding miscible displacement performance. Conventionally, dispersion is measured in the laboratory by fitting the solution of one-dimensional convection-dispersion equation (CDE) to the effluent concentration from a core flood. However dispersion is anisotropic and mixing occurs in both longitudinal and transverse directions. This dissertation uses the analytical solution of the two-dimensional CDE to simultaneously determine longitudinal and transverse dispersion. The two-dimensional analytical solution for an instantaneous finite volume source is used to investigate anisotropic mixing in miscible displacements. We conclude that transverse mixing becomes significant with large a concentration gradient in the transverse direction and significant local variation in flow directions owing to heterogeneity. We also utilized simulation models similar to Blackwell's (1962) experiments to determine transverse dispersion. This model coupled with the analytical solution for two-dimensional CDE for continuous injection source is used to determine longitudinal and transverse dispersivity for the flow medium. The validated model is used to investigate the effect of heterogeneity and other first contact miscible (FCM) scaling groups on dispersion. We derive the dimensionless scaling groups that affect FCM displacements and determine their impact on dispersion. Experimental design is used to determine the impact and interactions of significant scaling groups and generate a response surface function for dispersion based on the scaling groups. The level of heterogeneity is found to most significantly impact longitudinal dispersion, while transverse dispersion is most significantly impacted by the dispersion number. Finally, a mathematical procedure is developed to use the estimated dispersivities to determine a-priori the maximum grid-block size to maintain an equivalent level of dispersion between fine-scale and upscaled coarse models. Non-uniform coarsening schemes is recommended and validated for reservoir models with sets of different permeability distributions. Comparable sweep and recovery are observed when the procedure was extended to multi-contact miscible (MCM) displacements.<br>text

碩士<br>逢甲大學<br>材料與製造工程所<br>97<br>The thermal spray technology gives the advantage of providing fast forming and high quality protective coating on products. This technology can be used to improve the physical or mechanical property of the product surface that extends the product life. The materials which be used with the thermal spray technology include pottery, metal, cermets, macromolecule and composite, etc. In order to optimize the product, the manufacturing parameters need to be adjusted and the new coating technology needs to be developed. Besides, it is more important to understand the mechanical property of the spray product in order to prevent producing defective products during manufacture production and to determine the cause of defects. The primary study of this thesis is an experiment, which is conducted by combining Dial indicator and four-point bending test to investigate the transverse displacements and interface shearing stress of the spray films coated on a beam sample. Four-point bending test is an approach for measuring transverse deformation of a beam which is under pure bending external loading. Finite element method is used to analyze the transverse deformations and Hsu''s theory is also applied for the theoretical solution. Therefore, a comparison analysis will be conducted on the acquired data to determine the significant relationship between the results from those methods. The theoretical solution method can also be conducted to obtain the interface shearing stress. The results of these analyses can be used during the product''s pre-construction stage to confirm if the spray parameter is in accordance with the quality demand. The experimental results show that under the different loads, the linear distribution of deformation is similar between the combination of Dial indicator and four-point bending test and the numerical analysis. Through the theoretical solution method of spray films in different loads of the interface shear stress analysis, it can be found that both ends of the coating area are the zones which carry the maximum shearing stress.

碩士<br>國立聯合大學<br>土木與防災工程學系碩士班<br>97<br>Based on the theory of elasticity, the solutions of displacements and stresses subjected to a vertical point load in an inclined transversely isotropic full-space, are generated in this thesis. The generalized Hooke’s law, the strain-displacement relationships, and the equilibrium equations are integrated to constitute the government equations. The analytical solutions are derived by performing the double Fourier integral transforms, the variation of parameters, and co-operating the relative boundary conditions at infinity, the integral expressions of displacement and stress in the Fourier transformed domain can be obtained. Then, the double inverse Fourier integral transforms and residue calculus are utilized to integrate the contours. The present solutions demonstrate that the displacements and stresses are profoundly influenced by the following factors: (1) the rotation of the transversely isotropic planes (??, (2) the type and degree of material anisotropy (specified by , , and ), (3) the geometric positions (x, y, z). The proposed solutions are identical with the existing ones if ?淂0. Eventually, a parametric study is conducted to elucidate the influence of aforementioned factors on the non-dimensional displacements and non-dimensional stresses. Computed results reveal that the induced displacements and stresses in the inclined isotropic/transversely isotropic soils caused by a vertical point load are quite different from those by using the previous solutions (?淂0). Hence, the dip at an angle of inclination should be rigorously considered in estimating the displacements and stresses for an inclined transversely isotropic medium owing to applied loads.

碩士<br>國立聯合大學<br>土木與防災工程學系碩士班<br>99<br>Based on the theory of elasticity, the solutions of displacements and stresses subjected to a 3D point load in a vertical transversely isotropic half-space are generated in this thesis. The stress-strain relationships, the displacement-strain relationships, and the equilibrium equations are integrated to constitute the government equations. The analytical solutions are derived by performing the double Fourier integral transforms, and the variation of parameters. Co-operating the boundary conditions at infinity, the integral expressions of displacement in the full-space of Fourier transformed domain can be obtained. Then, replacing the co-ordinate z of the general and homogeneous solutions in the full-space by z-h, the particular and homogeneous solutions to constitute the general solution of the half-space can be constructed. Sequentially, applying the stress free surface boundary conditions (z=0,σzz=τyz=τzx=0), the three undetermined coefficients can be obtained. Eventually, the double inverse Fourier integral transforms and residue calculus are utilized to integrate the contours. The parametric study reveals that the vertical displacement owing to the point load in the full-space is equal to Yang’s solution (2009) when the dip angle of stratum is 90°. The vertical displacement in the half-space is the identical with Mindlin’s solution (1936) when the medium is isotropic. However, the calculated values have trace imaginary numbers when the half-space is vertical transversely isotropic. The present solution is compared with Dai’s solution (2010), and it is found that her solution also have the same problem. In addition, Dai’s (2010) solution has no trend for the vertical displacement should decrease as increasing of z when x and y are fixed. As for the obtained results have trace imaginary numbers might be induced by the huge operation in this study. Furthermore, the characteristic equation contains imaginary numbers in the radical, and it could cause errors during the numerical calculations. Therefore, a further investigation on this topic is required.

博士<br>國立交通大學<br>土木工程學系<br>97<br>Three-dimensional fundamental solutions of displacements and stresses due to three-dimensional point loads in a transversely isotropic material, where the planes of transverse isotropy are inclined with respect to the horizontal loading surface, are presented in this thesis. Generally, the governing equations for infinite or semi-infinite solids are partial differential equations. The Fourier and Laplace integral transforms are commonly two efficient methods for solving the corresponding boundary value problems of full or half space. Employing the Fourier transform, the partial differential equations can be simplified as ordinary differential equations (ODE). Then, three distinct approaches were used to solve the ODE and the solutions were presented for both infinite and semi-infinite solids in this thesis. Firstly, we solve traditionally the nonhomogeneous ordinary differential equations by the methods of undetermined coefficients and separate variables Secondly, the method of an imaginary space was proposed for deriving the solutions of the problems. Thirdly, the method of algebraic is adopted for deriving the solutions for both full space and half space problems. Finally, the present fundamental solutions are derived by performing the required triple inverse Fourier transforms, or double inverse Fourier and Laplace transforms. These transformations are powerful to generate the displacements and stresses resulting from the three-dimensional point loads, acting in an inclined transversely isotropic material. The yielded solutions demonstrate that the displacements and stresses are profoundly influenced by: (1) the rotation of the transversely isotropic planes (??, (2) the type and degree of material anisotropy (E/E?S, ????S, G/G?S), (3) the geometric position (r, ?? ??, and (4). the types of three-dimensional loading (Px, Py, Pz). The proposed solutions are exactly the same as those of Wang and Liao (1999) if the full-space is homogeneous, linearly elastic, and the planes of transversely isotropy are parallel to the horizontal loading surface. Additionally, a parametric study is conducted to elucidate the influence of the above-mentioned factors on the displacements and stresses. Computed results reveal that the induced displacements and stresses in the planes of transversely isotropic are parallel to the horizontal loading surface of isotropic/transversely isotropic rocks by a vertical point load are quite different from those from Wang and Liao (1999). Therefore, in the fields of practical engineering, the dip at an angle of inclination should be taken into account in estimating the displacements and stresses in a transversely isotropic rock subjected to applied loads.

碩士<br>國立聯合大學<br>防災科技研究所<br>95<br>Based on the theory of elasticity, this thesis derives the fundamental solutions of displacements and stresses due to horizontal and vertical line loads acting on an inhomogeneous plane strain orthotropic medium with Young’s moduli (E, E'), and shear modulus (G') varying exponentially with depth. The government equations can be obtained by combining the generalized Hooke’s law, the strain-displacement relationships, and the equilibrium equations. Then, utilizing the Fourier integral transforms, the governing equations can be transformed into ordinary differential equations. Additionally, by using the variation of parameters in cooperation with the boundary conditions at infinity, the fundamental solutions of displacements in the Fourier domain can be yielded. However, the stress solutions in the same domain also can be acquired by employing the stress-strain-displacement relationships. Eventually, performing the inverse Fourier transforms and writing some numerical integration programs in FORTRAN language, the displacements and stresses induced by horizontal and vertical line loads can be calculated. The solutions indicate that the displacements and stresses are profoundly influenced by following factors (1) the inhomogeneous parameter (k), (2) the type and degree of material anisotropy (E/E', G'/E', ν/ν'), (3) the types of loading (Px, Pz), and (4) the adopted nondimensional horizontal distance. The proposed solutions are identical with those of Wang and Liao (1999) if the full-space is a homogeneous plane strain orthotropic medium. A series of parametric study is conducted to demonstrate the presented solutions, and to elucidate the effect of aforementioned factors on the vertical normal stress. The results reveal that the estimations of displacements and stresses should be taken the effect of inhomogenity into account when the anisotropic soil mass/rock mass subjected to applied loads.

碩士<br>國立交通大學<br>土木工程系<br>90<br>Based on the theory of anisotropic elasticity, the solutions of displacements and stresses in nonhomogrneous and transversely isotropic full/half spaces subjected to a point load are presented in this thesis. The plane of transversely isotropy is assumed to be parallel to the horizontal loading surface. Three elastic constants 、 、 in the form of exponential increase with the increase of depth. The derved solutions can be simplified to campare with those existed solutions of homogeneous and transversely isotropic full/half spaces. Besides, a series of parametric study was conducted to investigate the degree of nonhomogeneity on the distributions of displacements and stresses induced by the applied point load in the isotropic/transversely isotropic full/half spaces.

碩士<br>國立交通大學<br>土木工程學系<br>99<br>The failure of a foundation in soil/rock is often caused by over loading or large displacements. This fact is particularly important to analyze stresses and displacements when structures impose very large loads on the underlying soil/rock. However, it is also important for understanding the influence of the "anisotropy" of soil/rock on stresses, strains and displacements. Based on the orientation of geological structures or direction of planes of elastic symmetry, Elastic materials can be divided into general anisotropic, orthogonal or transversely isotropic materials. The nature of anisotropy of soils/rocks is caused by depositing via sedimentation over a long period of time, cutting by regular discontinuities, such as cleavages, foliations, stratifications and joints. Anisotropic soils/rocks are commonly modeled as transversely isotropic materials based on the practical engineering considerations. Nevertheless, the inclination of planes of elastic symmetry is not always horizontal, and hence, this thesis extending the approach proposed by Hu (2009) to study the closed form solutions for displacements in an half space with vertical transversely isotropy subjected to a surface 3D point load. To obtain the closed form solutions, the double Fourier transform was used to reduce the partial differential equations to ordinary differential equations, firstly. Then, the solutions of displacement and stress in Fourier domain can be determinednd from the boundary conditions. Finally, the closed form solutions for stresses and displacements in a vertical transversely isotropic half space material subjected to a 3D point load can be obtained using the double inverse Fourier transform and residue theorem. The present closed-form solutions demonstrate that the material anisotropy could affect the displacements and stresses in a vertical transversely isotropy. The illustrative examples show that the calculated displacements in a horizontal transversely isotropic half space are the same/similar as those presented by Hu (2009) and Ding et, al., (2006). Hence, the closed form solutions for stresses and displacements in a vertical transversely isotropic half space can be reasonably solved if the all of residue of integrals in the inverse Fourier domain can be determined exactly.

Герасимова Д. С. Математична модель гомогенізації композиційного матеріалу на основі енергетичних умов узгодження : кваліфікаційна робота магістра спеціальності 111 "Математика" / наук. керівник М. І. Клименко. Запоріжжя : ЗНУ, 2020. 86 с.<br>UA : Робота викладена на 86 сторінках друкованого тексту, містить 2 рисунка, 2 таблиці, 12 джерел, 2 додатки. Об’єкт дослідження: методика визначення ефективного поздовжнього модуля пружності в’язкопружного композиту. Мета роботи: визначення ефективних характеристик інтегрального оператора поздовжнього модуля пружності для в’язкопружного трансверсально-ізотропного композитного матеріалу, що складається з в’язкопружної трансверсально-ізотропної матриці та пружного трансверсально-ізотропного волокна. Метод дослідження: операційний. У даній роботі пропонується ознайомитися з основними принципами математичного моделювання властивостей в’язкопружних трансверсально-ізотропних композитів. Для цього було розглянуто особливості застосування інтегрального перетворення Лапласа до дослідження лінійної моделі спадковості для в’язкопружного середовища. Застосовано методику визначення ефективного поздовжнього модуля пружності для в’язкопружного композита, що ґрунтується на використанні кінематичних умов узгодження, для знаходження характеристик відповідного інтегрального оператора. Було визначено ефективний поздовжній модуль пружності трансверсально- ізотропного композиту з використанням енергетичного критерію узгодження деформування матриці, волокна та однорідного композиту.<br>EN : The work is presented on 86 pages of printed text, 2 figures, 2 tables, 12 references, 2 supplements. The object of the study is methodology for identifying the effective spring module of elasticity in a viscoelastic composite. The aim of the study is identifying the effective characteristics of the integral operator of the spring module of elasticity for a viscoelastic transverse isotropic composite material, which can be stored in a viscoelastic transverse isotropic matrix and a spring transversal isotropic fiber. The methods of research is operating. In this study we propose to get acquainted with the basic principles of mathematical modeling of the properties of viscoelastic transversal isotropic composites. For this purpose, the peculiarities of applying the Laplace integral transform to the study of a linear model of heredity for a viscoelastic medium were considered. We applied the technique for determining the effective spring modulus of elasticity for a viscoelastic composite based on the kinematic matching conditions for finding the characteristics of the corresponding integral operator. An effective spring modulus of elasticity of the transversely isotropic composite was determined using the energy criterion for the deformation of the matrix.