Famous problems of elementary geometry; the duplication of the cube, the trisection of an angle; the quadrature of the circle;

Lettered on cover: Problems in geometry. Beman and Smith. 1922.

Cognitive models for the concept of angle

Tese de doutoramento em Filosofia

An approach for reliability-based robust design optimisation of angle-ply composites

Variations of manufacturing process parameters and environmental aspects may affect the quality and performance of composite materials, which consequently affects their structural behaviour. Reliability-based design optimisation (RBDO) and robust design optimisation (RDO) searches for safe structural systems with minimal variability of response when subjected to uncertainties in material design parameters. An approach that simultaneously considers reliability and robustness is proposed in this paper. Depending on a given reliability index imposed on composite structures, a trade-off is established between the performance targets and robustness. Robustness is expressed in terms of the coefficient of variation of the constrained structural response weighted by its nominal value. The Pareto normed front is built and the nearest point to the origin is estimated as the best solution of the bi-objective optimisation problem.

Influence of Angle of Air Injection and Particles in Bed Hydrodynamics of Swirling Fluidized Bed

The thesis presented here unveils an experimental study of the hydrodynamic characteristics of swirling fluidized bed viz. pressure drop across the distributor and the bed, minimum fluidizing velocity, bed behaviour and angle of air injection. In swirling fluidized bed the air is admitted to the bed at an angle 'Ѳ' to the horizontal. The vertical component of the velocity v sin Ѳ causes fluidization and the horizontal component v cos Ѳ contributes to swirl motion of the bed material.The study was conducted using spherical particles having sizes 3.2 mm, 5.5 mm & 7.4 mm as the bed materials. Each of these particles was made from high density polyethylene, nylon and acetal having relative densities of 0.93, 1.05 and 1.47 respectively.The experiments were conducted using conidour type distributors having four rows of slits. Altogether four distributors having angles of air injection (Φ)- 0°, 5°, 10° & 15° were designed and fabricated for the study. The total number of slits in each distributor was 144. The area of opening was 6220 mm2 making the percentage area of opening to 9.17. But the percentage useful area of opening of the distributor was 96.The experiments on the variation of distributor pressure drop with superficial velocity revealed that the distributor pressure drop decreases with angle of air injection. Investigations related to bed hydrodynamics were conducted using 2.5 kg of bed material. The bed pressure drop measurements were made along the radial direction of the distributor at distances of 60 mm, 90 mm, 120 mm & 150 mm from the centre of the distributor. It was noticed that after attaining minimum fluidizing velocity, the bed pressure drop increases along the radial direction of the distributor. But at a radial distance of 90 mm from the distributor centre, after attaining minimum fluidizing velocity the bed pressure drop remains almost constant. It was also observed that the bed pressure drop varies inversely with particle size as well as particle density.An attempt was made to determine the effect of various parameters on minimum fluidizing velocity. It was noticed that the minimum fluidizing velocity varies directly with angle of air injection (Φ), particle size and particle density.The study on the bed behaviour showed that the superficial velocity required for initiating various bed phenomena (such as swirl motion and separation of particles from the cone at the centre) increase with increase in particle size as well as particle density. It was also observed that the particle size and particle density directly influence the superficial velocity required for various regimes of bed behaviour such as linear variation of bed pressure drop, constant bed pressure drop and sudden increase or decrease in bed pressure drop.Experiments were also performed to study the effect of angle of air injection (Φ). It was noticed that the bed pressure drop decreases with angle of air injection. It was also noticed that the angle of air injection directly influence the superficial velocity required for initiating various bed phenomena as well as the various regimes of bed behaviour.

Evaluation of angle-dependent absorption: Computer simulation and listening test for an objective and subjective evaluation

The aim of this thesis is the subjective and objective evaluation of angledependent absorption coefficients. As the assumption of a constant absorption coefficient over the angle of incidence is not always held, a new model acknowledging an angle-dependent reflection must be considered, to get a more accurate prediction in the sound field. The study provides information about the behavior of different materials in several rooms, depending on the reflection modeling of incident sound waves. An objective evaluation was run for an implementation of angle-dependent reflection factors in the image source and ray tracing simulation models. Results obtained were analysed after comparison to diffuse-field averaged data. However, changes in acoustic characteristics of a room do not always mean a variation in the listener’s perception. Thus, additional subjective evaluation allowed a comparison between the different results obtained with the computer simulation and the response from the individuals who participated in the listening test. The listening test was designed following a three-alternative forced-choice (3AFC) paradigm. In each interaction asked to the subjects a sequence of either three pink noise bursts or three natural signals was alternated. These results were supposed to show the influence and perception of the two different ways to implement surface reflection –either with diffuse or angle-dependent absorption properties. Results show slightly audible effects when material properties were exaggerated. El objetivo de este trabajo es la evaluación objetiva y subjetiva del coeficiente de absorción en función del ángulo de incidencia de la onda de sonido. La suposición de un coeficiente de absorción constante con respecto al ángulo de incidencia no siempre se sostiene. Por ello, un nuevo modelo considerando la reflexión dependiente del ángulo se debe tener en cuenta para obtener predicciones más certeras en el campo del sonido. El estudio proporciona información sobre el comportamiento de diferentes materiales en distintos recintos, dependientes del modelo de reflexión de las ondas de sonido incidentes. Debido a las dificultades a la hora de realizar las medidas y, por lo tanto, a la falta de datos, los coeficientes de absorción dependientes del ángulo a menudo no se tienen en cuenta a la hora de realizar las simulaciones. Hoy en día, aún no hay una tendencia de aplicar el coeficiente de absorción dependiente del ángulo para mejorar los modelos de reflexión. Por otra parte, para una medición satisfactoria de la absorción dependiente del ángulo, sólo hay unos pocos métodos. Las técnicas de medición actuales llevan mucho tiempo y hay algunos materiales, condiciones y ángulos que no pueden ser reproducidos y, por lo tanto, no es posible su medición. Sin embargo, en el presente estudio, los ángulos de incidencia de las ondas de sonido son conocidos y almacenados en una de base de datos para cada uno de los materiales, de modo que los coeficientes de absorción para el ángulo dado pueden ser devueltos siempre que sean requeridos por el usuario. Para realizar el estudio se llevó a cabo una evaluación objetiva, por medio de la implementación del factor de reflexión dependiente del ángulo en los modelos de fuentes imagen y trazado de rayos. Los resultados fueron analizados después de ser comparados con el promedio de los datos obtenidos en medidas en el campo difuso. La simulación se hizo una vez se configuraron un número de materiales creados por el autor, a partir de los datos existentes en la literatura y los catálogos de fabricantes. Los modelos de Komatsu y Mechel sirvieron como referencia para los materiales porosos, configurando la resistividad al aire o el grosor, y para los paneles perforados, introduciendo el radio de los orificios y la distancia entre centros, respectivamente. Estos materiales se situaban en la pared opuesta a la que se consideraba que debía alojar a la fuente sonora. El resto de superficies se modelaban con el mismo material, variando su coeficiente de absorción y/o de dispersión. Al mismo tiempo, una serie de recintos fueron modelados para poder reproducir distintos escenarios de los que obtener los resultados. Sin embargo, los cambios en las características acústicas de un recinto no significan variaciones en la percepción por parte del oyente. Por ello, una evaluación subjetiva adicional permitió una comparación entre los diferentes resultados obtenidos mediante la simulación informática y la respuesta de los individuos que participaron en la prueba de escucha. Ésta fue diseñada bajo las pautas del modelo de test three-alternative forced-choice (3AFC), con treinta y dos preguntas diferentes. En cada iteración los sujetos fueron preguntados por una secuencia alterna entre tres señales, siendo dos de ellas iguales. Éstas podían ser tanto ráfagas de ruido rosa como señales naturales, en este test se utilizó un fragmento de una obra clásica interpretada por un piano. Antes de contestar al cuestionario, los bloques de preguntas eran ordenados al azar. Para cada ensayo, la mezcla era diferente, así los sujetos no repetían la misma prueba, evitando un sesgo por efectos de aprendizaje. Los bloques se barajaban recordando siempre el orden inicial, para después almacenar los resultados reordenados. La prueba de escucha fue realizada por veintitrés personas, toda ellas con conocimientos dentro del campo de la acústica. Antes de llevar a cabo la prueba de escucha en un entorno adecuado, una hoja con las instrucciones fue facilitada a cada persona. Los resultados muestran la influencia y percepción de las dos maneras distintas de implementar las reflexiones de una superficie –ya sea con respecto a la propiedad de difusión o de absorción dependiente del ángulo de los materiales. Los resultados objetivos, después de ejecutar las simulaciones, muestran los datos medios obtenidos para comprender el comportamiento de distintos materiales de acuerdo con el modelo de reflexión utilizado en el caso de estudio. En las tablas proporcionadas en la memoria se muestran los valores del tiempo de reverberación, la claridad y el tiempo de caída temprana. Los datos de las características del recinto obtenidos en este análisis tienen una fuerte dependencia respecto al coeficiente de absorción de los diferentes materiales que recubren las superficies del cuarto. En los resultados subjetivos, la media de percepción, a la hora de distinguir las distintas señales, por parte de los sujetos, se situó significativamente por debajo del umbral marcado por el punto de inflexión de la función psicométrica. Sin embargo, es posible concluir que la mayoría de los individuos tienden a ser capaces de detectar alguna diferencia entre los estímulos presentados en el 3AFC test. En conclusión, la hipótesis de que los valores del coeficiente de absorción dependiente del ángulo difieren es contrastada. Pero la respuesta subjetiva de los individuos muestra que únicamente hay ligeras variaciones en la percepción si el coeficiente varía en intervalos pequeños entre los valores manejados en la simulación. Además, si los parámetros de los materiales acústicos no son exagerados, los sujetos no perciben ninguna variación. Los primeros resultados obtenidos, proporcionando información respecto a la dependencia del ángulo, llevan a una nueva consideración en el campo de la acústica, y en la realización de nuevos proyectos en el futuro. Para futuras líneas de investigación, las simulaciones se deberían realizar con distintos tipos de recintos, buscando escenarios con geometrías irregulares. También, la implementación de distintos materiales para obtener resultados más certeros. Otra de las fases de los futuros proyectos puede realizarse teniendo en cuenta el coeficiente de dispersión dependiente del ángulo de incidencia de la onda de sonido. En la parte de la evaluación subjetiva, realizar una serie de pruebas de escucha con distintos individuos, incluyendo personas sin una formación relacionada con la ingeniería acústica.

Traverse tables; computed to 4 places decimals for every ́of angle up to 100 distance. For the use of surveyors and engineers.

Mode of access: Internet.

Study of the uncertainty of angle measurement for a rotary-laser automatic theodolite (R-LAT)

This paper shows how the angular uncertainties can be determined for a rotary-laser automatic theodolite of the type used in (indoor-GPS) iGPS networks. Initially, the fundamental physics of the rotating head device is used to propagate uncertainties using Monte Carlo simulation. This theoretical element of the study shows how the angular uncertainty is affected by internal parameters, the actual values of which are estimated. Experiments are then carried out to determine the actual uncertainty in the azimuth angle. Results are presented that show that uncertainty decreases with sampling duration. Other significant findings are that uncertainty is relatively constant throughout the working volume and that the uncertainty value is not dependent on the size of the reference angle. © 2009 IMechE.

De undecimo Euclidis axiomate iudicium cui accedunt pauca De trisectione anguli /

"In certamine litterario civium Academiae Ienensis die VI septembris MDCCCXXIII praemio principum munificentia constituto ex sententia illustris philosophorum ordinis ornatum."

Uncertainty analysis based on sensitivity applied to angle-ply composite structures

This article describes a finite element-based formulation for the statistical analysis of the response of stochastic structural composite systems whose material properties are described by random fields. A first-order technique is used to obtain the second-order statistics for the structural response considering means and variances of the displacement and stress fields of plate or shell composite structures. Propagation of uncertainties depends on sensitivities taken as measurement of variation effects. The adjoint variable method is used to obtain the sensitivity matrix. This method is appropriated for composite structures due to the large number of random input parameters. Dominant effects on the stochastic characteristics are studied analyzing the influence of different random parameters. In particular, a study of the anisotropy influence on uncertainties propagation of angle-ply composites is carried out based on the proposed approach.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.

Angle Parking on Iowa's Low Volume Primary Extentions in Small Towns, January 2003

On-street parking has been considered problematic by engineers for many years. In fact, numerous studies have concluded that diagonal or angle parking in particular is potentially more of a safety concern than parallel or no parking at all. It is a common position of many states, including Iowa, to discourage or completely prohibit angle parking on primary road extensions in urban areas. However, with the acceptance of “context sensitive design” and traffic calming techniques, policies for on-street parking are receiving re -consideration in many agencies including the FHWA. This study was undertaken to analyze operational and safety histories in the state of Iowa where various types of on-street parking have existed for many years, concentrating in particular on smaller communities. Specifically of interest was a comparison of diagonal parking locations to other types with regard to related crash histories. If possible, it was intended to develop guidelines to assist Iowa Department of Transportation designers in the consideration of parking requirements for road improvements through small communities. In this regard, several criteria were analyzed to determine possible contribution to crash history including road width, clearance to parked vehicles, traffic volumes, community population, and length of parking area. None of these factors, with the possible exception of population, displayed a clearly definable relationship to crash history. However, when average crash rates for various parking types were compared for non-intersection crashes, differences in rates between areas with diagonal parking and those with parallel parking were almost negligible. In fact, those observed rates were less than sample locations with no parking at all. These results seem to indicate that indeed there may exist no compelling justification for blanket prohibition of angle parking along Iowa’s primary extensions in all urban areas. Rather, a case-by-case investigation with each project design of the most applicable parking type would seem appropriate in smaller communities.

Strengthening of Existing Single Span Steel Beam and Concrete Deck Bridges, HR-238, Part 1, 1983

The Phase I research, Iowa Department of Transportation (IDOT) Project HR-214, "Feasibility Study of Strengthening Existing Single Span Steel Beam Concrete Deck Bridges," verified that post-tensioning can be used to provide strengthening of the composite bridges under investigation. Phase II research, reported here, involved the strengthening of two full-scale prototype bridges - one a prototype of the model bridge tested during Phase I and the other larger and skewed. In addition to the field work, Phase II also involved a considerable amount of laboratory work. A literature search revealed that only minimal data existed on the angle-plus-bar shear connectors. Thus, several specimens utilizing angle-plus-bar, as well as channels, studs and high strength bolts as shear connectors were fabricated and tested. To obtain additional shear connector information, the bridge model of Phase I was sawed into four composite concrete slab and steel beam specimens. Two of the resulting specimens were tested with the original shear connection, while the other two specimens had additional shear connectors added before testing. Although orthotropic plate theory was shown in Phase I to predict vertical load distribution in bridge decks and to predict approximate distribution of post-tensioning for right-angle bridges, it was questioned whether the theory could also be used on skewed bridges. Thus, a small plexiglas model was constructed and used in vertical load distribution tests and post-tensioning force distribution tests for verification of the theory. Conclusions of this research are as follows: (1) The capacity of existing shear connectors must be checked as part of a bridge strengthening program. Determination of the concrete deck strength in advance of bridge strengthening is also recommended. (2) The ultimate capacity of angle-plus-bar shear connectors can be computed on the basis of a modified AASHTO channel connector formula and an angle-to-beam weld capacity check. (3) Existing shear connector capacity can be augmented by means of double-nut high strength bolt connectors. (4) Post-tensioning did not significantly affect truck load distribution for right angle or skewed bridges. (5) Approximate post-tensioning and truck load distribution for actual bridges can be predicted by orthotropic plate theory for vertical load; however, the agreement between actual distribution and theoretical distribution is not as close as that measured for the laboratory model in Phase I. (6) The right angle bridge exhibited considerable end restraint at what would be assumed to be simple support. The construction details at bridge abutments seem to be the reason for the restraint. (7) The skewed bridge exhibited more end restraint than the right angle bridge. Both skew effects and construction details at the abutments accounted for the restraint. (8) End restraint in the right angle and skewed bridges reduced tension strains in the steel bridge beams due to truck loading, but also reduced the compression strains caused by post-tensioning.

Electromyographic study of the temporal, masseter and suprahyoid muscles in the mandibular rest position

The temporal muscles (anterior position), and the masseter and suprahyoid muscles were studied electromyographically in 15 subjects with ages ranging from 18 to 35 years, showing normal occlusion (Class I of angle), complete dentition and no dysfunction of the stomatognathic system. The volunteers sat comfortably in a chair, keeping the Frankfurt plane parallel to the boor; the muscles were analysed in the mandibular resting position through a number of stages: with minimum exteroceptive stimuli, relaxation with soft music, abolition of the intrabuccal negative pressure through a plastic tube, stress provoked by an electronic game, disocclusion of posterior teeth using the occlusal splint and finally withdrawal of this device. The electromyographic results were analysed statistically. The samples, were analysed for all of the frequencies of motor units, in a 1-min period. It was found that there were statistically significant difference between the relaxation stages as compared with the withdrawal of negative intraoral pressure and mainly with the stress phase, being this only on the suprahyoid muscles, with 5% significance.

Avaliação das dimensões e relacionamentos dos arcos dentários no tratamento da má-oclusão classe II, divisão 1 de Angle com aparelho bionator de Balters

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)