Two-dimensional mesh optimization in the finite element method

The solution to the problem of finding the optimum mesh design in the finite element method with the restriction of a given number of degrees of freedom, is an interesting problem, particularly in the applications method. At present, the usual procedures introduce new degrees of freedom (remeshing) in a given mesh in order to obtain a more adequate one, from the point of view of the calculation results (errors uniformity). However, from the solution of the optimum mesh problem with a specific number of degrees of freedom some useful recommendations and criteria for the mesh construction may be drawn. For 1-D problems, namely for the simple truss and beam elements, analytical solutions have been found and they are given in this paper. For the more complex 2-D problems (plane stress and plane strain) numerical methods to obtain the optimum mesh, based on optimization procedures have to be used. The objective function, used in the minimization process, has been the total potential energy. Some examples are presented. Finally some conclusions and hints about the possible new developments of these techniques are also given.

Analytical bearing capacity of strip footing in weightless materials with power-law failure criteria

Sokolovskii’s method of characteristics is extended to provide analytical solutions for the ultimate load at the moment of plastic failure under plane-strain conditions of shallow strip foundations on weightless rigid-plastic media with a noncohesive power-law failure envelope. The formulation is made parametrically in terms of the instantaneous friction angle, and the key idea to obtain the bearing capacity is that information can be transmitted from the free surface (where external loads are known) to the contact plane of the foundation. The methodology can consider foundations adjacent to a slope, external surcharges at the free surface, and inclined loads (both on the slope and on the foundation). Sensitivity analyses illustrate the influence on bearing capacity of changes in the different geometrical parameters involved. An application example is presented and design plots are provided, and model predictions are compared with results of bearing capacity tests under low gravity.

Development and Testing of a Fiber Bragg Grating Strain Sensor for Uniaxial Compression of Rock Specimens

Los sensores de fibra óptica son una tecnología que ha madurado en los últimos años, sin embargo, se requiere un mayor desarrollo de aplicaciones para materiales naturales como las rocas, que por ser agregados complejos pueden contener partículas minerales y fracturas de tamaño mucho mayor que las galgas eléctricas usadas tradicionalmente para medir deformaciones en las pruebas de laboratorio, ocasionando que los resultados obtenidos puedan ser no representativos. En este trabajo fueron diseñados, fabricados y probados sensores de deformación de gran área y forma curvada, usando redes de Bragg en fibra óptica (FBG) con el objetivo de obtener registros representativos en rocas que contienen minerales y estructuras de diversas composiciones, tamaños y direcciones. Se presenta el proceso de elaboración del transductor, su caracterización mecánica, su calibración y su evaluación en pruebas de compresión uniaxial en muestras de roca. Para verificar la eficiencia en la transmisión de la deformación de la roca al sensor una vez pegado, también fue realizado el análisis de la transferencia incluyendo los efectos del adhesivo, de la muestra y del transductor. Los resultados experimentales indican que el sensor desarrollado permite registro y transferencia de la deformación fiables, avance necesario para uso en rocas y otros materiales heterogénos, señalando una interesante perspectiva para aplicaciones sobre superficies irregulares, pues permite aumentar a voluntad el tamaño y forma del área de registro, posibilita también obtener mayor fiabilidad de resultados en muestras de pequeño tamaño y sugiere su conveniencia en obras, en las cuales los sistemas eléctricos tradicionales tienen limitaciones. ABSTRACT Optical fiber sensors are a technology that has matured in recent years, however, further development for rock applications is needed. Rocks contain mineral particles and features larger than electrical strain gauges traditionally used in laboratory tests, causing the results to be unrepresentative. In this work were designed, manufactured, and tested large area and curved shape strain gages, using fiber Bragg gratings in optical fiber (FBG) in order to obtain representative measurement on surface rocks samples containing minerals and structures of different compositions, sizes and directions. This reports presents the processes of manufacturing, mechanical characterization, calibration and evaluation under uniaxial compression tests on rock samples. To verify the efficiency of rock deformation transmitted to attached sensor, it was also performed the analysis of the strain transfer including the effects of the bonding, the sample and the transducer. The experimental results indicate that the developed sensor enables reliable measurements of the strain and its transmission from rock to sensor, appropriate for use in heterogeneous materials, pointing an interesting perspective for applications on irregular surfaces, allowing increasing at will the size and shape of the measurement area. This research suggests suitability of the optical strain gauge for real scale, where traditional electrical systems have demonstrated some limitations.

Elastic (stress-strain) halo associated to ion-induced nano-tracks in lithium niobate: role of crystal anisotropy

The elastic strain/stress fields (halo) around a compressed amorphous nano-track (core) caused by a single high-energy ion impact on LiNbO3 are calculated. A method is developed to approximately account for the effects of crystal anisotropy of LiNbO3 (symmetry 3m) on the stress fields for tracks oriented along the crystal axes (X, Y or Z). It only considers the zero-order (axial) harmonic contribution to the displacement field in the perpendicular plane and uses effective Poisson moduli for each particular orientation. The anisotropy is relatively small; however, it accounts for some differential features obtained for irradiations along the crystallographic axes X, Y and Z. In particular, the irradiation-induced disorder (including halo) and the associated surface swelling appear to be higher for irradiations along the X- or Y-axis in comparison with those along the Z-axis. Other irradiation effects can be explained by the model, e.g. fracture patterns or the morphology of pores after chemical etching of tracks. Moreover, it offers interesting predictions on the effect of irradiation on lattice parameters

Failure mechanism of reinforced concrete structural walls with and without confinement

This paper presents the results of cyclic loading tests on two large-scale reinforced concrete structural walls that were conducted at Purdue University. One of the walls had confinement reinforcement meeting ACI-318-11 requirements while the other wall did not have any confinement reinforcement. The walls were tested as part of a larger study aimed at indentifying parameters affecting failure modes observed to limit the drift capacity of structural walls in Chile during the Maule Earthquake of 2010. These failure modes include out-of-plane buckling (of the wall rather tan individual reinforcing bars), compression failure, and bond failure. This paper discusses the effects of confinement on failure mode. Distributions of unit strain and curvature obtained with a dense array of non-contact coordinate-tracking targets are also presented.

Packaging and testing of fiber Bragg gratings for use as strain sensor for rock specimens

This paper reports a packaging and calibration procedure for surface mounting of fiber Bragg grating (FBG) sensors to measure strain in rocks. The packaging of FBG sensors is performed with glass fiber and polyester resin, and then subjected to tensile loads in order to obtain strength and deformability parameters, necessaries to assess the mechanical performance of the sensor packaging. For a specific package, an optimal curing condition has been found, showing good repeatability and adaptability for non-planar surfaces, such as occurs in rock engineering. The successfully packaged sensors and electrical strain gages were attached to standard rock specimens of gabbro. Longitudinal and transversal strains under compression loads were measured with both techniques, showing that response of FBG sensors is linear and reliable. An analytical model is used to characterize the influences of rock substrate and FBG packaging in strain transmission. As a result, we obtained a sensor packaging for non-planar and complex natural material under acceptable sensitivity suitable for very small strains as occurs in hard rocks.

Comportamiento estructural de elementos de fábrica reforzados con materiales compuestos avanzados solicitados a flexión y flexocompresión

El refuerzo de estructuras existentes mediante el encolado exterior de láminas de polímeros reforzados con fibras (FRP) se ha convertido en la aplicación más común de los materiales compuestos avanzados en construcción. Estos materiales presentan muchas ventajas frente a los materiales convencionales (sin corrosión, ligeros, de fácil aplicación, etc.). Pero a pesar de las numerosas investigaciones realizadas, aún persisten ciertas dudas sobre algunos aspectos de su comportamiento y las aplicaciones prácticas se llevan a cabo sólo con la ayuda de guías, sin que haya una normativa oficial. El objetivo de este trabajo es incrementar el conocimiento sobre esta técnica de refuerzo, y más concretamente, sobre el refuerzo a flexión de estructuras de fábrica. Con frecuencia el elemento reforzado es de hormigón armado y las láminas de FRP encoladas al exterior sirven para mejorar su resistencia a flexión, cortante o compresión (encamisados). Sin embargo su empleo en otros materiales como las estructuras de fábrica resulta muy prometedor. Las fábricas se caracterizan por soportar muy bien los esfuerzos de compresión pero bastante mal los de tracción. Adherir láminas de materiales compuestos puede servir para mejorar la capacidad resistente de elementos de fábrica sometidos a esfuerzos de flexión. Pero para ello, debe quedar garantizada una correcta adherencia entre el FRP y la fábrica, especialmente en edificios antiguos cuya superficie puede estar deteriorada por encontrarse a la intemperie o por el propio paso del tiempo. En el capítulo II se describen los objetivos fundamentales del trabajo y el método seguido. En el capítulo III se hace una amplia revisión del estado de conocimiento sobre el tema. En el apartado III.1 se detallan las principales características y propiedades mecánicas de fibras, matrices y materiales compuestos así como sus principales aplicaciones, haciendo especial hincapié en aspectos relativos a su durabilidad. En el apartado III.2 se incluye una revisión histórica de las líneas de investigación, tanto teóricas como empíricas, publicadas sobre estructuras de hormigón reforzadas a flexión encolando materiales compuestos. El apartado III.3 se centra en el aspecto fundamental de la adherencia refuerzo-soporte. Se hace un repaso a distintos modelos propuestos para prevenir el despegue distinguiendo si éste se inicia en la zona de anclaje o si está inducido por fisuras en la zona interior del elemento. Se observa falta de consenso en las propuestas. Además en este punto se relatan las campañas experimentales publicadas acerca de la adherencia entre materiales compuestos y fábricas. En el apartado III.4 se analizan las particularidades de las estructuras de fábrica. Además, se revisan algunas de las investigaciones relativas a la mejora de su comportamiento a flexión mediante láminas de FRP. El comportamiento mecánico de muros reforzados solicitados a flexión pura (sin compresión) ha sido documentado por varios autores, si bien es una situación poco frecuente en fábricas reales. Ni el comportamiento mecánico de muros reforzados solicitados a flexocompresión ni la incidencia que el nivel de compresión soportado por la fábrica tiene sobre la capacidad resistente del elemento reforzado han sido suficientemente tratados. En cuanto a los trabajos teóricos, las diferentes propuestas se basan en los métodos utilizados para hormigón armado y comparten los principios habituales de cálculo. Sin embargo, presentan diferencias relativas, sobre todo, a tres aspectos: 1) la forma de modelar el comportamiento de la fábrica, 2) el valor de deformación de cálculo del refuerzo, y 3) el modo de fallo que se considera recomendable buscar con el diseño. A pesar de ello, el ajuste con la parte experimental de cada trabajo suele ser bueno debido a una enorme disparidad en las variables consideradas. Cada campaña presenta un modo de fallo característico y la formulación que se propone resulta apropiada para él. Parece necesario desarrollar un método de cálculo para fábricas flexocomprimidas reforzadas con FRP que pueda ser utilizado para todos los posibles fallos, tanto atribuibles a la lámina como a la fábrica. En el apartado III.4 se repasan algunas lesiones habituales en fábricas solicitadas a flexión y se recogen ejemplos de refuerzos con FRP para reparar o prevenir estos daños. Para mejorar el conocimiento sobre el tema, se llevan a cabo dos pequeñas campañas experimentales realizadas en el Instituto de Ciencias de la Construcción Eduardo Torroja. La primera acerca de la adherencia de materiales compuestos encolados a fábricas deterioradas (apartado IV.1) y la segunda sobre el comportamiento estructural a flexocompresión de probetas de fábrica reforzadas con estos materiales (apartado IV.2). En el capítulo V se analizan algunos de los modelos de adherencia propuestos para prevenir el despegue del extremo del refuerzo. Se confirma que las predicciones obtenidas con ellos resultan muy dispares. Se recopila una base de datos con los resultados experimentales de campañas sobre adherencia de FRP a fábricas extraídas de la literatura y de los resultados propios de la campaña descrita en el punto IV.1. Esta base de datos permite conocer cual de los métodos analizados resulta más adecuado para dimensionar el anclaje de láminas de FRP adheridas a fábricas. En el capítulo VI se propone un método para la comprobación en agotamiento de secciones de fábrica reforzadas con materiales compuestos sometidas a esfuerzos combinados de flexión y compresión. Está basado en el procedimiento de cálculo de la capacidad resistente de secciones de hormigón armado pero adaptado a las fábricas reforzadas. Para ello, se utiliza un diagrama de cálculo tensión deformación de la fábrica de tipo bilineal (acorde con el CTE DB SE-F) cuya simplicidad facilita el desarrollo de toda la formulación al tiempo que resulta adecuado para predecir la capacidad resistente a flexión tanto para fallos debidos al refuerzo como a la fábrica. Además se limita la deformación de cálculo del refuerzo teniendo en consideración ciertos aspectos que provocan que la lámina adherida no pueda desarrollar toda su resistencia, como el desprendimiento inducido por fisuras en el interior del elemento o el deterioro medioambiental. En concreto, se propone un “coeficiente reductor por adherencia” que se determina a partir de una base de datos con 68 resultados experimentales procedentes de publicaciones de varios autores y de los ensayos propios de la campaña descrita en el punto IV.2. También se revisa la formulación propuesta con ayuda de la base de datos. En el capítulo VII se estudia la incidencia de las principales variables, como el axil, la deformación de cálculo del refuerzo o su rigidez, en la capacidad final del elemento. Las conclusiones del trabajo realizado y las posibles líneas futuras de investigación se exponen en el capítulo VIII. ABSTRACT Strengthening of existing structures with externally bonded fiber reinforced polymers (FRP) has become the most common application of advanced composite materials in construction. These materials exhibit many advantages in comparison with traditional ones (corrosion resistance, light weight, easy to apply, etc.). But despite countless researches have been done, there are still doubts about some aspects of their behaviour and applications are carried out only with the help of guidelines, without official regulations. The aim of this work is to improve the knowledge on this retrofitting technique, particularly in regard to flexural strengthening of masonry structures. Reinforced concrete is often the strengthened material and external glued FRP plates are used to improve its flexural, shear or compressive (by wrapping) capacity. However the use of this technique on other materials like masonry structures looks promising. Unreinforced masonry is characterized for being a good material to support compressive stresses but really bad to withstand tensile ones. Glue composite plates can improve the flexural capacity of masonry elements subject to bending. But a proper bond between FRP sheet and masonry must be ensured to do that, especially in old buildings whose surface can be damaged due to being outside or ageing. The main objectives of the work and the methodology carried out are described In Chapter II. An extensive overview of the state of art is done in Chapter III. In Section III.1 physical and mechanical properties of fibers, matrix and composites and their main applications are related. Durability aspects are especially emphasized. Section III.2 includes an historical overview of theoretical and empirical researches on concrete structures strengthened gluing FRP plates to improve their flexural behaviour. Section III.3 focuses on the critical point of bonding between FRP and substrate. Some theoretical models to prevent debonding of FRP laminate are reviewed, it has made a distinction between models for detachment at the end of the plate or debonding in the intermediate zones due to the effects of cracks. It is observed a lack of agreement in the proposals. Some experimental studies on bonding between masonry and FRP are also related in this chapter. The particular characteristics of masonry structures are analyzed in Section III.4. Besides some empirical and theoretical investigations relative to improve their flexural capacity with FRP sheets are reviewed. The mechanical behaviour of strengthened walls subject to pure bending (without compression) has been established by several authors, but this is an unusual situation for real masonry. Neither mechanical behaviour of walls subject to bending and compression nor influence of axial load in the final capacity of the strengthened element are adequately studied. In regard to theoretical studies, the different proposals are based on reinforced concrete analytical methods and share common design principles. However, they present differences, especially, about three aspects: 1) the constitutive law of masonry, 2) the value of ultimate FRP strain and 3) the desirable failure mode that must be looked for. In spite of them, a good agreement between each experimental program and its theoretical study is often exhibited due to enormous disparity in considered test parameters. Each experimental program usually presents a characteristic failure mode and the proposed formulation results appropriate for this one. It seems necessary to develop a method for FRP strengthened walls subject to bending and compression enable for all failure modes (due to FRP or masonry). Some common damages in masonry subject to bending are explained in Section III.4. Examples of FRP strengthening to repair or prevent these damages are also written. Two small experimental programs are carried out in Eduardo Torroja Institute to improve the knowledge on this topic. The first one is concerned about the bond between FRP plates and damaged masonry (section IV.1) and the second one is related to the mechanical behaviour of the strengthened masonry specimens subject to out of plane bending combined with axial force (section IV.2). In the Chapter V some bond models to prevent the debonding at the FRP plate end are checked. It is confirmed that their predictions are so different. A pure-shear test database is compiled with results from the existing literature and others from the experimental program described in section IV.1. This database lets know which of the considered model is more suitable to design anchorage lengths of glued FRP to masonry. In the Chapter VI a method to check unreinforced masonry sections with external FRP strengthening subject to bending and compression to the ultimate limit state is proposed. This method is based on concrete reinforced one, but it is adapted to strengthened masonry. A bilinear constitutive law is used for masonry (according to CTE DB SE-F). Its simplicity helps to develop the model formulation and it has proven to be suitable to predict bending capacity either for FRP failures or masonry crushing. With regard to FRP, the design strain is limited. It is taken into account different aspects which cause the plate can’t reach its ultimate strength, like intermediate FRP debonding induced by opening cracking or environmental damage. A “bond factor” is proposed. It is obtained by means of an experimental bending test database that includes 68 results from the existing literature and from the experimental program described in section IV.2. The proposed formulation has also been checked with the help of bending database. The effects of the main parameters, like axial load, FRP design effective strain or FRP stiffness, on the bending capacity of the strengthened element are studied in Chapter VII. Finally, the main conclusions from the work carried out are summarized in Chapter VIII. Future lines of research to be explored are suggested as well.

High temperature micropillar compression of Al/SiC nanolaminates

The effect of the temperature on the compressive stress–strain behavior of Al/SiC nanoscale multilayers was studied by means of micropillar compression tests at 23 °C and 100 °C. The multilayers (composed of alternating layers of 60 nm in thickness of nanocrystalline Al and amorphous SiC) showed a very large hardening rate at 23 °C, which led to a flow stress of 3.1 ± 0.2 GPa at 8% strain. However, the flow stress (and the hardening rate) was reduced by 50% at 100 °C. Plastic deformation of the Al layers was the dominant deformation mechanism at both temperatures, but the Al layers were extruded out of the micropillar at 100 °C, while Al plastic flow was constrained by the SiC elastic layers at 23 °C. Finite element simulations of the micropillar compression test indicated the role played by different factors (flow stress of Al, interface strength and friction coefficient) on the mechanical behavior and were able to rationalize the differences in the stress–strain curves between 23 °C and 100 °C.

Optimal design of a beam subjected to compression forces in the framework of different structural models

The optimal design of a vertical cantilever beam is presented in this paper. The beam is assumed immersed in an elastic Winkler soil and subjected to several loads: a point force at the tip section, its self weight and a uniform distributed load along its length. lbe optimal design problem is to find the beam of a given length and minimum volume, such that the resultant compressive stresses are admisible. This prohlem is analyzed according to linear elasticity theory and within different alternative structural models: column, Navier-Bernoulli beam-column, Timoshenko beamcolumn (i.e. with shear strain) under conservative loads, typically, constant direction loads. Results obtained in each case are compared, in order to evaluate the sensitivity of model on the numerical results. The beam optimal design is described by the section distribution layout (area, second moment, shear area etc.) along the beam span and the corresponding beam total volume. Other situations, some of them very interesting from a theoretical point of view, with follower loads (Beck and Leipholz problems) are also discussed, leaving for future work numerical details and results.