Analysis of fatigue crack growth in RC beams

In this work, a fatigue crack propagation model developed using dimensional analysis for plain concrete is used in conjunction with the steel closing force to predict the crack growth behavior of reinforced concrete beams. A numerical procedure is followed using the proposed model to compute the fatigue life of RC beams and the dissipated energy in the steel reinforcement due to shake down behavior. Through a sensitivity study, it is found that the structural size is the most sensitive parameter on which the crack growth rate is dependent. Furthermore, the moment carrying capacity of an RC beam is computed as function of crack size by considering the effect of bond slip.

Analysis of fatigue crack growth in reinforced concrete beams

Mechanical behavior of reinforced concrete members is influenced by the action of unknown crack bridging reactions of rebars. Under cyclic loading, due to progressive growth of cracks, this bridging action contributes to the overall strength, stiffness and hysteretic behavior of the member. In this work, fatigue behavior of reinforced concrete beams are studied using a crack propagation law, developed using dimensional analysis for plain concrete with the effect of reinforcement being simulated through constraint exerted on the crack opening. The parameters considered in the model are fracture toughness, crack length, loading ratio and structural size. A numerical procedure is followed to compute fatigue life of RC beams and the dissipated energy in the steel reinforcement due to the shake down phenomenon under cyclic loading. Through a sensitivity study, it is concluded that the structural size is the most sensitive parameter in the fatigue crack propagation phenomenon. Furthermore, the residual moment carrying capacity of an RC member is determined as a function of crack extension by including the bond-slip mechanism.

Analysis of indentation loading curves obtained using conical indenters

Using dimensional analysis and finite-element calculations we determine the functional form of indentation loading curves for a rigid conical indenter indenting into elastic-perfectly plastic solids. The new results are compared with the existing theories of indentation using conical indenters, including the slip-line theory for rigid-plastic solids, Sneddon's result for elastic solids, and Johnson's model for elastic-perfectly plastic solids. In the limit of small ratio of yield strength (Y) to Young's modulus (E), both the new results and Johnson's model approach that predicted by slip-line theory for rigid-plastic solids. In the limit of large Y/E, the new results agree with that for elastic solids. For a wide range of Y/E, some difference is found between Johnson's model-and the present result. This study also demonstrates the possibilities and limitations of using indentation loading curves to extract fundamental mechanical properties of solids.

A surface energy model and application to mechanical behavior analysis of single crystals at sub-micron scale

Size effects of mechanical behaviors of materials are referred to the variation of the mechanical behavior due to the sample sizes changing from macroscale to micro-/nanoscales. At the micro-/nanoscale, since sample has a relatively high specific surface area (SSA) (ratio of surface area to volume), the surface although it is often neglected at the macroscale, becomes prominent in governing the energy effect, although it is often neglected at the macroscale, becomes prominent in governing the mechanical behavior. In the present research, a continuum model considering the surface energy effect is developed through introducing the surface energy to total potential energy. Simultaneously, a corresponding finite element method is developed. The model is used to analyze the axial equilibrium strain problem for a Cu nanowire at the external loading-free state. As another application of the model, from dimensional analysis, the size effects of uniform compression tests on the microscale cylinder specimens for Ni and Au single crystals are analyzed and compared with experiments in literatures. (C) 2009 Elsevier B.V. All rights reserved.

Simplifying mooring analysis for deepwater systems using truncation

Over recent years academia and industry have engaged with the challenge of model testing deepwater structures at conventional scales. One approach to the limited depth problem has been to truncate the lines. This concept will be introduced, highlighting the need to better understand line dynamic processes. The type of line truncation developed here models the upper sections of each line in detail, capturing wave action and all coupling effects with the vessel, terminating to an approximate analytical model that aims to simulate the remainder of the line. A rationale for this is that in deep water transverse elastic waves of a line are likely to decay before they are reflected at the seabed because of nonlinear hydrodynamic drag forces. The first part of this paper is centered on verification of this rationale. A simplified model of a mooring line that describes the transverse dynamics in wave frequency is used, adopting the equation of motion of an inextensible taut string. The line is submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a universal curve for the decay of transverse vibrations along the line, which is suitable for any kind of line with any top motion. This has a significant engineering benefit, allowing for a rapid assessment of line dynamics - it can be useful in deciding whether a truncated line model is appropriate, and if so, at which point truncation might be applied. This is followed by developing a truncation mechanism, formulating an end approximation that can reproduce the correct impedance, had the line been continuous to full depth. It has been found that below a certain length criterion, which is also universal, the transverse vibrational characteristics for each line are inertia driven. As such the truncated model can assume a linear damper whose coefficient depends on the line properties and frequency of vibration. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).

Whitney's type theorems for infinite dimensional spaces

It is proved that for any $f$ is an element of $C^k(L,R)$, where k is a natural number and L is a closed linear subspace of a nuclear Frechet space $X$, the function $f$ can be extended to a function of class $C^{k-1}$ defined on the entire space $X$. It is also proved that for any $f$ is an element of $C^k(L, R)$, where $k$ is a natural number of infinity and L is a closed linear subspace of a dual $X$ of a nuclear Frechet space, the function $f$ can be extended to a function of class $C^k$ defined on the entire space $X$. In addition, it is proved that under these conditions, the existence of a linear extension operator is equivalent to the complementability of the subspace.

Ranking of microRNA target prediction scores by Pareto front analysis

Over the past ten years, a variety of microRNA target prediction methods has been developed, and many of the methods are constantly improved and adapted to recent insights into miRNA-mRNA interactions. In a typical scenario, different methods return different rankings of putative targets, even if the ranking is reduced to selected mRNAs that are related to a specific disease or cell type. For the experimental validation it is then difficult to decide in which order to process the predicted miRNA-mRNA bindings, since each validation is a laborious task and therefore only a limited number of mRNAs can be analysed. We propose a new ranking scheme that combines ranked predictions from several methods and - unlike standard thresholding methods - utilises the concept of Pareto fronts as defined in multi-objective optimisation. In the present study, we attempt a proof of concept by applying the new ranking scheme to hsa-miR-21, hsa-miR-125b, and hsa-miR-373 and prediction scores supplied by PITA and RNAhybrid. The scores are interpreted as a two-objective optimisation problem, and the elements of the Pareto front are ranked by the STarMir score with a subsequent re-calculation of the Pareto front after removal of the top-ranked mRNA from the basic set of prediction scores. The method is evaluated on validated targets of the three miRNA, and the ranking is compared to scores from DIANA-microT and TargetScan. We observed that the new ranking method performs well and consistent, and the first validated targets are elements of Pareto fronts at a relatively early stage of the recurrent procedure. which encourages further research towards a higher-dimensional analysis of Pareto fronts. (C) 2010 Elsevier Ltd. All rights reserved.

On the strong uniqueness of some finite dimensional Dirichlet operators

We prove essential self-adjointness of a class of Dirichlet operators in ℝn using the hyperbolic equation approach. This method allows one to prove essential self-adjointness under minimal conditions on the logarithmic derivative of the density and a condition of Muckenhoupt type on the density itself.

Problems in four-dimensional data assimilation

With the introduction of new observing systems based on asynoptic observations, the analysis problem has changed in character. In the near future we may expect that a considerable part of meteorological observations will be unevenly distributed in four dimensions, i.e. three dimensions in space and one in time. The term analysis, or objective analysis in meteorology, means the process of interpolating observed meteorological observations from unevenly distributed locations to a network of regularly spaced grid points. Necessitated by the requirement of numerical weather prediction models to solve the governing finite difference equations on such a grid lattice, the objective analysis is a three-dimensional (or mostly two-dimensional) interpolation technique. As a consequence of the structure of the conventional synoptic network with separated data-sparse and data-dense areas, four-dimensional analysis has in fact been intensively used for many years. Weather services have thus based their analysis not only on synoptic data at the time of the analysis and climatology, but also on the fields predicted from the previous observation hour and valid at the time of the analysis. The inclusion of the time dimension in objective analysis will be called four-dimensional data assimilation. From one point of view it seems possible to apply the conventional technique on the new data sources by simply reducing the time interval in the analysis-forecasting cycle. This could in fact be justified also for the conventional observations. We have a fairly good coverage of surface observations 8 times a day and several upper air stations are making radiosonde and radiowind observations 4 times a day. If we have a 3-hour step in the analysis-forecasting cycle instead of 12 hours, which is applied most often, we may without any difficulties treat all observations as synoptic. No observation would thus be more than 90 minutes off time and the observations even during strong transient motion would fall within a horizontal mesh of 500 km * 500 km.

Analysis of spherical indentation of superelastic shape memory alloys

Dimensional analysis and the finite element method are applied in this paper to study spherical indentation of superelastic shape memory alloys. The scaling relationships derived from dimensional analysis bridge the indentation response and the mechanical properties of a superelastic shape memory alloy. Several key variables of a superelastic indentation curve are revealed and examined. We prove that the bifurcation force in a superelastic indentation curve only relies on the forward transformation stress and the elastic properties of the initial austenite; and the return force in a superelastic indentation curve only relies on the reverse transformation stress and the elastic properties of the initial austenite. Furthermore, the dimensionless functions to determine the bifurcation force and the return force are proved to be identical. These results not only enhance our understanding of spherical indentation of superelastic shape memory alloys, but also provide the theoretical basis for developing a practicable method to calibrate the mechanical properties of a superelastic material from the spherical indentation test.

Slope stability charts for two-layered purely cohesive soils based on finite-element limit analysis methods

Stability charts for soil slopes, first produced in the first half of the twentieth century, continue to be used extensively as design tools, and draw the attention of many investigators. This paper uses finite-element upper and lower bound limit analysis to assess the short-term stability of slopes in which the slopematerial and subgrade foundation material have two distinctly different undrained strengths. The stability charts are proposed, and the exact theoretical solutions are bracketed to within 4.2% or better. In addition, results from the limit-equilibrium method (LEM) have been used for comparison. Differences of up to 20% were found between the numerical limit analysis and LEM solutions. It also shown that the LEM sometimes leads to errors, although it is widely used in practice for slope stability assessments.

Comparação entre planejamento estatístico experimental e análise dimensional em operações de mistura e separação para sistema óleo-água

This work aims to determine a better methodology to help predicting some operational parameters to a new design of mixer-settler on treating wastewater produced by petroleum industry, called MDIF (Misturador-Decantador à Inversão de Fases/ Mixer-Settler based on Phase Inversion MSPI). The data from this research were obtained from the wastewater treatment unit, called MSPI-TU, installed on a wastewater treatment plant (WTP) of PETROBRAS/UO-RNCE. The importance in determining the better methodology to predict the results of separation and extraction efficiency of the equipment, contributes significantly to determine the optimum operating variables for the control of the unit. The study was based on a comparison among the experimental efficiency (E) obtained by operating MSPI-TU, the efficiency obtained by experimental design equation (Eplan) from the software Statistica Experimental Design® (version 7.0), and the other obtained from a modeling equation based on a dimensional analysis (Ecalc). The results shows that the experimental design equation gives a good prediction of the unit efficiencies with better data reliability, regarding to the condition before a run operation. The average deviation between the proposed by statistic planning model equation and experimental data was 0.13%. On the other hand, the efficiency calculated by the equation which represents the dimensional analysis, may result on important relative deviations (up 70%). Thus, the experimental design is confirmed as a reliable tool, with regard the experimental data processing of the MSPI-TU

A local-global scheme for tracking crack path in three-dimensional solids

This paper aims to contribute to the three-dimensional generalization of numerical prediction of crack propagation through the formulation of finite elements with embedded discontinuities. The analysis of crack propagation in two-dimensional problems yields lines of discontinuity that can be tracked in a relatively simple way through the sequential construction of straight line segments oriented according to the direction of failure within each finite element in the solid. In three-dimensional analysis, the construction of the discontinuity path is more complex because it requires the creation of plane surfaces within each element, which must be continuous between the elements. In the method proposed by Chaves (2003) the crack is determined by solving a problem analogous to the heat conduction problem, established from local failure orientations, based on the stress state of the mechanical problem. To minimize the computational effort, in this paper a new strategy is proposed whereby the analysis for tracking the discontinuity path is restricted to the domain formed by some elements near the crack surface that develops along the loading process. The proposed methodology is validated by performing three-dimensional analyses of basic problems of experimental fractures and comparing their results with those reported in the literature.

Slope stability analysis of the Pacaya Volcano, Guatemala, using limit equilibrium and finite element method

The Pacaya volcanic complex is part of the Central American volcanic arc, which is associated with the subduction of the Cocos tectonic plate under the Caribbean plate. Located 30 km south of Guatemala City, Pacaya is situated on the southern rim of the Amatitlan Caldera. It is the largest post-caldera volcano, and has been one of Central America’s most active volcanoes over the last 500 years. Between 400 and 2000 years B.P, the Pacaya volcano had experienced a huge collapse, which resulted in the formation of horseshoe-shaped scarp that is still visible. In the recent years, several smaller collapses have been associated with the activity of the volcano (in 1961 and 2010) affecting its northwestern flanks, which are likely to be induced by the local and regional stress changes. The similar orientation of dry and volcanic fissures and the distribution of new vents would likely explain the reactivation of the pre-existing stress configuration responsible for the old-collapse. This paper presents the first stability analysis of the Pacaya volcanic flank. The inputs for the geological and geotechnical models were defined based on the stratigraphical, lithological, structural data, and material properties obtained from field survey and lab tests. According to the mechanical characteristics, three lithotechnical units were defined: Lava, Lava-Breccia and Breccia-Lava. The Hoek and Brown’s failure criterion was applied for each lithotechnical unit and the rock mass friction angle, apparent cohesion, and strength and deformation characteristics were computed in a specified stress range. Further, the stability of the volcano was evaluated by two-dimensional analysis performed by Limit Equilibrium (LEM, ROCSCIENCE) and Finite Element Method (FEM, PHASE 2 7.0). The stability analysis mainly focused on the modern Pacaya volcano built inside the collapse amphitheatre of “Old Pacaya”. The volcanic instability was assessed based on the variability of safety factor using deterministic, sensitivity, and probabilistic analysis considering the gravitational instability and the effects of external forces such as magma pressure and seismicity as potential triggering mechanisms of lateral collapse. The preliminary results from the analysis provide two insights: first, the least stable sector is on the south-western flank of the volcano; second, the lowest safety factor value suggests that the edifice is stable under gravity alone, and the external triggering mechanism can represent a likely destabilizing factor.

Radiographic volume analysis as a novel tool to determine nasopalatine duct cyst dimensions and its association with presenting symptoms and postoperative complications

OBJECTIVES The aims of the study were to use cone beam computed tomography (CBCT) images of nasopalatine duct cysts (NPDC) and to calculate the diameter, surface area, and 3D-volume using a custom-made software program. Furthermore, any associations of dimensions of NPDC with age, gender, presence/absence of maxillary incisors/canines (MI/MC), endodontic treatment of MI/MC, presenting symptoms, and postoperative complications were evaluated. MATERIAL AND METHODS The study comprised 40 patients with a histopathologically confirmed NPDC. On preoperative CBCT scans, curves delineating the cystic borders were drawn in all planes and the widest diameter (in millimeter), surface area (in square millimeter), and volume (in cubic millimeter) were calculated. RESULTS The overall mean cyst diameter was 15 mm (range 7-47 mm), the mean cyst surface area 566 mm(2) (84-4,516 mm(2)), and the mean cyst volume 1,735 mm(3) (65-25,350 mm(3)). For 22 randomly allocated cases, a second measurement resulted in a mean absolute aberration of ±4.2 % for the volume, ±2.8 % for the surface, and ±4.9 % for the diameter. A statistically significant association was found for the CBCT determined cyst measurements and the need for preoperative endodontic treatment to MI/MC and for postoperative complications. CONCLUSION In the hands of a single experienced operator, the novel software exhibited high repeatability for measurements of cyst dimensions. Further studies are needed to assess the application of this tool for dimensional analysis of different jaw cysts and lesions including treatment planning. CLINICAL RELEVANCE Accurate radiographic information of the bone volume lost (osteolysis) due to expansion of a cystic lesion in three dimensions could help in personalized treatment planning.