Corrective Eccentricities Research Articles

Hole-drilling method eccentricity error correction using a convolutional neural network

Hole eccentricity is an important error source when residual stress is measured via the hole-drilling method. The conventional ways to correct eccentricity error for hole-drilling residual stress measurement rely on complicated mathematical processes and are difficult to use. To overcome this shortcoming, this paper proposes a method that uses a convolutional neural network to correct for the hole-drilling method eccentricity error. First, the hole-drilling method measurement process in uniform biaxial stress field is simulated via the finite element method. The influence of the eccentric distance, eccentric angle, and stress ratio on the strain measurement error is discussed. Then, a convolutional neural network is trained using simulated data and the hole-drilling method strain measurement error is predicted for arbitrary eccentricity conditions. Finally, the residual stress is corrected by introducing the strain error into its equation. The simulated residual stresses of ten eccentric measurement points in predefined stress fields are corrected using this procedure to conducted numerical tests. The maximum error of simulated stresses decreased from 30.46% to −4.67% after correction. Therefore, the hole eccentricity has a significant influence on the residual stress measurement accuracy of hole-drilling method. The proposed correction method can effectively eliminate this error.

Potential softening and eccentricity dynamics in razor-thin, nearly-Keplerian discs.

In many astrophysical problems involving discs (gaseous or particulate) orbiting a dominant central mass, gravitational potential of the disc plays an important dynamical role. Its impact on the motion of external objects, as well as on the dynamics of the disc itself, can usually be studied using secular approximation. This is often done using softened gravity to avoid singularities arising in calculation of the orbit-averaged potential — disturbing function — of a razor-thin disc using classical Laplace-Lagrange theory. We explore the performance of several softening formalisms proposed in the literature in reproducing the correct eccentricity dynamics in the disc potential. We identify softening models that, in the limit of zero softening, give results converging to the expected behavior exactly, approximately or not converging at all. We also develop a general framework for computing secular disturbing function given an arbitrary softening prescription for a rather general form of the interaction potential. Our results demonstrate that numerical treatments of the secular disc dynamics, representing the disc as a collection of N gravitationally interacting annuli, are rather demanding: for a given value of the (dimensionless) softening parameter, ς ≪ 1, accurate representation of eccentricity dynamics requires N ∼ Cς−χ ≫ 1, with C ∼ O(10), 1.5 ≲ χ ≳. In discs with sharp edges a very small value of the softening parameter ς (≲ 10−3) is required to correctly reproduce eccentricity dynamics near the disc boundaries; this finding is relevant for modelling planetary rings.

Generalized corrective eccentricities for nonlinear static analysis of buildings with framed or braced structure

The nonlinear static method of analysis has become the most popular tool for the seismic assessment of existing buildings. However, seismic codes do not allow its use for in-plan irregular buildings because it does not provide accurate predictions of the deck rotation. To overcome this limitation, the “corrective eccentricity method” evaluates the maximum seismic response as the envelope of the results of two nonlinear static analyses. In these analyses, the lateral force is applied with two different (corrective) eccentricities with respect to the centre of mass of the deck. The corrective eccentricities were calibrated on single-storey systems with unidirectional resisting elements, i.e. with elements that are representative of walls or braced frames. This paper proposes new corrective eccentricities aiming at generalizing and simplifying the previous corrective eccentricity method. In particular, new equations are defined for the corrective eccentricities devoted to predict the displacement demand on the stiff side of the building. These equations are defined based on the response of a set of single-storey systems representative of buildings with uni-directional or bi-directional resisting elements (e.g. moment resisting frames). Further, the displacement demand on the flexible side of the building is determined assuming a null eccentricity of the lateral force. The response of a set of multi-storey buildings is predicted by means of the new and original corrective eccentricities and compared to the maximum response obtained by nonlinear dynamic analysis. This comparison is made in terms of floor displacements, storey drifts and storey shears. The set of the examined structural systems comprises buildings with steel braced structure as well as buildings with r.c. framed structure.

Evolution of circumbinary planets around eccentric binaries: The case of Kepler-34

The existence of planets orbiting a central binary star system immediately raises questions regarding their formation and dynamical evolution. Recent discoveries of circumbinary planets by the Kepler space telescope has shown that some of these planets reside close to the dynamical stability limit where it is very difficult to form planets in situ. For binary systems with nearly circular orbits, such as Kepler-38, the observed proximity of planetary orbits to the stability limit can be understood by an evolutionary process in which planets form farther out in the disk and migrate inward to their observed position. The Kepler-34 system has a high orbital eccentricity of 0.52. Here, we analyse evolutionary scenarios for the planet observed around this system using two-dimensional hydrodynamical simulations. The highly eccentric binary opens a wide inner hole in the disk which is also eccentric, and displays a slow prograde precession. As a result of the large, eccentric inner gap, an embedded planet settles in a final equilibrium position that lies beyond the observed location of Kepler-34 b, but has the correct eccentricity. In this configuration the planetary orbit is aligned with the disk in a state of apsidal corotation.To account for the closer orbit of Kepler-34 b to the central binary, we considered a two-planet scenario and examined the evolution of the system through joint inward migration and capture into mean-motion resonances. When the inner planet orbits inside the gap of the disk, planet-planet scattering ensues. While often one object is thrown into a large, highly eccentric orbit, at times the system is left with a planet close to the observed orbit, suggesting that Kepler 34 might have had two circumbinary planets where one might have been scattered out of the system or into an orbit where it did not transit the central binary during the operation of Kepler.

Predicting displacement demand of multi-storey asymmetric buildings by nonlinear static analysis and corrective eccentricities

Nonlinear static methods are not always effective in the assessment of multi-storey asymmetric structures because of the errors committed in the evaluation of the deck rotation. To overcome this problem, some of the authors have recently proposed the use of two nonlinear static analyses, characterised by lateral forces applied to different points of the deck. For each of these two analyses, the distance between the point of application of the lateral force and the centre of mass of the deck (corrective eccentricity) is given by relations resulting from a parametric study on a large set of single-storey systems subjected to bidirectional ground motions. The corrective eccentricity depends on four parameters: the rigidity eccentricity, the strength eccentricity, the ratio of the uncoupled torsional to lateral frequencies and the ratio of the elastic strength demand to the actual strength of the system. In this paper, the effectiveness of the proposed method is evaluated for different values of the abovementioned parameters, considering two seismic excitation levels and multi-storey buildings with r.c. framed structure or steel structure equipped with buckling restrained braces. The seismic response of the structures is evaluated by nonlinear time-history analysis and compared with that resulting from the application of the proposed nonlinear static method. To highlight the accuracy of the proposed method, a comparison is also made with the response obtained from the standard application of the nonlinear static method, i.e. without corrective eccentricities, and with the response predicted by the extended N2 method.

Seismic assessment of existing r.c. framed structures with in-plan irregularity by nonlinear static methods

This paper evaluates the effectiveness of three nonlinear static methods for the prediction of the dynamic response of in-plan irregular buildings. The methods considered are the method suggested in Eurocode 8, a method previously proposed by some of the authors and based on corrective eccentricities and a new method in which two pushover analyses are considered, one with lateral forces applied to the centres of mass of the floors and the other with only translational response. The numerical analyses are carried out on a set of refined models of reinforced concrete framed buildings. The response predicted by the nonlinear static analyses is compared to that provided by nonlinear dynamic analyses. The effectiveness of the nonlinear static methods is evaluated in terms of absolute and interstorey displacements.

Corrective eccentricities for assessment by the nonlinear static method of 3D structures subjected to bidirectional ground motions

SUMMARYNonlinear static methods are reliable in the evaluation of the seismic response of planar structural schemes, but they are not very effective in the assessment of three‐dimensional building structures. The authors of this paper have recently proposed a nonlinear static approach for asymmetric structures, which is an improvement on that stipulated by seismic codes. This method is based on the observation that the distribution of the maximum dynamic displacements of the deck can be enveloped by two pushover analyses performed by applying the lateral force with two eccentricities with respect to the center of mass of the deck. These eccentricities, named “corrective eccentricities”, are defined so that the two corresponding pushover analyses provide displacements that are equal to those evaluated by nonlinear dynamic analysis at the two sides of the deck. In this paper, the corrective eccentricities are determined for a wide set of single‐story systems. The equations for their analytical evaluation are determined and their reliability is demonstrated. Finally, the analysis of a multi‐story structure is conducted to show how the method can be applied to real buildings. Copyright © 2012 John Wiley & Sons, Ltd.

Corrective Eccentricities for the Evaluation of the Seismic Response of One-Storey Asymmetric Systems by Nonlinear Static Analysis

Corrective Eccentricities for the Evaluation of the Seismic Response of One-Storey Asymmetric Systems by Nonlinear Static Analysis

Static vs. Modal Analysis of Asymmetric Buildings: Effectiveness of Dynamic Eccentricity Formulations

The use of modal analysis appears necessary in order to reduce both displacement demand under weak seismic events and ductility demand under strong earthquakes. Static analysis can be effective only if used with proper values of additional eccentricities. To overcome the inaccuracy of the code formulations, the authors propose a simple procedure that gives the exact values of these eccentricities and discuss the influence of the main parameters that govern the structural behavior. They also point out the difficulty in evaluating some parameters (stiffness radius of gyration, structural eccentricity) in the case of multistory buildings and discuss the validity of simplified formulations proposed to overcome this problem. The effectiveness of static analysis, applied to three-dimensional multistory structures with properly evaluated corrective eccentricities, is analyzed with reference both to regularly asymmetric multistory schemes and to an actual irregularly asymmetric structure (the main building of the Faculty of Engineering at the University of Catania, Italy).

Application of Ball Bar System and Genetic Algorithms for CNC Lathe Contouring Compensation

There is considerable interest in the development and improvement of contouring test devices for CNC machines. When ball bar systems are employed to test CNC lathes, the eccentricity cannot be determined accurately from the sampled quadrant contouring data via the least-squares method. Geometric errors, such as squareness and deformation errors, are underestimated, causing significant errors in eccentricity values. Thus, one device with one method is suggested herein for improved lathe compensation for a given radius. Further, it is found that by adjusting a lathe during initial setting-up, for the eccentricity determined via the proposed methodology, the real geometric error of the turned part can be significantly reduced. Thus, it is very important to obtain the correct eccentricity and minimum zone solution. In this paper, genetic algorithms (GAs) are employed to solve the minimum zone solution. Simulated data and analysed results prove that the proposed method is superior to the least-squares method.