Circular Discontinuity Research Articles

Multi-element polynomial chaos expansion based on automatic discontinuity detection for nonlinear systems

This article focuses on the stochastic modeling of nonlinear systems featuring discontinuities in their response surface. More specifically, original developments are presented to improve the efficiency of multi-element polynomial chaos expansion for such systems. First, an automated detection procedure of the discontinuities is proposed. It relies on an iterative algorithm with a polynomial annihilation edge detection method and support vector machine classification algorithms leading to the representation of the discontinuity as a B-spline curve. Based on this curve, an ad-hoc decomposition of the variable space is considered and an original approach for the application of polynomial chaos expansion on each subdomain yields a robust and versatile way to compute the response surface of the system of interest. The proposed methodology is detailed and applied to several nonlinear academic systems such as a circular discontinuity and the Duffing oscillator including one or two discontinuities in its response surface. Through these applications, it is evidenced that, compared to the classical polynomial chaos and multi-element polynomial chaos expansions, the proposed methodology yields an approximation of the discontinuous responses that is both more accurate and less computationally expensive. The influence of the main parameters of the proposed methodology is also analyzed in details. This parametric analysis underlines the robustness of the methodology and highlights the key parameters in terms of computational cost and accuracy of the discontinuities. The proposed methodology is finally applied to an industrial application, it allows to efficiently compute the surface response of an industrial compressor blade undergoing structural contacts.

Static strain-based identification of extensive damages in thin-walled structures

Interest has been expressed during the past few years toward incorporating structural health monitoring (SHM) systems in ship hull structures for detecting damages that cause significant load-carrying reductions and subsequent load redistributions. The guiding principle of the damage identification strategy considered in this work is based upon measuring, through a limited number of sensors, the static strain redistributions caused by an extensive damage. The problem is tackled as a statistical pattern recognition one, and therefore, methods sourcing from machine learning (ML) are applied. The SHM strategy is both virtually and experimentally applied to a thin-walled prismatic geometry that represents an idealized hull form solely subjected to principal bending stresses (sagging/hogging). Damage modes causing extensive stress redistribution, are abstractly represented by a circular discontinuity. The damage identification problem is treated in a hierarchical order, initialized by damage detection and moving to an increasingly more localized prediction of the damage location. Training datasets for the ML tools are generated from numerical finite element simulations. Measurement uncertainty is propagated in the theoretical strains by information inferred from experimental data. Two different sensor architectures were assessed. An experimental programme is performed for testing the accuracy of the proposed damage identification strategy, yielding promising results and providing valuable insights.

Model-Based Structural Health Monitoring of Box Girders

In the recent years, interest has been expressed towards incorporating Structural Health Monitoring (SHM) systems to ship hulls in order to transition from preventive to predictive maintenance procedures. In this work, an initial approach is undertaken to investigate the capabilities of a model-based method treating damage identification as an optimization problem solved using a genetic algorithm. An idealization of the hull structure is considered based on hull girder theory that allows for lab scale experimental testing. Specifically, a box girder is considered with a circular discontinuity as the generalized damage that causes extensive stress redistribution, replicating the effect of hull damage modes of interest. A three-point bending load case is considered to emulate still water bending loads. Damage is considered to exist, and the goal of the proposed strategy is to provide a prediction on its location and magnitude (level 2 SHM). This is achieved using strain measurements obtained from sensors located on theoretical zero-strain directions as inputs to the optimization scheme treating the damage identification problem. Results from both assessment strategies highlighted the influence of measurement-related uncertainties on the method’s predictive capabilities.

Study of Martensitic Transformation in 304L Austenitic Stainless Steel after Tensile and Low Cycle Fatigue Tests

There are many studies on austenitic stainless steels with transformation induced plasticity (TRIP). Basically, in these steels, there is a significant increase in strength and toughness with the transformation of austenite to martensite. 304L steel finds extensive application in industry. Studies relating to martensitic transformation with plastic deformation are quite common. Many studies involve monotonic loading relating to the martensite formed. In practice, 304L steels are subject to distinct types of loading and possibly with stress concentrators. Thus, also in smaller quantities, it is possible to find in the literature studies involving cyclic loading with the TRIP effect. To contribute to the literature on the analysis of the TRIP effect on these steels, 304L steel samples with stress concentrators underwent interrupted monotonic tensile tests. Optical microscopy (OM) and x-ray diffraction (XRD) technique characterized the martensitic transformation. Other 304L steel samples with a stress concentrator underwent a low cycle fatigue test. The martensitic transformation, in this case, was possible to follow with the electron backscatter diffraction technique (EBSD). The samples after the interrupted monotonic tests show a high martensite volume fraction formed 1mm away from the notch (30% to 50%), due to the plastic deformation suffered. From 5.5mm of the notch, the samples again display a microstructure like that of the as-received (AR) sample. For the low cycle fatigue tested sample, the high concentration of deformation-induced martensite was within 15mm of the discontinuity. Approximately 0.5mm from the circular discontinuity, the sample again has a microstructure like the initial sample (IS).

Analysis of Spur Gear with Tooth Circular Discontinuity for Weight Reduction

The design of gears and gear drives are becoming challenging in automobile applications in which low contact ratio gears are required to transmit higher loads and be lighter in weight. There are various methods available for optimizing the design. Some researches have been taken place in the areas of gear tooth profile modifications for providing internal stress relief and weight reduction. In most cases, the maximum loads are assumed to be acting on the tip of the tooth. In this study, investigations are carried out on the effect of circular discontinuity on the weight reduction without affecting the root stress. The maximum tangential load is applied on the highest point of single tooth contact. The results show that with the modified gear tooth having a combination of two circular discontinuities of size 0.4 times the module not only provides weight reduction but also gives stress relief at the root.

Damage detection using the signal entropy of an ultrasonic sensor network

Piezoelectric ultrasonic sensors used to propagate guided waves can potentially be implemented to inspect large areas in engineering structures. However, the inherent dispersion and noise of guided acoustic signals, multiple echoes in the structure, as well as a lack of an approximate or exact model, limit their use as a continuous structural health monitoring system. In this work, the implementation of a network of piezoelectric sensors randomly placed on a plate-like structure to detect and locate artificial damage is studied. A network of macro fiber composite (MFC) sensors working in a pitch–catch configuration was set on an aluminum thin plate 1.9 mm in thickness. Signals were analyzed in the time-scale domain using the discrete wavelet transform. The objectives of this work were threefold, namely to first develop a damage index based on the entropy distribution using short time wavelet entropy of the ultrasonic waves generated by a sensor network, second to determine the performance of an array of spare MFC sensors to detect artificial damage, and third to implement a time-of-arrival (TOA) algorithm on the gathered signals for damage location of an artificial circular discontinuity. Our preliminary test results show that the proposed methodology provides sufficient information for damage detection, which, once combined with the TOA algorithm, allows localization of the damage.

Stress Fields and Concentrations around Circular Discontinuity: A Methodological Review with Principles of Elasticity

Stress Fields and Concentrations around Circular Discontinuity: A Methodological Review with Principles of Elasticity

Characterization of Laser Generated Lamb Wave Modes after Interaction with a Thickness Reduction Discontinuity Using Ray Tracing Theory

The effect that a circular discontinuity (due to thickness reduction) in an Aluminum plate has on the direction of Lamb wave propagation was experimentally and theoretically studied. Broadband Lamb waves were generated by a pulsed Nd:YAG laser and optically detected with a photo-EMF detector to increase spatial resolution. The experimental results show that thickness reduction modifies the time of flight (TOF) for S0 and A0 vibration modes and generates a change in direction of the ultrasonic Lamb wave. The change in the TOF as a function of distance and thickness reduction was numerically determined using ray theory and then compared to experimental results. It is shown that the change in the direction of propagation depends on the vibrational mode and frequency of the Lamb waves and this can affect the detection and characterization of a hidden discontinuity.

Experimentally Observed Strain Distributions Near Circular Discontinuities of AA6061-T6 Extrusions During Axial Crush

An experimental investigation to determine the strain distribution and collapse behaviour for AA6061-T6 square cross-sectional extrusions with and without circular discontinuities under quasi-static axial compressive loading was completed. Three-dimensional digital image correlation (DIC) was utilized for strain assessment. In order to validate the results of the optical strain measurement system, tensile tests were first conducted employing both the DIC technique and a traditional extensometer. Strain observations from both methods were found to be very consistent prior to strain localization in the test specimen. Quasi-static axial crushing tests were then conducted. Extrusions considered for the present research had a nominal side width, wall thickness and length of 38.1 mm, 3.15 mm, and 200 mm, respectively. A centrally-located circular hole with diameter of either 14.29 mm, 10.72 mm or 7.14 mm was incorporated into the extrusion. Square tubes without any discontinuities were also considered in the experimental testing program. Testing results showed that the collapse mode of the extrusion altered from global bending to a cutting and splitting deformation mode with the presence of the circular discontinuity. Strain localization occurred near the vicinity of the holes for all specimens. For discontinuities sized 14.29 mm and 10.72 mm the location of strain localization and the initiation of material fracture was at the edge of the discontinuity while the location for extrusions with a 7.14 mm hole was found to occur at the intersection of the extrusion side walls. Maximum values of the effective strain were found to vary from approximately 60% to 100%. The region of strain localization was consistent with the location where material fracture initiated.

OS1-3-1 Full-field stress determination around circular discontinuity in a tensile loaded plate using x-displacements only

OS1-3-1 Full-field stress determination around circular discontinuity in a tensile loaded plate using x-displacements only

Experimental observations on the crush characteristics of AA6061 T4 and T6 structural square tubes with and without circular discontinuities

Quasi-static compressive testing of extruded aluminum alloy 6061-T4 and 6061-T6 square cross-sectional tubular specimens, with and without the presence of dual centrally located circular hole discontinuities, was completed to investigate the load management and energy absorption characteristics of these structural members. The tubular geometries selected (tube lengths of 200 mm and 300 mm, wall thickness of 3.15 mm, and nominal side width of 38.1 mm) had parameters which result in predicted global bending collapse under compressive loading. Centrally located circular holes, machined into the two opposing walls of the tubes, were used as crush initiators to commence the plastic buckling process. Holes with diameters of 7.1 mm and 14.2 mm were considered. In addition to progressive buckling, collapse modes involving cracking and splitting were observed in many tests and are characterized using photographs of the experimental process. The collapse modes and energy absorption of the crush test specimens were found to be dependent largely on material properties and to a lesser extent on the diameter of the discontinuity. Significant increases in the crush force efficiency, up to a maximum of approximately 22%, were observed for the shorter length tube geometry. However, the presence of the circular discontinuity within the AA6061 T4 300 mm tubes slightly degraded the crush force efficiency compared to the same length tubular member without any discontinuity. Energy absorption capabilities were substantially improved for all AA6061- T6 specimens containing a circular discontinuity relative to the specimens without any crush initiators. With the addition of the discontinuity, energy absorption was improved for the 200 mm length AA6061-T4 specimens but slightly decreased for the 300 mm length members.

Experimental observations on the crush characteristics of AA6061 T4 and T6 structural square tubes with and without circular discontinuities

Abstract Quasi-static compressive testing of extruded aluminum alloy 6061-T4 and 6061-T6 square cross-sectional tubular specimens, with and without the presence of dual centrally located circular hole discontinuities, was completed to investigate the load management and energy absorption characteristics of these structural members. The tubular geometries selected (tube lengths of 200 mm and 300 mm, wall thickness of 3.15 mm, and nominal side width of 38.1 mm) had parameters which result in predicted global bending collapse under compressive loading. Centrally located circular holes, machined into the two opposing walls of the tubes, were used as crush initiators to commence the plastic buckling process. Holes with diameters of 7.1 mm and 14.2 mm were considered. In addition to progressive buckling, collapse modes involving cracking and splitting were observed in many tests and are characterized using photographs of the experimental process. The collapse modes and energy absorption of the crush test specimens were found to be dependent largely on material properties and to a lesser extent on the diameter of the discontinuity. Significant increases in the crush force efficiency, up to a maximum of approximately 22%, were observed for the shorter length tube geometry. However, the presence of the circular discontinuity within the AA6061 T4 300 mm tubes slightly degraded the crush force efficiency compared to the same length tubular member without any discontinuity. Energy absorption capabilities were substantially improved for all AA6061- T6 specimens containing a circular discontinuity relative to the specimens without any crush initiators. With the addition of the discontinuity, energy absorption was improved for the 200 mm length AA6061-T4 specimens but slightly decreased for the 300 mm length members.

Liquid flow on a rotating disk prior to centrifugal atomization and spray deposition

Video observations of the flow patterns that develop on a rotating disk during centrifugal atomization and spray deposition, and subsequent metallographic studies conducted on solid skulls removed from the disk after processing, have indicated a circular discontinuity or hydraulic jump, which is manifested by a rapid increase in the thickness of the liquid metal and by a corresponding decrease in the radial velocity. A mathematical model has been developed that is capable of predicting both the occurrence and location of the jump, and the associated changes in the thickness profile and in the radial and tangential velocities of the liquid metal. Good correlations have been observed between model predictions and the flow patterns observed on the skull after atomization, and the effects of changes in material and operational parameters such as kinematic viscosity, volume flow rate, metallostatic head, and disk rotation speed have been quantified. Liquid metal flow is controlled primarily by the volume flow rate and by the metallostatic head prior to the hydraulic jump and by the centrifugal forces after the jump. The implications of these observations in terms of the atomization process are discussed.

The production of multiringed Laguerre–Gaussian modes by computer-generated holograms

A computer-generated hologram is used for the production of high-order multiringed Laguerre–Gaussian modes. These holograms differ from those previously reported in that they have an additional circular discontinuity. The holograms are used in transmission and are designed to convert the fundamental Hermite–Gaussian laser mode into a Laguerre–Gaussian mode with specific azimuthal and radial indices. The optical efficiency exceeds 40% with a radial mode purity of approximately 80%.

Detection of spatial discontinuities in first-order optical flow fields

We investigated the extent to which the human visual system can detect discontinuities in first-order optical flow fields. We constructed two types of spatial discontinuities: a circular split field with a straight edge and a disk with annular surround. We used two different first-order optical flow components: an expansion and a rotation. We found an intriguing difference in the detection thresholds for straight and circular discontinuities. Whereas straight discontinuities yielded thresholds of 10%-50% difference in expansion or rotation, circular discontinuities could, at first, only be detected at extreme differences (>> 100%). After a learning period, thresholds for such stimuli decreased, but they remained significantly higher than thresholds for the straight edge. Thresholds rose for stimuli that formed a gradual transition between a circular and a straight edge, and they decreased with increasing eccentricity of the circular discontinuity. Results suggest that symmetry in this stimulus, defined by the coincidence of the center of expansion or rotation and the center of the circular discontinuity, was responsible for the difference in thresholds for circular and straight discontinuities.

An investigation of graphite PEEK composite under compression with a centrally located circular discontinuity

The failure characteristic of graphite polyetheretherketone (Gr/PEEK) under compression with a centrally located circular discontinuity was investigated through experimentation and a nonlinear ply-by-ply finite element technique. The stacking sequence of the laminates investigated were: [0 ° 16], [90 ° 16], [±45 °] 4 S [0 °/90 °] 4S, and [0 °/ ± 45 0°/90 °] 2S. In the experimentation, [90 °] 16, [0 °/90 °] 4S, and [0 °/ ±45 °/90 °] 2S laminates, as well as three of the [0 °] 16, failed due to a crack that was normal to the loading direction and initiated from the edge of the hole progressing to the outer edges of the specimen. The [±45 °] 4 S specimens failed to support the load due to an internal crack that originated from the hole's edge and then traveled at an angle of about 42% to the direction of loading. The finite element method used to analytically model the failure of Gr/PEEK accurately modeled the response of the specimens tested experimentally.

Pressure Transient Behavior In Reservoirs With An Internal Circular Discontinuity

Abstract This paper presents the pressure transient response for reservoirs with an internal circular subregion. The solution is a generalization of that previously presented in the literature, which assumed that the subregion was either an impermeable barrier or a constant pressure circle. Two cases were considered, with the well located either inside or outside the circular discontinuity. When the well is located inside the circular subregion, the solution developed in the study is also a generalization of the well-known pressure response for a composite two-region system. The solution was obtained by using the concept of Green's function and by applying the Laplace transformation technique. The Laplace space response, although very complex, was inverted to real space with the Stehfest1 algorithm. When the well is located inside the circular subregion, the wellbore pressure response shows a behavior typical of radial composite systems, except for the effect of the well eccentricity, which acts as a skin factor. For the case where the active well is external to the subregion, three flow regimes are observed. The initial infinite-acting behavior and the late-time pseudoradial flow produce semilog straight lines which are parallel and reflect the transmissivity of the external region. The long-time effect of the discontinuity can be regarded as an apparent skin effect. The dependence of the solution on the diffusivity ratio, the mobility ratio, the geometric configuration and the size of the system was also investigated in the study. The solution can be used to simulate the pressure behavior for reservoirs which contain circular or approximately circular discontinuities, such as those caused by variations in rock and/or fluid properties due to the presence of shale lenses or fluid injection, for instance. The pressure solution can also be used to interpret single-well or interference tests in systems with these configurations.

Physicomathematical models for theories of nondestructive testing of thermophysical properties

The present work is devoted to the solution of some two-dimensional unsteady heat conduction problems for an infinite orthotropic cylinder with boundary conditions of the first- and second kind with a circular discontinuity line of temperature and specific heat flux. A solution of the two-dimensional unsteady heat conduction problem for an orthotropic cylinder is obtained with the aid of Laplace-Hankel transformations.

Failure characteristics in thermoplastic composite laminates due to an eccentric circular discontinuity

Abstract : The purpose of this thesis was to determine (both experimentally and analytically) the initiation and progression of failure, stress-strain response, and the failure loads of Graphite/Polyetheretherketone (Gr/PEEK) laminates, incorporating an eccentric 0.4 inch circular discontinuity, loaded in axial tension at room temperature. For each ply lay-up, three values of eccentricity were considered (the three values of eccentricity were determined by the hole location within each specimen). In addition, experimentation was conducted to study the effects of boundary conditions on the failure characteristics of the Gr/PEEK laminates; this was accomplished through the use of a special mounting fixture which allowed in-plane rotation of the specimens. Finally, experimentation was conducted, using photoelasticity, to verify the gross stress states of the Gr/PEEK laminates predicted by the analytical study. Analytically, a nonlinear material finite element program was used to predict the initiation and progression of failure, stress-strain response, and the failure loads of the Gr/Peek laminates. In addition, the effects of boundary conditions on the failure modes of the Gr/Peek laminates was studied analytically. And finally, the gross stress states of the Gr/PEEK laminates were considered in the analytical portion of this thesis.

Thermal stresses in a cylindrical shell containing a circular hole or a rigid inclusion

The thermal stress problem of a circular discontinuity in a cylindrical shell has been solved by continuum approach. Two types of discontinuities are considered: (i) a circular hole and (ii) a circular regid inclusion. The effect of a uniform temperature or a linearly varying temperature across the thickness has been studied. The problem is converted into an equivalent boundary value problem and boundary conditions are specified around the discontinuity. The results are presented in a graphical form for ready use.