Geometric Discontinuities Research Articles

Experimental and numerical study on multiaxial creep behavior of 16MND5 steel at 700℃

In-vessel retention (IVR) is an effective strategy of ensuring the structural integrity of RPV under severe accidents. In the IVR condition, due to the geometric discontinuity of pressure vessel, multiaxial creep is the main form of failure of RPV. Moreover, 16MND5 steel undergoes a phase transition from bainite to austenite. In order to study the multiaxial creep failure mechanism, creep tests on different notched bar are carried out at 700℃. The influence of grain boundary precipitation on creep behaviors was studied by micro-structural observation. Furthermore, based on the Kachanov-Robotnov continuous damage model (CDM), the term of activation energy Q is adopted in the newly-developed model as the correction parameter that is used to study the damage evolution and multiaxial creep behaviors of 16NND5 steel. Finally, the good agreement is achieved between theoretical prediction and experimental results.

Anisotropic Metamaterials Filled Rectangular Metallic Waveguides Propagation Study and Analysis

In this paper, we propose a novel generalized S-matrix characterization approach. The goal is to keep track of all observed discontinuities as efficiently as possible. In terms of reflection value, the proposed control strategy is based on transmission coefficients and one-axis rectangular guides. We successfully manipulate metal rectangular waveguide filters with both geometrical and physical discontinuity. Lossless discontinuity is depicted as a periodic structure that contains Metamaterials. The modal development of transverse fields provides the basis for the generalized S-matrix approach. The approach works by breaking down electromagnetic fields for each of the guides that make up the discontinuity on an orthonormal basis. When the Galerkin method is used, the matrix of diffraction of the junction is obtained directly.

Influence of local stiffeners and cutout shapes on the vibration and stability characteristics of quasi-isotropic laminates under hygro-thermo-mechanical loadings

Abstract s The perforated stiffened panel is generally found as a sub-component of sophisticated structures. The fundamental purpose of this panel is to withstand against buckling under complicated loading and environmental conditions. Hence, an accurate knowledge of critical buckling behaviour of stiffened panels is very much essential for a reliable and lightweight structural design. In this paper, the focus is on quasi-laminated panels with different cutout shapes of various sizes and their responses to hygrothermal environments under nonlinearly varying edge loads and is compared with the locally stiffened panels. Towards this, the modelling of the panel and stiffener is done by adopting nine-noded heterosis plate elements and three noded beam elements respectively. The stiffener formulation is suitably modified in order to take the torsional effect also into consideration along with the effect of shear deformation. Initially, the plate and the stiffener elements are treated separately, and then the displacement compatibility is maintained between them by using the transformation matrix. For a given loading and geometric discontinuity, the stress distribution within the perforated panel is highly non-uniform in nature and hence a dynamic approach has been used to calculate buckling loads by adopting two sets of boundary conditions, one set for pre-buckling stress analysis and the second set for buckling analysis. Four different quasi-isotropic stacking sequences are deliberated in this work by varying different ply-orientation in each scheme. The study also addresses the effect of various parameters such as nonlinear loads, hygro-thermal loads, cutout size and shapes, position of cutout, stiffener parameters, stacking sequences, thickness of plate and boundary conditions.

A NURBS-discontinuous and enriched isogeometric boundary element formulation for two-dimensional fatigue crack growth

A new extended isogeometric boundary element method (XIGABEM) formulation is proposed for simulating multiple fatigue crack propagation in two-dimensional domains. The classical use of NURBS in isogeometric formulations is further extended by repeated knot insertion to introduce a C−1 continuity within the approximation space as an elegant approach to representing geometrical discontinuities at crack intersections. This strategy is also used to restrict the enrichment term to the portion of the NURBS defining the tip, where it is necessary. At this near-tip zone, the linear elastic fracture mechanics solutions are embedded into the displacement approximation to represent the theoretical square root behaviour. The enrichment procedure introduces just two degrees of freedom per crack tip, and a tying constraint is used to yield a square linear system. In this direct approach, the stress intensity factors (SIFs) are found as terms in the solution vector without requiring post-processing techniques.Several examples are presented to illustrate the application of the XIGABEM. The accuracy of the results compares favourably against those from the literature, and also against solutions obtained from unenriched and enriched indirect methods that employ the J-integral for SIF extraction. Furthermore, the proposed direct approach is capable of significantly reducing the execution time.

Strut-and-tie models obtained by way of topological optimisation

The strut-and-tie model is widely used for the analysis and design of reinforced concrete structures under a plane stress state. To apply this model, it is necessary to define strut-and-tie systems that represent the flow of stresses generated in the analysed structure. To make the concept of the model less dependent on designer experience for regions or structures with geometric or static discontinuity, this strut-and-tie model is defined through an evolutionary structural optimisation (ESO) considering linear isotropic material, which provides the automatic generation of strut-and-tie models. The evolution criterion adopted by the topological optimisation method considers the elimination of less requested elements in terms of tension, based on the elastic-linear analysis. The aim of this study is to develop and implement various strategies to control the removal of these elements, which leads to different final configurations. In this context, optimised solutions to complex problems involving reinforced concrete structures can be obtained. The results of two out of the three practical applications presented were compared with the results provided in the literature to validate the efficiency of the proposed algorithm.

On applicability of MQ-RPIM and MLPG meshless methods with 3D extended-enriched base functions for estimation of mode I stress intensity factor and fatigue crack growth in cyclic tensile and bending load of an un-notched and notched shaft

In this study, a numerical meshless method is used to solve the weak form of the linear elastic equations in solid mechanics. Evaluation and comparison of the numerical meshless methods have been carried out via the radial point interpolation meshless method with multi-quadrics base functions (MQ-RPIM) and meshless local Petrov-Galerkin method (MLPG). Using these two methods, stress intensity factors in an elastic medium containing geometric discontinuities and cracks are estimated based on tensile and bending cyclic loading. The analysis domain has been identified via three-dimensional modeling of the notched and un-notched shafts with an initial surface semi-elliptical crack subjected to tensile or bending cyclic loadings. To enhance the accuracy of calculations, the RPIM meshless method is applied using polynomial and extended-enriched 3D base functions. Shape functions have been developed using standard and optimal parameters and values with Mono-Objective Function in PSO algorithm. In the MLPG meshless method with the extended-enriched functions, discretization is performed via direct and penalty factor methods, to reach more efficient results and meet the boundary conditions. Efficiency comparison of the selected numerical methods with the experimental findings and the numerical analysis of finite elements method indicates that in comparison with the MLPG method, MQ-RPIM enriched meshless method can be utilized with fewer nodes in the analysis domain while reaching the accuracy and convergence with lower stress intensity factors and gentler slope. However, the processing time of the MLPG meshless method is lower than that of the other methods.

The Possibility of Fault Location in Cross-Bonded Cables by Broadband Impedance Spectroscopy

Broadband impedance spectroscopy (BIS) provides a new method for cable fault location, however, this method has not been properly used in locating cable fault of cross-bonded (CB) cables due to the geometric discontinuity of impedance spectroscopy measurement loop. This study addresses the possibility of fault location by BIS in CB cables. First, this paper proposes a fault location method by transforming BIS in frequency domain into the location function in space domain with the aid of integral transformation (IT). The kernel function e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j2βx</sup> is used to obtain fault location function. Second, this paper demonstrates an impedance spectroscopy measurement loop in CB cables. BIS in CB cables is observed having a generalized orthogonality with the kernel function e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j2βx</sup> . Given this, the IT method is applicable for fault location of CB cables. Finally, this study carries out the location experiment of cable joints on a 110 kV CB cable in cable trench. The experiment shows that BIS in CB cables could be obtained by the loop proposed in this paper. Besides, the results verify the possibility of fault location in CB cables by IT method using BIS.

Vibration and sensitivity analysis of double-layered non-uniform piezoelectric microcantilever as a self-sensing mass sensor

Piezoelectric microcantilevers are specially popular in microelectromechanical system (MEMS) devices due to their high accuracy, environmental friendliness, low response time, and compatibility with compact designs. Since mass sensors are an important application of piezoelectric microcantilevers (PMCs), it is particularly important to determine PMCs sensitivity to nanoparticle absorption. For this purpose, a dynamic analysis was carried out to derive the equation governing vibrations of a PMC in air and water environments. A sphere chain model was used to model hydrodynamic forces acting on the PMC. In order to utilize the bending of the PMC for determining the output current from the piezoelectric layer, the resulting equation was solved by taking into account how the PMC geometrical discontinuities affected eigenvalues. In addition to the sensitivity of natural frequency and amplitude of these sensors, sensitivity of output electric current from their piezoelectric layer is also important. Therefore, the sensitivity of these parameters to nanoparticle absorption was analyzed and compared so as to select the suitable parameter for achieving satisfactory performance of PMC mass sensors in air and liquid working environments. The importance of selecting proper geometrical dimensions in the design of PMC mass sensors is realized by considering the fact that their sensitivity can be enhanced by properly selecting their dimensions. Accordingly, the effects of geometrical dimensions of the sensor on its sensitivity were determined through Sobol sensitivity analysis. The simulation results indicated that the sensitivity of output current from the piezoelectric layer and that of the vibration amplitude in the first three modes were the suitable parameters determining the performance of the PMC mass sensor in air and fluid environments, respectively.

Path-space differentiable rendering of participating media

Physics-based differentiable rendering---which focuses on estimating derivatives of radiometric detector responses with respect to arbitrary scene parameters---has a diverse array of applications from solving analysis-by-synthesis problems to training machine-learning pipelines incorporating forward-rendering processes. Unfortunately, existing general-purpose differentiable rendering techniques lack either the generality to handle volumetric light transport or the flexibility to devise Monte Carlo estimators capable of handling complex geometries and light transport effects. In this paper, we bridge this gap by showing how generalized path integrals can be differentiated with respect to arbitrary scene parameters. Specifically, we establish the mathematical formulation of generalized differential path integrals that capture both interfacial and volumetric light transport. Our formulation allows the development of advanced differentiable rendering algorithms capable of efficiently handling challenging geometric discontinuities and light transport phenomena such as volumetric caustics. We validate our method by comparing our derivative estimates to those generated using the finite differences. Further, to demonstrate the effectiveness of our technique, we compare both differentiable rendering and inverse rendering performance with state-of-the-art methods.

The exact solution to the Shallow water Equations Riemann problem at width jumps in rectangular channels

Riemann problems at geometric discontinuities are a classic and fascinating topic of hydraulics. In the present paper, the exact solution to the Riemann problem of the one-dimensional (1-d) Shallow water Equations at monotonic width discontinuities is completely determined for any initial condition. This solution is based on the assumption that the relationship between the states immediately to the left and to the right of the discontinuity is a stationary weak solution of the 1-d variable-width Shallow water Equations. Under this hypothesis, it is demonstrated that the solution to the Riemann problem always exists, although there are cases where the solution is triple. This proves that it is possible to define width-jump interior boundary conditions of Saint Venant models that lead to well-posed problems, and that additional physical information is required to pick the relevant Riemann wave configuration among the alternatives when the solution is multiple. The analysis of an existing Finite Volume numerical scheme from the literature, based on flow variables reconstruction with preservation of specific energy and discharge, shows that the algorithm captures the solution with supercritical flow through the width discontinuity when multiple solutions are possible. This suggests that it is possible to change the algorithm accordingly to the structure of the physically relevant solution. Interestingly, the 1-d variable-width Shallow water Equations are formally identical to the 1-d Porous Shallow water Equations, implying that the exact solutions provided in the present paper are relevant for two-dimensional (2-d) Porous Shallow water numerical models aiming at urban flooding simulations.The procedure presented in this paper may be used not only to construct new challenging benchmarks for numerical schemes, but also as a guide for the construction of new algorithms, and for the interpretation of on-field and laboratory data related to transients at rapid channel width variations. The appearance of multiple solutions, which is connected to the hydraulic hysteresis phenomenon observed in the case of supercritical flows impinging a cross-section contraction, requires a criterion for the disambiguation of solutions. This will be the object of future research.

On the effect of the node and building orientation on the fatigue behavior of L‐PBF Ti6Al4V lattice structure sub‐unital elements

Despite the great potential of additively manufactured (AM) metallic lattice materials, a comprehensive understanding of their mechanical behavior, particularly fatigue, has yet to be achieved. The role of the sub-unital lattice elements, that is, the struts and the nodes (or strut junctions), is rarely explored, even though it is well known that fatigue is a local phenomenon, determined by the small features of a structure (defects and local geometrical discontinuities). In this work, the mechanical behavior of nodes and struts has been investigated by designing laser powder bed fusion (L-PBF) Ti6Al4V single strut specimens, with a node placed in the central part of the gauge length. The specimens were manufactured according to four different building orientations, namely, 90°, 45°, 15°, and 0° to the build plane. The influence of the fillet radius at the node and of the printing direction on the fatigue strength has been examined.

Evaluation of stress intensity factors under thermal effect employing domain integral method and ordinary state based peridynamic theory

In this article, several thermoelastic benchmark cases are studied within the framework of ordinary state based peridynamic theory (OSPD). By using OSPD, the limitations of geometrical discontinuity in fracture analysis can be overcome. Meanwhile, double nodes can also be avoided during crack definition. A domain integral method with thermal effect is applied in calculating the thermal stress intensity factors (TSIFs). Meanwhile, peridynamic differential operators are utilized to rewrite the spatial derivatives in the domain integral. Numerical investigations of TSIFs in the single and mixed-mode crack scenarios are provided respectively, and verified by the reference solutions. Good agreements between OSPD and the reference solutions show high performance and capability of the proposed method in thermoelastic fracture analysis.

Optimization of placement of piezoelectric wafers based on a hybrid model using pitch-catch and pulse-echo configurations

The development of Structural Health Monitoring (SHM) systems and integration in our structures is a necessity. It has proven to provide a robust and low-cost solution for monitoring structural integrity and can predict the remaining life of our structures. One of the most important aspects of SHM systems is the design and implementation of sensor networks. This study proposes a new hybrid model for optimizing sensor placement on convex and non-convex structures. We propose a novel framework in which two detection mechanisms are considered: pitch-catch and pulse-echo to provide coverage for a given surface. These two mechanisms will complement each other to minimize the number of sensors used while maintaining a high coverage. This combination also allows for better coverage of the corners and regions in the proximity of geometrical discontinuity (such as holes and openings). The monitored area is discretized into a set of control points. For a control point to be covered, it should satisfy the user-defined coverage level which is the number of sensing paths crossing that point. These sensing paths are provided by two modes of communications (pitch-catch and pulse-echo) between the actuator-sensor pairs. The model, which is solved using a genetic algorithm (GA), provides flexibility by allowing the user to input different parameters such as the attenuation distance of the propagating waves and the sensing path limits of both coverage configurations that can be determined through experimentation. The efficiency of the proposed model is then demonstrated by simulating different geometrical shapes. Significant improvement in the coverage of the monitored area, reaching 34.6%, was achieved when compared to the coverage provided by some preliminary solutions such as uniformly placing the sensors on the plate under study. Also, the advantage of combining both configurations (pitch-catch and pulse-echo) in the same model was investigated. It was shown that the latter highly impacted the coverage in the blind zones (corners and edges) where a single configuration is not effective. Afterward, experimental validation was carried out to evaluate the model’s accuracy in damage localization within the optimized sensor networks. The results demonstrated the proficiency of the model developed in distributing the sensors on the tested specimens.

Vibration response of a geometrically discontinuous bi-directional functionally graded plate resting on elastic foundations in thermal environment with initial imperfections

The present study includes the free vibration analysis of geometrically imperfect and discontinuous porous functionally graded bi-directional plate (B-FGP) resting on an elastic foundation in a thermal environment. The geometric discontinuity is present in the form of a circular cutout at the center of the plate whereas initial imperfections have been incorporated in terms of geometric as well as porosity inclusions. The kinematic formulation is based on the refined non-polynomial trigonometric higher-order shear deformation theory (HSDT). A new porosity model has been developed to incorporate the influence of the microstructure defect on the effective material properties of the B-FGP. The gradation of properties is done along the thickness (z-direction) as well as the length (x-direction) of the plate using the power-law distribution. A new expression has been given to obtain the solution of the non-linear temperature rise along the thickness of the B-FGP. A continuous Lagrangian four-noded quadrilateral element has been used to perform the finite element formulation with eight degrees of freedom per node. The equations of motion have been derived using a variational approach. The validation and comparative study have been done to authenticate the present formulation. The influence of the cutout radius, elastic foundation parameters, porosity, thermal environment, geometric imperfection, and volume fraction indexes has been discussed in detail.

Image stitching for fringe projection profilometry

There are many optical methods for extracting the geometric information of an object from an image. The structured light method based on digital fringe projection is widely employed. Sometimes the fringe patterns have some undesired invalid areas due to drastic surface profile changes of the tested object, or geometric discontinuities. In addition, a large projection angle affects the quality of the acquired data. These invalid areas may introduce difficulties for further processing. We propose to combine image fusion methods and a typical structured light system to alleviate the shadow problems created by a single projector.

Automation of tow wise modelling for automated fibre placement and filament wound composites

Automated Fibre Placement (AFP) and Filament Winding (FW) provide flexibility to tailor not only fibre angles but the distribution of fibres and orientations within the structure, with huge potential for laminate performance optimization. These advanced technologies, however, create intrinsic defects that result in potentially critical geometric discontinuities (tow gaps/overlaps, tow weaving, etc.). This paper presents a high-fidelity geometric modelling tool of tow-wise manufactured laminates that will serve as the foundation of finite element analysis for more accurate prediction of local and global structural performance. The main feature of this tool is the capability of modelling each tow individually to offer an opportunity of depicting the gaps /overlaps, tow drops, and out-of-plane waviness explicitly. In this study, the modelling technique and algorithms implemented in this tool are thoroughly elaborated and the functionalities able to capture the complex 3D architectures of AFP composites are demonstrated through several case studies.

Thermoelectric Metamaterials: Nano‐Waveguides for Thermoelectric Energy Conversion and Heat Management at the Nanoscale

AbstractThe idea of using metamaterials for thermoelectrics was proposed 10 years ago. Enhanced thermoelectric effects and decreased thermal conduction are theoretically demonstrated due to modification of electrons and phonons by quantum interference between propagating and scattered waves at geometrical discontinuities. These structures are now considered promising for breakthrough in thermoelectric energy conversion and heat management at the nanoscale. They could ideally power the Internet of things. This review is devoted to electron and phonon transport properties of thermoelectric metamaterials in the quantum confinement regime. Enhanced thermoelectric effects and decreased thermal conductivity are related with geometrically induced fluctuations, resonances, quasi‐localized states, and minibands. Conduction fluctuations show generic behavior amenable to experimental confirmation. It is emphasized that both electrons and phonons are affected by geometry modulation and that, contrary to what is often assumed, their properties cannot be a priori tuned independently. Effects of periodicity and disorder on electrons and phonons in the same structures indicate strategies to design geometry modulation for high thermoelectric efficiency. Generic principles of operation boost prospects to make technologically important materials (e.g., Si, III–Vs, graphene) efficient thermoelectric materials. Geometrically enhanced thermoelectric properties and controlled heat conduction can cooperate with other functionalities of metamaterials for next‐generation nanodevices.

Three-Dimensional Stress Analysis for Semi-Elliptical Cracks in the Connection of Cylinder-Hemispherical Head for Thick-Walled Cylindrical Pressure Vessels

These pressure vessels are made by different type of heads. One of them is hemi-spherical head. The area of geometrical discontinuity, like the connection of the cylinder to its hemi-spherical head, are the most susceptible areas for crack initiation along their welds. So it is worthwhile to consider cracks located at this connection. The purpose of this article is to investigate the effect of variation of stress field and geometry of problem on distribution of Stress Intensity Factor (SIF) for a semi-elliptical surface crack which is located at the connection of cylinder to its hemispherical head. The three dimensional finite element analysis is performed by employing singular elements along the crack front. The ratio of crack depth to crack length (a/c) ranged from 0.3 to 1.2; the ratio of crack depth to wall thickness (a/t) ranged from 0.2 to 0.8; and the cylinder geometry parameter of vessel ranged from 1.2 to 2. For better comparison the results are normalized and reported in non-dimensional formats. The results show that the crack configuration, vessel thickness and radius have significant influence on the stress intensity factor distribution along the crack front. Also For a fixed and the maximum value of SIF occur in the cylindrical part and approximately near the deepest point of crack; not on the deepest point of crack depth and this may be due to changing stress field in this connection. The stress intensity factors are presented in suitable curves for various geometrical configurations providing useful tool for the fracture mechanics design of cracked pressure vessels.

Probabilistic fatigue life prediction of notched components using strain energy density approach

To meet various functional requirements, engineering components are usually designed with geometrical discontinuities, which raise stress concentrations undergoing external loadings. Comparing with other locations, these regions with high levels of stress incline to initiate cracks under cyclic loadings, which determine fatigue strength of the whole part. Accordingly, a novel strain energy density-based model for notch fatigue life prediction is developed, and a P–W–Nf curve is raised to consider the fatigue life scatter originating from material dispersity. Experimental data of different notched specimens made with TC4 alloys are used for model validation and comparison. Results indicate that the proposed model predictions show higher accuracy than the other four models. Finally, fatigue life assessment of a compressor disk considering material and load uncertainties is conducted.

An assessment of SPH simulations of sudden expansion/contraction 3-D channel flows

In this paper, we investigate the application of smoothed particle hydrodynamics (SPH) to the computation of 3-D flows in channels with sudden expansion or contraction. In the same context, we also discuss 2-D SPH computations applicable to channels characterized by cross-sections of large aspect ratios. The particle nature of SPH allows us to treat macro-systems similarly to atomic systems, transferring knowledge from molecular dynamics (MD) and dissipative particle dynamics (DPD) and suggesting a common framework for simulations at different scales. Computations are carried out by making use of tools previously used for atomic-scale systems (usually MD) and mesoscopic systems (usually DPD). The results obtained suggest that SPH captures the main flow characteristics and achieves good accuracy both in 2-D and 3-D, at least for Re values in the range 0.0177 to 55.4 investigated here. Minor numerical artifacts may be observed near the solid boundaries, especially at corner discontinuities. Such localized inaccuracies near points of geometric discontinuity are common in all numerical simulation methods.