Continuity Conditions Research Articles

A novel isogeometric coupling approach for assembled thin-walled structures

In the aerospace field, there are numerous assembled thin-walled structures with complex geometric continuity conditions. This makes isogeometric analysis (IGA) inevitably meet multi-patch issues. In previous work on 5-DOFs shell, when encountering G0 continuity or kinks, the approach often involved converting two local coordinate system rotations into three global coordinate system rotations to achieve multi-patch coupling. This often introduces additional DOFs and may destabilize the stiffness matrix. In this study, inspired by the concept of solid coupling, a new shell coupling approach is proposed, developing a 5-DOFs shell coupling framework suitable for different geometric continuities, providing a more efficient and simpler framework. When calculating the coupling stiffness matrix, there is no need for prior classification of the control points. Within this framework, the Nitsche, Penalty, and Mortar methods based on IGA are implemented. To demonstrate the effectiveness of the proposed framework in static and linear buckling analyzes, four different numerical examples were constructed, including G1, G0 continuity, and kinks. Under different continuity conditions, the results are sensitive to the parameter selection of the Nitsche and Penalty methods. Appropriate parameter selection can lead to better results for them. Compared to others, the Mortar method avoids this problem, making it easier to apply in engineering. The core codes are publicly available at https://github.com/tasteofbbq/ICA4ATWS.

Nitsche's method enhanced isogeometric homogenization of unidirectional composites with cylindrically orthotropic carbon/graphite fibers

An isogeometric homogenization (IGH) technique is constructed for the homogenization and localization of unidirectional composites with radially or circumferentially orthotropic carbon/graphite fibers. The proposed theory employs multiple non-conforming Non-Uniform Rational B-Splines (NURBS) patches to depict repeating unit cells (RUCs) representative of composite microstructures. Displacements are formulated using a two-scale expansion that integrates macroscopic and microscopic contributions, with the latter addressed through the isogeometric analysis technique. Nitsche's method is utilized to apply the interfacial traction and displacement continuity and periodicity conditions. The capability and accuracy of the IGH theory were validated upon comparison with the elasticity solutions that take into account explicitly fiber morphologies, along with classical micromechanics solutions based on equivalent fiber moduli. A comparative analysis with conventional finite-element techniques showcases the developed theory's ability to accurately replicate the singular stress field at the fiber center and to capture smooth stress distributions where significant stress gradients are encountered.

A refined model for functionally graded graphene nanoplatelets reinforced composite beams under thermal loads

Graphene is highly regarded as a promising material for various engineering purposes due to its remarkable physical characteristics. However, existing higher-order shear deformation theories may struggle to accurately capture the interlaminar mechanical response of functionally graded graphene nanoplatelets (FG-GNP) reinforced composite beams subjected to thermal loads. This arises from the pronounced discrepancies in material properties and thermal expansion coefficients among the various layers, making the interlaminar mechanical behavior of composite structures exceedingly complex under thermal loading. As a result, a meticulous analysis of interlaminar stresses becomes necessary for the structural assessment of GNP-reinforced composite beams under temperature variations. To overcome this limitation, we propose an advanced model incorporating transverse normal thermal deformation, tailored specifically for FG-GNP reinforced composite beams subjected to thermal loads. The developed model primarily boasts two advantages. Firstly, although transverse normal deformation is introduced into the displacement field, no additional displacement variables are increased, thereby maintaining model simplicity and efficiency. Secondly, the model achieves a high-precision interlaminar shear stress field taking into account the interlaminar continuity conditions and temperature effects. Furthermore, the elimination of second-order derivatives of in-plane displacement parameters from the transverse shear stress components leads to a simplification in the finite element implementation. Based on the proposed model, a simple three-node beam element is constructed. The 3D elasticity solutions and the results from alternative modeling frameworks are used to assess the performance of the developed model. Additionally, a comprehensive investigation is conducted to explore the effects of various parameters on the deformations and stresses of GNP-reinforced composite beams.

Operant ethanol self-administration behaviors do not predict sex differences in continuous access home cage drinking

Understanding sex differences in disease prevalence is critical to public health, particularly in the context of alcohol use disorder (AUD). The goal of this study was to understand sex differences in ethanol drinking behavior and define the precise conditions under which sex differences emerge. Consistent with prior work, C57BL/6J females drank more than males under continuous access two-bottle choice conditions. However, using ethanol self-administration - where an operant response results in access to an ethanol sipper for a fixed time period - we found no sex differences in operant response rates or ethanol consumption (volume per body weight consumed, as well as lick behavior). This remained true across a wide range of parameters including acquisition, when the ethanol sipper access period was manipulated, and when the concentration of the ethanol available was scaled. The only sex differences observed were in total ethanol consumption, which was explained by differences in body weight between males and females, rather than by sex differences in motivation to drink. Using dimensionality reduction approaches, we found that drinking behavior in the operant context did not cluster by sex, but rather clustered by high and low drinking phenotypes. Interestingly, these high and low drinking phenotypes in the operant context showed no correlation with those same categorizations in the home cage context within the same animals. These data underscore the complexity of sex differences in ethanol consumption, highlighting the important role that drinking conditions/context plays in the expression of these differences.

Simulations of radiation damage accumulation in Fe-9Cr under pulsed irradiation conditions representative of inertial fusion energy

Structural materials for laser-based inertial fusion energy (IFE) reactor concepts are expected to operate under pulsed irradiation conditions, with cycles consisting of microsecond-long neutron bursts followed by inter-pulse periods of up to one second in duration. During each laser shot, irradiation damage is introduced at dose rates that are up to six orders of magnitude higher than those in their magnetic fusion energy (MFE) counterparts. Under certain conditions, the inter-pulse periods may last an amount of time sufficient to anneal much of the damage introduced during each shot. This phenomenon is highly temperature dependent, with pulsed heating directly linked to the pulsed damage, large surface temperature spikes may also occur. As such, this intermittent mode of operation has the potential to lead to fundamental differences in how irradiation damage accumulates in structural reactor materials. However, damage to structural materials under IFE conditions has received comparatively much less attention than in MFE, as pulsed conditions add yet an extra dimension to the already extremely challenging problem of microstructural evolution under fusion neutron irradiation in structural materials. In this work we use the stochastic cluster dynamics (SCD) method to simulate the evolution with time of defect cluster concentrations under IFE conditions. We consider the Laser Inertial Fusion Energy (LIFE) reactor concept as the representative IFE design for our study, for which detailed spectral information is available, including gas transmutant production. We simulate several pulse frequencies and three different temperatures, and compare the results with continuous irradiation cases under identical average dose rates. The simulations are run in Fe-9Cr system as a model alloy for reduced-activation ferritic/martensitic (RAFM) steels, which are the leading structural material candidates for first-wall structures in MFE and IFE devices. We find that, in practically all scenarios, pulsed irradiation restricts the formation of helium-vacancy clusters relative to the levels seen under equivalent steady irradiation conditions. As well, although self-interstitial atom clusters do accumulate under pulsed operation, their number densities remain up to an order of magnitude lower than in continuous irradiation conditions. Based on the SCD results, we provide a temperature-pulse rate map to identify regions where pulsed irradiation may lead to larger defect accumulation than under continuous irradiation.

Time-varying dynamic characteristic analysis of journal–thrust coupled bearings based on the transient lubrication considering thermal-pressure coupled effect

This work studied the time-varying dynamic coefficients of journal–thrust coupled (JTC) bearing within a diesel engine crankshaft system. A transient thermoelastohydrodynamic coupled lubrication model of JTC bearings was established by considering pressure, flow, and heat continuity conditions at journal–thrust interface. On this basis, the dynamic coefficients of three degrees of freedom were further calculated. A transient lubrication experiment was conducted on a test rig to validate the established model. Parametric analysis was conducted to explore the transient lubrication performance and the dynamic coefficient of JTC bearing under different input parameters. Moreover, for cases when the crankshaft undergoes large axial movement, the influence of the JTC bearing dynamic coefficients on the natural characteristics of crankshaft were further analyzed to provide an analysis method for crankshaft vibration characteristics.

Harnessing phosphate limestone waste as a cost-effective solution for acid mine drainage treatment

Mining mineral ores like pyrrhotite often generates positive and negative outcomes for the community. On the one hand these valuable minerals are explored to provide economic opportunities. On the other, mining pyrrhotite presents adverse environmental and health effects that relates to acid mine drainage (AMD) formation in abandoned mines. This suggest that the sustainable mining of valuable minerals in Pyrrhotite requires cost and environmentally friendly approaches. In this research, we simulate in-situ neutralisation effect of phosphate limestone waste (PLW) on AMD from two mining sites in Morocco under continuous oxic conditions. To this end, we conducted batch tests to assess the effectiveness of PLW in mitigating AMD and releasing contaminants. These tests involved reacting limestone particles (at two sizes: <2 cm and < 4 cm) with AMD leachates over a five-day period The results indicated that the AMD is characterised by a pH of 2.5 and an electrical conductivity of 11.8 mS/cm. The inductively coupled plasma optical emission spectroscopy (ICP-OES) analyses showed a high sulfate concentration of 3668.83 mg/L and the presence of some metals, notably copper, aluminium, and iron. The neutralisation process of the AMD using PLW under oxic conditions was highlighted by the variation in pH while the water was in contact with the PLW. The pH rose from 2.5 to 5.25 while the electrical conductivity decreased from 11.8 to 7.03 mS/cm. During the treatment of the AMD with PLW, the percentage of sulfate removal from the effluent was 35 %. In addition, iron and aluminium were significantly removed from the AMD with a percentage of 99 % in the leachate. Therefore, these results indicate that neutralising AMD using this passive treatment approach is effective and may serve as a cost-effective mitigation for AMD, since no excessive grinding is required for the PLW.

Long-Term Fuel-Optimal Collision Avoidance Maneuvers with Station-Keeping Constraints

This work presents a sequential convex program method to compute fuel-optimal collision avoidance maneuvers for long-term encounters. The low-thrust acceleration model is used to account for the control, but the method can compute high-thrust maneuvers by increasing the maximum available acceleration. Dealing with the long-term conjunction poses additional challenges compared to the short-term problem because the encounter is not instantaneous. Thus, under the assumption of Gaussian statistics, the probability of collision is replaced by a simpler metric, the instantaneous probability of collision (IPoC), and a keep-out zone constraint is formulated as a continuous condition to be respected throughout the time frame of interest. The robustness of the solution is improved by introducing a constraint on the sensitivity of IPoC. Furthermore, the collision avoidance problem is coupled with the classical station-keeping requirement for geostationary Earth orbit satellites and with a return to the nominal orbit condition for low Earth orbit satellites. Even though no guarantee is given for the recovery of the global optimum solution, numerical simulations in different orbital regimes show that the proposed approach can yield a local fuel-optimal solution with a run time suitable for autonomous applications.

Variations in photoperiods and their impact on yield, photosynthesis and secondary metabolite production in basil microgreens

BackgroundThe effects of different photoperiods on plant phytochemical synthesis can be improved by adjusting the daily light integral. Photoperiod is one of the most important environmental factors that control growth, plant’s internal rhythm and the synthesis of secondary metabolites. Information about the appropriate standard in terms of photoperiod for growing basil microgreens as one of the most important medicinal plants is limited. In this study, the effects of five different photoperiods, 6 (6 h × 3 cycles), 8 (8 h × 2 cycles), 16, 18, and 24 h day− 1 on the yield, photosynthesis and synthesis of secondary metabolites of three cultivars and one genotype of basil microgreens in floating system were evaluated. The purpose of this research was to determine the feasibility of using permanent light in growing basil microgreens and to create the best balance between beneficial secondary metabolites and performance.ResultsThe results showed that the effects of photoperiod and cultivar on all investigated traits and their interaction on photosynthetic pigments, antioxidant capacity, total phenolic compounds, proline content and net photosynthesis rate were significantly different at the 1% level. The highest levels of vitamin C, flavonoids, anthocyanins, yield and antioxidant potential composite index (APCI) were obtained under the 24-h photoperiod. The highest antioxidant capacity was obtained for the Kapoor cultivar, and the highest total phenolic compound and proline contents were measured for the Ablagh genotype under a 24-h photoperiod. The highest yield (4.36 kg m− 2) and APCI (70.44) were obtained for the Ablagh genotype. The highest nitrate content was obtained with a photoperiod of 18 h for the Kapoor cultivar. The highest net photosynthesis rate was related to the Violeto cultivar under a 24-hour photoperiod (7.89 μmol CO2 m− 2 s− 1). Antioxidant capacity and flavonoids had a positive correlation with phenolic compounds and vitamin C. Yield had a positive correlation with antioxidant capacity, flavonoids, vitamin C, APCI, and proline.ConclusionsUnder continuous light conditions, basil microgreens resistance to light stress by increasing the synthesis of secondary metabolites and the increase of these biochemical compounds made basil microgreens increase their performance along with the increase of these health-promoting compounds. The best balance between antioxidant compounds and performance was achieved in continuous red + blue light. Based on these results, the use of continuous artificial LED lighting, due to the increase in plant biochemical with antioxidant properties and yield, can be a suitable strategy for growing basil microgreens in floating systems.

Support vector machine-based optimisation of traction gear modifications for multiple-condition electric multiple unit

The traction gear train is subjected to various internal excitations under different traction conditions, such as stiffness excitation, error excitation, meshing shock excitation, and tooth side clearance. The optimal modification scheme is different for each state, and the optimal modification plan based on a single working condition may not be applicable to every working condition. In this paper, we investigate the vibration response characteristics of electric multiple unit gearing under multiple conditions and propose a multi-condition modification scheme. Under different traction conditions, the mapping between gear modification parameters and vibration acceleration in gear transmissions is investigated using support vector machines. Genetic algorithms are used to solve the gear-modifying parameters to minimise the maximum vibration acceleration. A weight assignment principle is proposed to calculate the electric multiple unit traction gear transmission under different conditions, with the operating time and the amount of vibration in each condition as the measurement index. The results of the simulation show that the vibration acceleration under continuous conditions is reduced by 3.55 m/s2, a decrease of 69.88%; the vibration acceleration under high-speed conditions is reduced by 3.301 m/s2, a reduction of 58.74%, and the results show that the overall index of the electric multiple unit traction gear transmission system under different conditions has been improved after the optimisation of the multi-conditions modification, the gear transmission system's vibration is significantly reduced.

Frequency analysis of open/closed polygonal channel aerostructures made of hybrid nanocomposite materials and supported by piecewise elastic foundation using GDQE technique

This research delves into the theoretical exploration of the generalized differential quadrature element (GDQE) method for analyzing the dynamic response and natural frequency of aerospace structures, specifically polygonal channels found in aircraft, satellites, and space vehicle components. These structures are critical in aerospace engineering, serving in various capacities such as airframe components and fluid conveyance systems. Emphasizing the practical significance of these structures, the study incorporates the influence of ground or support conditions, employing a two-parameter piecewise elastic foundation model. The investigated open or closed channels are characterized as laminated functionally graded hybrid nanocomposites, specifically denoted as FG-HNC, reinforced with Carbon nanotubes (CNTs) and Clay nanoparticles (CNP). Each composite layer is reinforced with randomly oriented and uniformly distributed tubes and particles. The homogenization of the hybrid composite domain is performed using the hierarchy Halpin-Tsai micromechanical rule. Utilizing the GDQE technique, the channels are discretized into plate elements, and motion equations for each plate element are calculated based on first-order shear deformation theory and Hamilton's principle. The resulting equations are then solved using the standard GDQ method, with subsequent application of appropriate continuity conditions at shared element boundaries. In this comprehensive study, the research scrutinizes the effects of structure dimensions, channel sides crank angles, composite characteristics, and boundary conditions on the free vibration behavior of the polygonal channels. By offering detailed insights into the vibrational characteristics of FG-HNC structures, this study contributes to the advancement of aerospace engineering design and analysis.

Molecular mechanism of a coastal cyanobacterium Synechococcus sp. PCC 7002 adapting to changing phosphate concentrations

Phosphorus concentration on the surface of seawater varies greatly with different environments, especially in coastal. The molecular mechanism by which cyanobacteria adapt to fluctuating phosphorus bioavailability is still unclear. In this study, transcriptomes and gene knockouts were used to investigate the adaptive molecular mechanism of a model coastal cyanobacterium Synechococcus sp. PCC 7002 during periods of phosphorus starvation and phosphorus recovery (adding sufficient phosphorus after phosphorus starvation). The findings indicated that phosphorus deficiency affected the photosynthesis, ribosome synthesis, and bacterial motility pathways, which recommenced after phosphorus was resupplied. Even more, most of the metabolic pathways of cyanobacteria were enhanced after phosphorus recovery compared to the control which was kept in continuous phosphorus replete conditions. Based on transcriptome, 54 genes potentially related to phosphorus-deficiency adaptation were selected and knocked out individually or in combination. It was found that five mutants showed weak growth phenotype under phosphorus deficiency, indicating the importance of the genes (A0076, A0549-50, A1094, A1320, A1895) in the adaptation of phosphorus deficiency. Three mutants were found to grow better than the wild type under phosphorus deficiency, suggesting that the products of these genes (A0079, A0340, A2284–86) might influence the adaptation to phosphorus deficiency. Bioinformatics analysis revealed that cyanobacteria exposed to highly fluctuating phosphorus concentrations have more sophisticated phosphorus acquisition strategies. These results elucidated that Synechococcus sp. PCC 7002 have variable phosphorus response mechanisms to adapt to fluctuating phosphorus concentration, providing a novel perspective of how cyanobacteria may respond to the complex and dynamic environments.

Photocatalyzed Cascade Hydrogen Atom Transfers for Assembly of Multi-Substituted α-SCF3 and α-SCF2H Cyclopentanones.

A photocatalyzed formal (3+2) cycloaddition has been developed to construct original polysubstituted α-SCF3 cyclopentanones in a regio- and diastereoselective manner. This building block approach leverages trifluoromethylthio alkynes and branched/linear aldehydes, as readily available reaction partners, in consecutive hydrogen atom transfers and C-C bond formations. Difluoromethylthio alkynes are also compatible substrates. Furthermore, the potential for telescoped reaction starting from alcohols instead of aldehydes was demonstrated, as well as process automatization and scale-up under continuous microflow conditions. This prompted density functional theory (DFT) calculations to support a radical-mediated cascade process.

Photocatalyzed Cascade Hydrogen Atom Transfers for Assembly of Multi‐Substituted α‐SCF3 and α‐SCF2H Cyclopentanones

AbstractA photocatalyzed formal (3+2) cycloaddition has been developed to construct original polysubstituted α‐SCF3 cyclopentanones in a regio‐ and diastereoselective manner. This building block approach leverages trifluoromethylthio alkynes and branched/linear aldehydes, as readily available reaction partners, in consecutive hydrogen atom transfers and C−C bond formations. Difluoromethylthio alkynes are also compatible substrates. Furthermore, the potential for telescoped reaction starting from alcohols instead of aldehydes was demonstrated, as well as process automatization and scale‐up under continuous microflow conditions. This prompted density functional theory (DFT) calculations to support a radical‐mediated cascade process.

Batch and Continuous Flow Total Synthesis of Cannabidiol.

Herein, we present a comprehensive total synthesis of cannabidiol integrating both batch and continuous flow conditions. Our approach is planned to streamline the synthesis of olivetolic acid derivatives and utilize an enantiomerically pure monoterpene moiety obtained from naturally occurring (R)-(+)-limonene by photocatalysis. Key reactions, including the synthesis of olivetolic ester and a Friedel-Crafts alkylation, are successfully adapted to continuous flow, resulting in improved yields and selectivities. This study not only offers a scalable and efficient route for cannabidiol synthesis but also contributes to the synthetic approaches to access cannabinoids (diversity synthesis), with potential applications in medicinal and industrial contexts.

Study on inclusion removal in two-strand tundish with gas curtain considering bubble-inclusion attachment

ABSTRACT Application of a gas curtain is one of the main means to improve the cleanliness of liquid steel in tundish. In particular, the bubble-inclusion attachment is one of the important ways to remove inclusions, which cannot be ignored. The bubble size and gas flow are the main parameters of the gas curtain. In this paper, the Euler–Lagrange–Lagrange approach is used to study the three-phase interaction behaviour of liquid steel, bubble, and inclusion. The effects of inclusion size, bubble diameter, and gas flow on inclusion removal rate were studied with normal continuous casting conditions. The calculation results show that the cleanliness of molten steel can be improved by replacing the dam with a gas curtain. In the range of gas flow rate from 1.35 to 2.15 Nm3 h−1, the removal rate of bubble-inclusion attachment and total inclusion removal rate increase with the increase of gas flow. In the range of diameter from 4.5 mm to 6.0 mm with the same gas flow, the total removal rate and bubble-inclusion attachment removal rate increase with the bubble size decrease. The results provide a reference for improving the cleanliness of molten steel by properly increasing the gas flow and reducing the bubble size in industrial operations.

Gas Hydrate Plugging Mechanisms during Transient Shut–In/Restart Operation in Fully Dispersed Systems

Gas hydrate formation poses a significant challenge in offshore oil and gas production, particularly during cold restarts after extended shut–ins, which can lead to pipeline blockages. Although steady–state models have traditionally been used to predict hydrate formation under continuous production conditions, these models are often inadequate for transient operations due to issues like near–zero fluid flow shear affecting the viscosity calculations of hydrate slurries. This study introduces novel conceptual models for dispersed water–in–crude oil systems specifically designed for cold restart scenarios. The models are supported by direct observations and various experimental approaches, including bottle tests, rheometer measurements, micromechanical force apparatus, and rocking cell studies, which elucidate the underlying mechanisms of hydrate formation. Additionally, this work introduces a modeling approach to represent conceptual pictures, incorporating particle settling and yield stress, to determine whether the system will plug or not upon restart. Validation is provided through transient large–scale flowloop tests, confirming the plugging mechanisms outlined. This comprehensive approach offers insights into conditions that may safely prevent or potentially lead to blockages in the fully dispersed system during field restarts, thereby enhancing the understanding and management of gas hydrate risks in offshore oil and gas operations.

Fault Diagnosis and Prediction of Remaining Useful Life (RUL) of Rolling Element Bearing : A review state of art

Fault diagnosis of rolling element bearings is a critical aspect of machine maintenance and reliability. Bearings are extensively used in various industrial applications, and their failure can lead to costly downtime and equipment damage. Rotating machinery under continuous overload conditions can indeed significantly degrade bearing life and lead to various other issues. To identify issues in rolling element bearings (REB), several techniques and methods are employed. Diagnosing faults in ball bearings while simultaneously estimating the Remaining Useful Life (RUL) of the bearing is a crucial aspect of predictive maintenance. This can be achieved through a combination of signal processing techniques, machine learning methods, and RUL prediction models. The estimation of a bearing Remaining Useful Life (RUL) is of significant importance in predictive maintenance strategies to avoid unexpected failures, reduce downtime, and optimize maintenance costs. This literature review aims to explore the methodologies, techniques, and advancements in predicting the remaining useful life of bearings.

Plane SV-waves scattering by seawater convex surface topography and underlying lined tunnel in a saturated half-space

Analytical solutions of boundary-valued problems for aboveground topography and underground buried structures, especially for sites with overlying seawater, have always been challenging. Based on the region decomposition technique (RDT) and Hankel integral transform method (HITM), SV-waves scattering by the convex circular topography with seawater and underlying tunnel in a saturated half-space is solved. The primary problem is tackling additional scattered waves introduced by the water–soil interface and convex topography, while ensuring boundary conditions are all met. To this end, scattering wave potential functions in cylindrical coordinates are first transformed into the Hankel integral form in Cartesian coordinates. This greatly facilitates the straightforward application of free boundary conditions at the soil–seawater flat interface, rather than making a large circular arc approximate assumption, which, in turn, avoids the resultant accumulating errors. Secondly, scattering problem to be solved is mathematically and analytically formulated as solving a 5 × 5 linear equation system comprised of wave functions inside the convex topography and lining tunnel while satisfying all physical continuous boundary conditions. This is the main innovation and resulting consequence from the theoretical derivation process. Finally, validation of numerical examples between this paper, existing studies and theoretical analysis further demonstrates the reliability and general adaptability of solutions. Parametric studies of the incident SV waves are conducted to investigate the spatially varying seismic response. The effects of SV-waves incident angles and frequencies, tunnel burial depth, tunnel lining thickness, saturated soil porosity, and seawater depth are investigated and analyzed in detail. This study provides a feasible scheme of investigating the dynamic response of complex submarine sites, which is of great significance for both theoretical value and engineering purposes.

Metric perturbations of Kerr spacetime in Lorenz gauge: circular equatorial orbits

We construct the metric perturbation in Lorenz gauge for a compact body on a circular equatorial orbit of a rotating black hole (Kerr) spacetime, using a newly-developed method of separation of variables. The metric perturbation is formed from a linear sum of differential operators acting on Teukolsky mode functions, and certain auxiliary scalars, which are solutions to ordinary differential equations in the frequency domain. For radiative modes, the solution is uniquely determined by the s=±2 Weyl scalars, the s = 0 trace, and s=0,1 gauge scalars whose amplitudes are determined by imposing continuity conditions on the metric perturbation at the orbital radius. The static (zero-frequency) part of the metric perturbation, which is handled separately, also includes mass and angular momentum completion pieces. The metric perturbation is validated against the independent results of a 2+1D time domain code, and we demonstrate agreement at the expected level in all components, and the absence of gauge discontinuities. In principle, the new method can be used to determine the Lorenz-gauge metric perturbation at a sufficiently high precision to enable accurate second-order self-force calculations on Kerr spacetime in future. We conclude with a discussion of extensions of the method to eccentric and non-equatorial orbits.