An adaptive scaled boundary finite element method by subdividing subdomains for elastodynamic problems

The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.

SPLITTING A CONCAVE DOMAIN TO CONVEX SUBDOMAINS

We will study the convergence property of Schwarz alternating method for concave region where the concave region is decomposed into convex subdomains. Optimality of regular preconditioner deduced from Schwarz alternating is also proved.It is shown that the convergent rate and the condition number are independent of the mesh size but dependent on the relative geometric position of subdomains.Special care is devoted to non-uniform meshes, exclusively, local properties like the shape regularity of the finite elements are utilized.

Role of autoantibodies against the linker subdomains of envoplakin and periplakin in the pathogenesis of paraneoplastic pemphigus

Background The presence of autoantibodies against multiple epidermal proteins is an important feature in paraneoplastic pemphigus （PNP）. Circulating anti-desmoglein 3 autoantibody, the major pathogenic autoantibody in pemphigus vulgaris （PV）, has been proved pathogenic in PNP. Because of many clinical differences between PNP and PV, we speculate about the involvement of other autoantibodies in the pathogenesis of PNP. Envoplakin （EPL） and periplakin （PPL） are recognized by most PNP sera. Their linker subdomains are highly homologous and necessary for the association of intermediate filaments. Methods We characterized the autoantibodies against the linker subdomains of EPL and PPL in PNP patients＇ sera and their associated tumors by enzyme-linked immunosorbent assay （ELISA） and immunofluorence. We also applied the purified autoantibodies against EPL and PPL from PNP sera to cultured human epidermal keratinocytes （HEK）, to evaluate the changes of cell-cell adhesion. Results Autoantibodies against EPL and PPL were detected in most PNP patients by ELISA, and the decrease of these autoantibodies after removal of the tumors was roughly comparable to the improvement of clinical symptoms. Cultured tumor cells from PNP patients secreted these autoantibodies. Specific immunoglobulin receptors for EPL and PPL were found on B lymphocytes in tumors from PNP. Furthermore, purified anti-EPL and anti-PPL autoantibodies from PNP sera were capable of dissociating cultured human epidermal keratinocytes. Conclusion Autoantibodies against EPL and PPL may also be pathogenic in PNP.

Dynamic Response of A Group of Cylindrical Storage Tanks with Baffles Considering the Effect of Soil Foundation

The sloshing in a group of rigid cylindrical tanks with baffles and on soil foundation under horizontal excitation is studied analytically.The solutions for the velocity potential are derived out by the liquid subdomain method.Equivalent models with mass-spring oscillators are established to replace continuous fluid.Combined with the least square technique,Chebyshev polynomials are employed to fit horizontal,rocking and horizontal-rocking coupling impedances of soil,respectively.A lumped parameter model for impedance is presented to describe the effects of soil on tank structures.A mechanical model for the soil-foundation-tank-liquid-baffle system with small amount of calculation and high accuracy is proposed using the substructure technique.The analytical solutions are in comparison with data from reported literature and numerical codes to validate the effectiveness and correctness of the model.Detailed dynamic properties and seismic responses of the soil-tank system are given for the baffle number,size and location as well as soil parameter.

Analytical Model and Topology Optimization of Doubly-fed Induction Generator

As the core component of energy conversion for large wind turbines,the output performance of doubly-fed induction generators (DFIGs) plays a decisive role in the power quality of wind turbines.To realize the fast and accurate design optimization of DFIGs,this paper proposes a novel hybriddriven surrogate-assisted optimization method.It firstly establishes an accurate subdomain model of DFIGs to analytically predict performance indexes.Furthermore,taking the inexpensive analytical dataset produced by the subdomain model as the source domain and the expensive finite element analysis dataset as the target domain,a high-precision surrogate model is trained in a transfer learning way and used for the subsequent multi-objective optimization process.Based on this model,taking the total harmonic distortion of electromotive force,cogging torque,and iron loss as objectives,and the slot and inner/outer diameters as parameters for optimizing the topology,achieve a rapid and accurate electromagnetic design for DFIGs.Finally,experiments are carried out on a 3MW DFIG to validate the effectiveness of the proposed method.

Time-Spectral Solution of Initial-Value Problems—Subdomain Approach

Temporal and spatial subdomain techniques are proposed for a time-spectral method for solution of initial-value problems. The spectral method, called the generalised weighted residual method (GWRM), is a generalisation of weighted residual methods to the time and parameter domains [1]. A semi-analytical Chebyshev polynomial ansatz is employed, and the problem reduces to determine the coefficients of the ansatz from linear or nonlinear algebraic systems of equations. In order to avoid large memory storage and computational cost, it is preferable to subdivide the temporal and spatial domains into subdomains. Methods and examples of this article demonstrate how this can be achieved.

Subdomain Model for Predicting Armature Reaction Field of Dual-Stator Consequent-Pole PM Machines Accounting for Tooth-Tips

This paper presents an exact analytical subdomain model of dual-stator consequent-pole permanent-magnet(DSCPPM)machines accounting for tooth-tips,which can accurately predict the armature reaction field distribution in DSCPPM machines.In the proposed subdomain model,the field domain is composed of four types of sub-regions,viz.magnets,outer/inner air gaps,slots and slot openings.The analytical expressions of vector potential in each sub-region are determined by boundary and interface conditions.In comparison to the analytically predicted results,the corresponding flux density field distributions computed by finite element(FE)method are analyzed,which confirms the excellent accuracy of the developed subdomain model.

Design and Performance Analysis of Axial Flux Permanent Magnet Machines with Double-Stator Dislocation Using a Combined Wye-Delta Connection

Conventional fractional slot concentrated winding three-phase axial flux permanent magnet machines have an abundance of armature reaction magnetic field harmonics which deteriorate the torque performance of the machine.This paper presents a double-stator dislocated axial flux permanent magnet machine with combined wye-delta winding.A wye-delta(Y-△)winding connection method is designed to eliminate the 6 th ripple torque generated by air gap magnetic field harmonics.Then,the accurate subdomain method is adopted to acquire the no-load and armature magnetic fields of the machine,respectively,and the magnetic field harmonics and torque performance of the designed machine are analyzed.Finally,a 6 k W,4000 r/min,18-slot/16-pole axial flux permanent magnet machine is designed.The finite element simulation results show that the proposed machine can effectively eliminate the 6 th ripple torque and greatly reduce the torque ripple while the average torque is essentially identical to that of the conventional three-phase machines with wye-winding connection.

Electromagnetic Performance Prediction for the Symmetrical Dual Three-phase Surface-mounted PMSM under Open-phase Faults Based on Accurate Subdomain Model

The paper presents an accurate analytical subdomain model for predicting the electromagnetic performance in the symmetrical dual three-phase surface-mounted permanent magnet synchronous machine(PMSM)under open-phase faulty conditions.The model derivations are extended from previous accurate subdomain models accounting for slotting effects.Compared with most conventional subdomain models for traditional three-phase machines with nonoverlapping winding arrangement,the subdomain model proposed in this paper applied for the 24-slot/4-pole dual three-phase machine with symmetrical overlapping winding arrangement.In order to investigate the postfault electromagnetic performance,the reconfigured phase currents and then current density distribution in stator slots under different open-circuit conditions are discussed.According to the developed model and postfault current density distribution,the steady-state electromagnetic performance,such as the electromagnetic torque and unbalanced magnetic force,under open-circuit faulty conditions are obtained.For validation purposes,finite element analysis(FEA)is employed to validate the analytical results.The result indicate that the postfault electromagnet performance can be accurately predicted by the proposed subdomain model,which is in good agreement with FEA results.

Decentralized damage diagnostic technique for tall buildings using VARMAX model

Civil infrastructure,especially buildings,are becoming more slender,tall,and multipurpose,creating a need to continuously monitor their health to ensure the safety and security of human lives and assets.While the majority of structural health monitoring techniques use measurements from the entire structure,in this study,an output-only damage diagnostic technique using a decentralized concept(subdomain-based)for tall buildings and employing a vector form of the autoregressive moving average with exogenous input(VARMAX)model is proposed,which offers reduced instrumentation and data handling requirements.Unlike other decentralized approaches,this technique predicts more than one DOF at a time so the number of subdomains required for the diagnosis of the complete structure is minimized.The proposed subdomain-based damage diagnostic algorithm works with ambient loads and does not require any correlated numerical models since it is solely based on measured data.The proposed algorithm can identify the time instant of damage,spatial location(s)and characterize the damage intensity.Efforts have been made to account for confounding factors such as environmental and operational variabilities separate from measurement noise to avoid false positive alarms.The effectiveness of the proposed technique is illustrated using synthetic time history responses from a twenty-story framed structure under ambient loading and an experimental study on a ten-story framed structure.Both numerical and experimental investigations confirm the effectiveness of the method and its robustness to environmental/operational variabilities and measurement noise.

Modeling of Fault-tolerant Flux-switching Permanent-magnet Machines for Predicting Magnetic and Armature Reaction Fields

The paper develops accurate analytical subdomain models for predicting the magnetic and armature reaction fields in fault-tolerant flux-switching permanent-magnet machines.The entire region is divided into five subdomains,followed by rotor slots,air-gap,stator slots,PM,and external air-gap imported to account for flux leakage.The coil turns and the remanence of magnets are adjusted by keeping the magnetic and electrical loading on the motor constant.The distance between the centers of two adjacent stator slots varies due to the introduction of faulttolerant teeth.According to the variable separation method,the general solution expression of each region can be determined by solving the partial differential systems of equations.The magnetic field distributions of subdomains are obtained by applying the continuity conditions between adjacent regions.Some analytical field expressions are represented as new forms under armature reaction field condition compared to those under no-load condition.Based on the developed analytical models,the flux density distribution and the electromagnetic performance can be calculated under no-load or armature reaction field condition separately.The finite element analysis is carried out to verify the validity of the proposed analytical model.

Uniform Hölder Bounds for Competition Systems with Strong Interaction on a Subdomain

We prove the uniform Hölder bounds of solutions to a singularly perturbed elliptic system arising in competing models in population dynamics. In this system, two species compete to some extent throughout the whole domain but compete strongly on a subdomain. The proof relies upon the blow up technique and the monotonicity formula by Alt, Caffarelli and Friedman.

3D Gravity Inversion with Correlation Image in Space Domain and Application to the Northern Sinai Peninsula

We present a 3D inversion method to recover density distribution from gravity data in space domain.Our method firstly employs 3D correlation image of the vertical gradient of gravity data as a starting model to generate a higher resolution image for inversion.The 3D density distribution is then obtained by inverting the correlation image of gravity data to fit the observed data based on classical inversion method of the steepest descent method.We also perform the effective equivalent storage and subdomain techniques in the starting model calculation,the forward modeling and the inversion procedures,which allow fast computation in space domain with reducing memory consumption but maintaining accuracy.The efficiency and stability of our method is demonstrated on two sets of synthetic data and one set of the Northern Sinai Peninsula gravity data.The inverted 3D density distributions show that high density bodies beneath Risan Aniza and low density bodies exist to the southeast of Risan Aniza at depths between 1~10 and 20 km,which may be originated from hot anomalies in the lower crust.The results show that our inversion method is useful for 3D quantitative interpretation.

ON ALGEBROID FUNCTIONS IN A SUBDOMAIN OF THE COMPLEX PLANE

This paper discusses some basic properties of algebroid functions in a subdomain of the complex plane and some similar results (to those in the whole complex plane) and a new situation are showed.

Analytical Solution of a Fractional-slot Double-layer-winding Open-slot Vernier Permanent Magnet Machine with Tooth Tips

An analytical solution(ANA)for a fractional-slot double-layer-winding open-slot vernier permanent magnet(VPM)machine with tooth tips is presented.Magnetic vector potential equations are analytically solved using the technique of variable separation in four subdomains in a two-dimensional polar coordinate system.Based on the solved magnetic vector potential,the flux density distribution,torque,flux linkage,inductance,electromotive force(EMF)and power factor are analytically developed.An 18-slot/32-rotor-pole prototype is analyzed,and the results match well with the finite element analysis(FEA),which validates that the ANA consumes less time than FEA.Therefore,the tooth tips are optimized using the ANA to improve the average torque.Moreover,the ANA can be used to evaluate the demagnetization withstand capabilities of permanent magnets.The material utilization,slot-filling factor,EMF,and torque are compared between the models with three and four subdomains.Finally,an experimental prototype is constructed and tested,and the results validate the ANA.

An Improved Support Vector Clustering Approach to Dynamic Aggregation of Large Wind Farms

In this paper,we propose an improved support vector clustering(SVC)algorithm to cluster wind turbines(WTs)in a wind farm(WF).A boundary points(BPs)detecting method based on the grid theory and the connected subdomain(CS)are proposed.Thus the efficiency of SVC is enhanced while maintaining the accuracy of the algorithm.As for the multi-wind condition equivalent of WF,a method to determine the number and capacity of each of the aggregated wind turbines(AWTs)based on historical wind data is proposed.Only wind speed(WS)and wind direction(WD)of the WF are needed to calculate the WSs of each AWT.Results demonstrate that the algorithm proposed in this paper can cluster WTs quickly and accurately.And the dynamic aggregated models of the WFs are suitable for both the single-wind condition and multi-wind condition simulations,with high accuracy being obtained.

RAPID EXACT CONTROLLABILITY OF THE WAVE EQUATION BY CONTROLS DISTRIBUTED ON A TIME-VARIANT SUBDOMAIN

Consider the wave equation with distributed controls supported on a subdomain, calledcontrol subdomain, which is allowed to be variant in time. For any prescribed time duration,the authors work out a scheme for changing the control subdomain such that the wave equationis exactly controllable on this time duration, where the control subdomain at any time is allowedto have arbitrarily small measure and relatively simple shape.

Adaptive subdomain integration method for representing complex localized geometry in ANCF

In this work,we propose incorporating the finite cell method(FCM)into the absolute nodal coordinate formulation(ANCF)to improve the efficiency and robustness of ANCF elements in simulating structures with complex local features.In addition,an adaptive subdomain integration method based on a triangulation technique is devised to avoid excessive subdivisions,largely reducing the computational cost.Numerical examples demonstrate the effectiveness of the proposed method in large deformation,large rotation and dynamics simulation.

An Efficient Particle Subdomain Quadrature Scheme for the Material Point Method

The material point method(MPM)has been proved to be an effective numerical method for large deformation problems.However,the MPM suffers from the cell crossing error as that the material particles are used to represent the deformed material and to perform the particle quadrature.In this paper,an efficient subdomain quadrature material point method(sqMPM)is proposed to eliminate the cell crossing error efficiently.The particle domain is approximated to be the line segment,rectangle,and cuboid for the one-,two-,and three-dimensional problems,respectively,which are divided into several different subdomains based on the topological relationship between the particle domain and background grid.A single Gauss quadrature point is placed at the center of each subdomain and used for the information mapping.The material quantities of each Gauss quadrature point are determined by the corresponding material particle and the subdomain volume without the cumbersome reconstruction algorithm.Numerical examples for one-,two-,and three-dimensional large deformation problems demonstrate the effectiveness and highly enhanced convergence and efficiency of the proposed sqMPM.