Magneto-Electro-Elastic Analysis of Doubly-Curved Shells: Higher-Order Equivalent Layer-Wise Formulation

Recent engineering applications increasingly adopt smart materials,whose mechanical responses are sensitive to magnetic and electric fields.In this context,new and computationally efficient modeling strategies are essential to predict the multiphysic behavior of advanced structures accurately.Therefore,the manuscript presents a higher-order formulation for the static analysis of laminated anisotropic magneto-electro-elastic doubly-curved shell structures.The fundamental relations account for the full coupling between the electric field,magnetic field,and mechanical elasticity.The configuration variables are expanded along the thickness direction using a generalized formulation based on the Equivalent Layer-Wise approach.Higher-order polynomials are selected,allowing for the assessment of prescribed values of the configuration variables at the top and bottom sides of solids.In addition,an effective strategy is provided for modeling general surface distributions of mechanical pressures and electromagnetic external fluxes.The model is based on a continuum-based formulation which employs an analytical homogenization of the multifield material properties,based on Mori&Tanaka approach,of a magneto-electro-elastic composite material obtained from a piezoelectric and a piezomagnetic phase,with coupled magneto-electro-elastic effects.A semi-analytical Navier solution is applied to the fundamental equations,and an efficient post-processing equilibrium-based procedure is here used,based on the numerical assessment with the Generalized Differential Quadrature(GDQ)method,to recover the response of three-dimensional shells.The formulation is validated through various examples,investigating the multifield response of panels of different curvatures and lamination schemes.An efficient homogenization procedure,based on the Mori&Tanaka approach,is employed to obtain the three-dimensional constitutive relation of magneto-electro-elastic materials.Each model is validated against three-dimensional finite-element simulations,as developed in commercial codes.Furthermore,the full coupling effect between the electric and magnetic response is evaluated via a parametric investigation,with useful insights for design purposes of many engineering applications.The paper,thus,provides a formulation for the magneto-electro-elastic analysis of laminated structures,with a high computational efficiency,since it provides results with three-dimensional capabilities with a two-dimensional formulation.The adoption of higher-order theories,indeed,allows us to efficiently predict not only the mechanical response of the structure as happens in existing literature,but also the through-the-thickness distribution of electric and magnetic variables.A novel higher-order theory has been proposed in this work for the magneto-electro-elastic analysis of laminated shell structures with varying curvatures.This theory employs a generalized method to model the distribution of the displacement field components,electrostatic,and magneto-static potential,accounting for higher-order polynomials.The thickness functions have been defined to prescribe the arbitrary values of configuration variables at the top and bottom surfaces,even though the model is ESL-based.The fundamental governing equations have been derived in curvilinear principal coordinates,considering all coupling effects among different physical phenomena,including piezoelectric,piezomagnetic,and magneto-electric effects.A homogenization algorithm based on a Mori&Tanaka approach has been adopted to obtain the equivalent magneto-electro-mechanical properties of a two-phase transversely isotropic composite.In addition,an effective method has been adopted involving the external loads in terms of surface tractions,as well as the electric and magnetic fluxes.In the post-processing stage,a GDQ-based procedure provides the actual 3D response of a doubly-curved solid.The model has been validated through significant numerical examples,showing that the results of this semi-analytical theory align well with those obtained from 3D numerical models from commercial codes.In particular,the accuracy of the model has been verified for lamination schemes with soft layers and various curvatures under different loading conditions.Moreover,this formulation has been used to predict the effect of combined electric and magnetic loads on the mechanical response of panels with different curvatures and lamination schemes.As a consequence,this theory can be applied in engineering applications where the combined effect of electric and magnetic loads is crucial,thus facilitating their study and design.An existing limitation of this study is that the solution is that it is derived only for structures with uniform curvature,cross-ply lamination scheme,and simply supported boundary conditions.Furthermore,it requires that each lamina within the stacking sequence exhibits magneto-electro-elastic behavior.Therefore,at the present stage,it cannot be used for multifield analysis of classical composite structures with magneto-electric patches.A further enhancement of the research work could be the derivation of a solution employing a numerical technique,to overcome the limitations of the Navier method.In this way,the same theory may be adopted to predict the multifield response of structures with variable curvatures and thickness,as well as anisotropic materials and more complicated boundary conditions.Acknowledgement:The authors are grateful to the Department of Innovation Engineering of Univer-sity of Salento for the support.

THE HIGHER-ORDER CONSTRAINTS AND INTEGRABLE SYSTEMS ASSOCIATED WITH THE BOUSSINESQ EQUATION

There are only a few results concerned with the constraints and finite-dimensional integrable systems which are associated with the third-order eigenvalue problem tbr soliton equation. In particular, the higher-order constraints and corresponding integrable systems have not been studied yet. In the present note, using the Boussinesq equation as

Pipeline thickness estimation using the dispersion of higher-order SH guided waves

Thickness measurement plays an important role in the monitoring of pipeline corrosion damage. However, the requirement for prior knowledge of the shear wave velocity in the pipeline material for popular ultrasonic thickness measurement limits its widespread application. This paper proposes a method that utilizes cylindrical shear horizontal(SH) guided waves to estimate pipeline thickness without prior knowledge of shear wave velocity. The inversion formulas are derived from the dispersion of higher-order modes with the high-frequency approximation. The waveform of the example problems is simulated using the real-axis integral method. The data points on the dispersion curves are processed in the frequency domain using the wave-number method. These extracted data are then substituted into the derived formulas. The results verify that employing higher-order SH guided waves for the evaluation of thickness and shear wave velocity yields less than1% error. This method can be applied to both metallic and non-metallic pipelines, thus opening new possibilities for health monitoring of pipeline structures.

Research on the navigation method of large-scale differential tail-control improvised guided munitions based on rotational speed constraints

In the process of launching guided projectile under the conventional system, it is difficult to effectively obtain the precise navigation parameters of the projectile in the high dynamic environment. Aiming at this problem, this paper describes a new system of guided ammunition based on tail spin reduction. After analyzing the mechanism of the ammunition's tail spin reduction, a navigation method of large scale difference tail control simple guided ammunition based on speed constraint is proposed. In this method,the corresponding navigation constraints can be carried out by combining the rotation speed state of the ammunition itself, and the optimal solution of navigation parameters during the flight of the missile can be obtained by Extended Kalman Filter(EKF). Finally, the performance of the proposed method was verified by the simulation environment, and the hardware-in-the-loop simulation test and flight test were carried out to verify the performance of the method in the real environment. The experimental results show that the proposed method can achieve the optimal estimation of navigation parameters for simple guided ammunition with large-scale difference tail control. Under the conditions of simulation test and hardware-in-loop simulation test, the position and velocity errors calculated by the method in this paper converged. Under the condition of flight test, the spatial average error calculated by the method described in this paper is 6.17 m, and the spatial error of the final landing point is 3.50 m.Through this method, the accurate acquisition of navigation parameters in the process of projectile launching is effectively realized.

Prescribed Performance Tracking Control of Time-Delay Nonlinear Systems With Output Constraints

The problem of prescribed performance tracking control for unknown time-delay nonlinear systems subject to output constraints is dealt with in this paper. In contrast with related works, only the most fundamental requirements, i.e., boundedness and the local Lipschitz condition, are assumed for the allowable time delays. Moreover, we focus on the case where the reference is unknown beforehand, which renders the standard prescribed performance control designs under output constraints infeasible. To conquer these challenges, a novel robust prescribed performance control approach is put forward in this paper.Herein, a reverse tuning function is skillfully constructed and automatically generates a performance envelop for the tracking error. In addition, a unified performance analysis framework based on proof by contradiction and the barrier function is established to reveal the inherent robustness of the control system against the time delays. It turns out that the system output tracks the reference with a preassigned settling time and good accuracy,without constraint violations. A comparative simulation on a two-stage chemical reactor is carried out to illustrate the above theoretical findings.

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.

Photoinduced Floquet higher-order Weyl semimetal in C_(6) symmetric Dirac semimetals

Topological Dirac semimetals are a parent state from which other exotic topological phases of matter, such as Weyl semimetals and topological insulators, can emerge. In this study, we investigate a Dirac semimetal possessing sixfold rotational symmetry and hosting higher-order topological hinge Fermi arc states, which is irradiated by circularly polarized light. Our findings reveal that circularly polarized light splits each Dirac node into a pair of Weyl nodes due to the breaking of time-reversal symmetry, resulting in the realization of the Weyl semimetal phase. This Weyl semimetal phase exhibits rich boundary states, including two-dimensional surface Fermi arc states and hinge Fermi arc states confined to six hinges.Furthermore, by adjusting the incident direction of the circularly polarized light, we can control the degree of tilt of the resulting Weyl cones, enabling the realization of different types of Weyl semimetals.

Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

A fast forward computational method for nuclear measurement using volumetric detection constraints

Owing to the complex lithology of unconventional reservoirs,field interpreters usually need to provide a basis for interpretation using logging simulation models.Among the various detection tools that use nuclear sources,the detector response can reflect various types of information of the medium.The Monte Carlo method is one of the primary methods used to obtain nuclear detection responses in complex environments.However,this requires a computational process with extensive random sampling,consumes considerable resources,and does not provide real-time response results.Therefore,a novel fast forward computational method(FFCM)for nuclear measurement that uses volumetric detection constraints to rapidly calculate the detector response in various complex environments is proposed.First,the data library required for the FFCM is built by collecting the detection volume,detector counts,and flux sensitivity functions through a Monte Carlo simulation.Then,based on perturbation theory and the Rytov approximation,a model for the detector response is derived using the flux sensitivity function method and a one-group diffusion model.The environmental perturbation is constrained to optimize the model according to the tool structure and the impact of the formation and borehole within the effective detection volume.Finally,the method is applied to a neutron porosity tool for verification.In various complex simulation environments,the maximum relative error between the calculated porosity results of Monte Carlo and FFCM was 6.80%,with a rootmean-square error of 0.62 p.u.In field well applications,the formation porosity model obtained using FFCM was in good agreement with the model obtained by interpreters,which demonstrates the validity and accuracy of the proposed method.

Opinion consensus incorporating higher-order interactions in individual-collective networks

In the current information society, the dissemination mechanisms and evolution laws of individual or collective opinions and their behaviors are the research hot topics in the field of opinion dynamics. First, in this paper, a two-layer network consisting of an individual-opinion layer and a collective-opinion layer is constructed, and a dissemination model of opinions incorporating higher-order interactions(i.e. OIHOI dissemination model) is proposed. Furthermore, the dynamic equations of opinion dissemination for both individuals and groups are presented. Using Lyapunov's first method,two equilibrium points, including the negative consensus point and positive consensus point, and the dynamic equations obtained for opinion dissemination, are analyzed theoretically. In addition, for individual opinions and collective opinions,some conditions for reaching negative consensus and positive consensus as well as the theoretical expression for the dissemination threshold are put forward. Numerical simulations are carried to verify the feasibility and effectiveness of the proposed theoretical results, as well as the influence of the intra-structure, inter-connections, and higher-order interactions on the dissemination and evolution of individual opinions. The main results are as follows.(i) When the intra-structure of the collective-opinion layer meets certain characteristics, then a negative or positive consensus is easier to reach for individuals.(ii) Both negative consensus and positive consensus perform best in mixed type of inter-connections in the two-layer network.(iii) Higher-order interactions can quickly eliminate differences in individual opinions, thereby enabling individuals to reach consensus faster.

Characterization and quantification of multi-field coupling in lithium-ion batteries under mechanical constraints

The safety and durability of lithium-ion batteries under mechanical constraints depend significantly on electrochemical,thermal,and mechanical fields in applications.Characterizing and quantifying the multi-field coupling behaviors requires interdisciplinary efforts.Here,we design experiments under mechanical constraints and introduce an in-situ analytical framework to clarify the complex interaction mechanisms and coupling degrees among multi-physics fields.The proposed analytical framework integrates the parameterization of equivalent models,in-situ mechanical analysis,and quantitative assessment of coupling behavior.The results indicate that the significant impact of pressure on impedance at low temperatures results from the diffusion-controlled step,enhancing kinetics when external pressure,like 180 to 240 k Pa at 10℃,is applied.The diversity in control steps for the electrochemical reaction accounts for the varying impact of pressure on battery performance across different temperatures.The thermal expansion rate suggests that the swelling force varies by less than 1.60%per unit of elevated temperature during the lithiation process.By introducing a composite metric,we quantify the coupling correlation and intensity between characteristic parameters and physical fields,uncovering the highest coupling degree in electrochemical-thermal fields.These results underscore the potential of analytical approaches in revealing the mechanisms of interaction among multi-fields,with the goal of enhancing battery performance and advancing battery management.

Nonlinear Registration of Brain Magnetic Resonance Images with Cross Constraints of Intensity and Structure

Many deep learning-based registration methods rely on a single-stream encoder-decoder network for computing deformation fields between 3D volumes.However,these methods often lack constraint information and overlook semantic consistency,limiting their performance.To address these issues,we present a novel approach for medical image registration called theDual-VoxelMorph,featuring a dual-channel cross-constraint network.This innovative network utilizes both intensity and segmentation images,which share identical semantic information and feature representations.Two encoder-decoder structures calculate deformation fields for intensity and segmentation images,as generated by the dual-channel cross-constraint network.This design facilitates bidirectional communication between grayscale and segmentation information,enabling the model to better learn the corresponding grayscale and segmentation details of the same anatomical structures.To ensure semantic and directional consistency,we introduce constraints and apply the cosine similarity function to enhance semantic consistency.Evaluation on four public datasets demonstrates superior performance compared to the baselinemethod,achieving Dice scores of 79.9%,64.5%,69.9%,and 63.5%for OASIS-1,OASIS-3,LPBA40,and ADNI,respectively.

Adaptive H_(∞)Filtering Algorithm for Train Positioning Based on Prior Combination Constraints

To solve the problem of data fusion for prior information such as track information and train status in train positioning,an adaptive H∞filtering algorithm with combination constraint is proposed,which fuses prior information with other sensor information in the form of constraints.Firstly,the train precise track constraint method of the train is proposed,and the plane position constraint and train motion state constraints are analysed.A model for combining prior information with constraints is established.Then an adaptive H∞filter with combination constraints is derived based on the adaptive adjustment method of the robustness factor.Finally,the positioning effect of the proposed algorithm is simulated and analysed under the conditions of a straight track and a curved track.The results show that the positioning accuracy of the algorithm with constrained filtering is significantly better than that of the algorithm without constrained filtering and that the algorithm with constrained filtering can achieve better performance when combined with track and condition information,which can significantly reduce the train positioning error.The effectiveness of the proposed algorithm is verified.

Time-Domain Higher-Order Boundary Element Method for Simulating High Forward-Speed Ship Motions in Waves

The hydrodynamic performance of a high forward-speed ship in obliquely propagating waves is numerically examined to assess both free motions and wave field in comparison with a low forward-speed ship.This numerical model is based on the time-domain potential flow theory and higher-order boundary element method,where an analytical expression is completely expanded to determine the base-unsteady coupling flow imposed on the moving condition of the ship.The ship in the numerical model may possess different advancing speeds,i.e.stationary,low speed,and high speed.The role of the water depth,wave height,wave period,and incident wave angle is analyzed by means of the accurate numerical model.It is found that the resonant motions of the high forward-speed ship are triggered by comparison with the stationary one.More specifically,a higher forward speed generates a V-shaped wave region with a larger elevation,which induces stronger resonant motions corresponding to larger wave periods.The shoaling effect is adverse to the motion of the low-speed ship,but is beneficial to the resonant motion of the high-speed ship.When waves obliquely propagate toward the ship,the V-shaped wave region would be broken due to the coupling effect between roll and pitch motions.It is also demonstrated that the maximum heave motion occurs in beam seas for stationary cases but occurs in head waves for high speeds.However,the variation of the pitch motion with period is hardly affected by wave incident angles.

Optimal Trajectory Generation for Aircraft Engine-Off Taxi Towing System Under Stochastic Constraints

The novel aircraft engine-off taxi towing system featuring aircraft power integration has demonstrated significant advantages,including reduced energy consumption,diminished emissions,and enhanced efficiency.However,the aircraft engine-off taxi towing system lacks the consideration of attendant constraints in the trajectory generation process,which can potentially lead to ground accidents and constrain the improvement of traction speed.Addressing this challenge,the present work investigates the optimal control problem of trajectory generation for the taxiing traction system in the complex stochastic environment in the airport flight area.For the stochastic constraints,a strategy of deterministic processing is proposed to describe the stochastic constraints using random constraints.Furthermore,an adaptive pseudo-spectral method is introduced to transform the optimal control problem into a nonlinear programming problem,enabling its effective resolution.Simulation results substantiate that the generated trajectory can efficiently handle the stochastic constraints and accomplish the given task towards the time-optimization objective,thereby effectively enhancing the stability and efficiency of the taxiing traction system,ensuring the safety of the aircraft system,and improving the ground access capacity and efficiency of the airport.

Dynamic characteristics of multi-span spinning beams with elastic constraints under an axial compressive force

A theoretical model for the multi-span spinning beams with elastic constraints under an axial compressive force is proposed.The displacement and bending angle functions are represented through an improved Fourier series,which ensures the continuity of the derivative at the boundary and enhances the convergence.The exact characteristic equations of the multi-span spinning beams with elastic constraints under an axial compressive force are derived by the Lagrange equation.The efficiency and accuracy of the present method are validated in comparison with the finite element method(FEM)and other methods.The effects of the boundary spring stiffness,the number of spans,the spinning velocity,and the axial compressive force on the dynamic characteristics of the multi-span spinning beams are studied.The results show that the present method can freely simulate any boundary constraints without modifying the solution process.The elastic range of linear springs is larger than that of torsion springs,and it is not affected by the number of spans.With an increase in the axial compressive force,the attenuation rate of the natural frequency of a spinning beam with a large number of spans becomes larger,while the attenuation rate with an elastic boundary is lower than that under a classic simply supported boundary.

Dynamic Constraint-Driven Event-Triggered Control of Strict-Feedback Systems Without Max/Min Values on Irregular Constraints

This work proposes an event-triggered adaptive control approach for a class of uncertain nonlinear systems under irregular constraints.Unlike the constraints considered in most existing papers,here the external irregular constraints are considered and a constraints switching mechanism(CSM)is introduced to circumvent the difficulties arising from irregular output constraints.Based on the CSM,a new class of generalized barrier functions are constructed,which allows the control results to be independent of the maximum and minimum values(MMVs)of constraints and thus extends the existing results.Finally,we proposed a novel dynamic constraint-driven event-triggered strategy(DCDETS),under which the stress on signal transmission is reduced greatly and no constraints are violated by making a dynamic trade-off among system state,external constraints,and inter-execution intervals.It is proved that the system output is driven to close to the reference trajectory and the semi-global stability is guaranteed under the proposed control scheme,regardless of the external irregular output constraints.Simulation also verifies the effectiveness and benefits of the proposed method.

Constraints Separation Based Evolutionary Multitasking for Constrained Multi-Objective Optimization Problems

Constrained multi-objective optimization problems(CMOPs)generally contain multiple constraints,which not only form multiple discrete feasible regions but also reduce the size of optimal feasible regions,thus they propose serious challenges for solvers.Among all constraints,some constraints are highly correlated with optimal feasible regions;thus they can provide effective help to find feasible Pareto front.However,most of the existing constrained multi-objective evolutionary algorithms tackle constraints by regarding all constraints as a whole or directly ignoring all constraints,and do not consider judging the relations among constraints and do not utilize the information from promising single constraints.Therefore,this paper attempts to identify promising single constraints and utilize them to help solve CMOPs.To be specific,a CMOP is transformed into a multitasking optimization problem,where multiple auxiliary tasks are created to search for the Pareto fronts that only consider a single constraint respectively.Besides,an auxiliary task priority method is designed to identify and retain some high-related auxiliary tasks according to the information of relative positions and dominance relationships.Moreover,an improved tentative method is designed to find and transfer useful knowledge among tasks.Experimental results on three benchmark test suites and 11 realworld problems with different numbers of constraints show better or competitive performance of the proposed method when compared with eight state-of-the-art peer methods.

Stress tensor determination by modified hydraulic tests on pre-existing fractures:Method and stress constraints

The hydraulic testing of pre-existing fractures(HTPF)is one of the most promising in situ stress measurement methods,particularly for three-dimensional stress tensor determination.However,the stress tensor determination based on the HTPF method requires at least six tests or a minimum of 14-15 tests(under different conditions)for reliable results.In this study,we modified the HTPF method by considering the shear stress on each pre-existing fracture,which increased the number of equations for the stress tensor determination and decreased the number of tests required.Different shear stresses were attributed to different fractures by random sampling;therefore,the stress tensors were obtained by searching for the optimal solution using the least squares criterion based on the Monte Carlo method.Thereafter,we constrained the stress tensor based on the tensile strength criterion,compressive strength criterion,and vertical stress constraints.The inverted stress tensors were presented and analyzed based on the tensorial nature of the stress using the Euclidean mean stress tensor.Two stress-measurement campaigns in Weifang(Shandong Province,China)and Mercantour road tunnel(France)were implemented to highlight the validity and efficiency of the modified HTPF(M-HTPF)method.The results showed that the M-HTPF method can be applied for stress tensor inversion using only three to four tests on pre-existing fractures,neglecting the stress gradient.The inversion results were confined to relatively small distribution dispersions and were significantly reliable and stable due to the shear stresses on the fractures and the stress constraints employed.The M-HTPF method is highly feasible and efficient for complete stress tensor determination in a single borehole.

Guaranteed Cost Attitude Tracking Control for Uncertain Quadrotor Unmanned Aerial Vehicle Under Safety Constraints

In this paper,guaranteed cost attitude tracking con-trol for uncertain quadrotor unmanned aerial vehicle(QUAV)under safety constraints is studied.First,an augmented system is constructed by the tracking error system and reference system.This transformation aims to convert the tracking control prob-lem into a stabilization control problem.Then,control barrier function and disturbance attenuation function are designed to characterize the violations of safety constraints and tolerance of uncertain disturbances,and they are incorporated into the reward function as penalty items.Based on the modified reward function,the problem is simplified as the optimal regulation problem of the nominal augmented system,and a new Hamilton-Jacobi-Bellman equation is developed.Finally,critic-only rein-forcement learning algorithm with a concurrent learning tech-nique is employed to solve the Hamilton-Jacobi-Bellman equa-tion and obtain the optimal controller.The proposed algorithm can not only ensure the reward function within an upper bound in the presence of uncertain disturbances,but also enforce safety constraints.The performance of the algorithm is evaluated by the numerical simulation.