Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this cha...Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.展开更多
In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introduc...In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.展开更多
In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a ge...In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.展开更多
In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical a...In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.展开更多
Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly effi...Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly efficient calculations for O-CNOPs are still challenging in the field of ensemble forecasting.In this study,we combine a gradient-based iterative idea with the Gram‒Schmidt orthogonalization,and propose an iterative optimization method to compute O-CNOPs.This method is different from the original sequential optimization method,and allows parallel computations of O-CNOPs,thus saving a large amount of computational time.We evaluate this method by using the Lorenz-96 model on the basis of the ensemble forecasting ability achieved and on the time consumed for computing O-CNOPs.The results demonstrate that the parallel iterative method causes O-CNOPs to yield reliable ensemble members and to achieve ensemble forecasting skills similar to or even slightly higher than those produced by the sequential method.Moreover,the parallel method significantly reduces the computational time for O-CNOPs.Therefore,the parallel iterative method provides a highly effective and efficient approach for calculating O-CNOPs for ensemble forecasts.Expectedly,it can play an important role in the application of the O-CNOPs to realistic ensemble forecasts for high-impact weather and climate events.展开更多
The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to ...The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.展开更多
Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A no...Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.展开更多
This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NR...This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NREL),to research the effects of the nonlinear flap-wise vibration characteristics.The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam,and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first.Then,the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force.Lastly,it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method,and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration.The results indicated that the rotational speed of the impeller has a significant impact on blade vibration.When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16.From the amplitude-frequency curve,it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity.Closed phase trajectories in blade nonlinear vibration,exhibiting periodic motion characteristics,are found through phase diagrams and Poincare section diagrams.展开更多
This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
Elastic beams resting on an elastic foundation are frequently encountered in civil,mechanical,aeronautical,and other engineering disciplines,and the analysis of static and dynamic deflections is one of the essential r...Elastic beams resting on an elastic foundation are frequently encountered in civil,mechanical,aeronautical,and other engineering disciplines,and the analysis of static and dynamic deflections is one of the essential requirements related to various applications.The Galerkin method is a classical mathematical method for solving differential equations without a closed-form solution with a wide range of applications in engineering and scientific fields.In this study,a demonstration is presented to solve the nonlinear differential equation by transforming it into a series of nonlinear algebraic equations with the Galerkin method for asymptotic solutions in series,and the nonlinear deformation of beams resting on the nonlinear foundation is successfully solved as an example.The approximate solutions based on trigonometric functions are utilized,and the nonlinear algebraic equations are solved both numerically and iteratively.Although widely used in linear problems,it is worth reminding that the Galerkin method also provides an effective approach in dealing with increasingly complex nonlinear equations in practical applications with the aid of powerful tools for symbolic manipulation of nonlinear algebraic equations.展开更多
The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical h...The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.展开更多
In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigatio...In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
This paper analyzes the nonlinear dynamic characteristics and stability of Aero-Engine Dual-Rotor(AEDR)systems under high-frequency excitation,based on the Adaptive Harmonic Balance with the Asymptotic Harmonic Select...This paper analyzes the nonlinear dynamic characteristics and stability of Aero-Engine Dual-Rotor(AEDR)systems under high-frequency excitation,based on the Adaptive Harmonic Balance with the Asymptotic Harmonic Selection(AHB-AHS)method.A finite element dynamic equation for the AEDR system is introduced,considering complex nonlinearities of the intershaft bearing,unbalanced excitations,and high-frequency excitation.A solving strategy combining the AHB-AHS method and improved arclength continuation method is proposed to solve highdimensional dynamic equations containing complex nonlinearities and to track periodic solutions with parameter variations.The Floquet theory is used to analyze the types of bifurcation points in the system and the stability of periodic motions.The results indicate that high-frequency excitation can couple high-order and low-order modes,especially when the system undergoes superharmonic resonance.High-frequency excitation leads to more combination frequency harmonics,among which N_(f)ω_(1)-2ω_(2)dominates.Furthermore,changing the parameters(amplitude and frequency)of high-frequency excitation widens or shifts the unstable regions of the system.These findings contribute to understanding the mechanism of high-frequency excitation on aero-engines and demonstrate that the proposed AHB-AHS method is a powerful tool for analyzing highdimensional complex nonlinear dynamic systems under multi-frequency excitation.展开更多
Suppressing micro-amplitude vibrations is a critical issue in aerospace engineering.While nonlinear energy sinks(NES)are effective for passive vibration damping,their performance diminishes for micro-amplitude vibrati...Suppressing micro-amplitude vibrations is a critical issue in aerospace engineering.While nonlinear energy sinks(NES)are effective for passive vibration damping,their performance diminishes for micro-amplitude vibrations.This paper introduces a motion-amplified NES(MANES)to address this challenge.The system’s governing equations are derived using Hamilton’s principle,and an approximate analytical solution is validated by numerical methods.The effects of various parameters are explored,with higher vibration reduction efficiency achievable through parameter adjustments.Compared to cubic NES,MANES shows superior vibration suppression and a broader reduction bandwidth for micro-amplitude excitations.Additionally,MANES enters the effective vibration reduction range at lower excitation levels,indicating a reduced threshold for vibration suppression.This study provides insight into the vibration suppression mechanism of MANES,offering a theoretical foundation for mitigating micro-amplitude vibrations in engineering applications.展开更多
The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of t...The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.展开更多
In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensa...In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.展开更多
This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element couplin...This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.展开更多
A meshless particle method based on the smoothed particle hydrodynamics(SPH)method is first proposed for the numerical prediction of physical phenomena of nonlinear solitary wave propagation and complex phenomena aris...A meshless particle method based on the smoothed particle hydrodynamics(SPH)method is first proposed for the numerical prediction of physical phenomena of nonlinear solitary wave propagation and complex phenomena arising from the inelastic interactions of solitary waves.The method is a fully discrete implicit scheme.This method does not rely on a grid,avoids the need to solve for derivatives of kernel functions,and makes the calculation more convenient.Additionally,the unique solvability of the proposed implicit scheme is proved.To verify the effectiveness and flexibility of the proposed method,we apply it to solving various time fractional nonlinear Schrödinger equations(TF-NLSE)on both regular and irregular domains.This mainly includes general or coupled TF-NLSE with or without analytical solutions.Moreover,the proposed method is compared with the existing methods.Through examples,it has been verified that this method can effectively predict complex propagation phenomena generated by the collision of nonlinear solitary waves,such as the collapse phenomenon of solitary waves with increasing fractional-order parameters.Research results indicate that this method provides a new and effective meshless method for predicting the propagation of nonlinear solitary waves,which can better simulate TF-NLSE in complex domains.展开更多
Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton...Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.展开更多
基金funded by the National Key R&D Program of China(Grant No.2022YFC2903904)the National Natural Science Foundation of China(Grant Nos.51904057 and U1906208).
文摘Due to the heterogeneity of rock masses and the variability of in situ stress,the traditional linear inversion method is insufficiently accurate to achieve high accuracy of the in situ stress field.To address this challenge,nonlinear stress boundaries for a numerical model are determined through regression analysis of a series of nonlinear coefficient matrices,which are derived from the bubbling method.Considering the randomness and flexibility of the bubbling method,a parametric study is conducted to determine recommended ranges for these parameters,including the standard deviation(σb)of bubble radii,the non-uniform coefficient matrix number(λ)for nonlinear stress boundaries,and the number(m)and positions of in situ stress measurement points.A model case study provides a reference for the selection of these parameters.Additionally,when the nonlinear in situ stress inversion method is employed,stress distortion inevitably occurs near model boundaries,aligning with the Saint Venant's principle.Two strategies are proposed accordingly:employing a systematic reduction of nonlinear coefficients to achieve high inversion accuracy while minimizing significant stress distortion,and excluding regions with severe stress distortion near the model edges while utilizing the central part of the model for subsequent simulations.These two strategies have been successfully implemented in the nonlinear in situ stress inversion of the Xincheng Gold Mine and have achieved higher inversion accuracy than the linear method.Specifically,the linear and nonlinear inversion methods yield root mean square errors(RMSE)of 4.15 and 3.2,and inversion relative errors(δAve)of 22.08%and 17.55%,respectively.Therefore,the nonlinear inversion method outperforms the traditional multiple linear regression method,even in the presence of a systematic reduction in the nonlinear stress boundaries.
基金Supported by the National Natural Science Foundation of China(12061048)NSF of Jiangxi Province(20232BAB201026,20232BAB201018)。
文摘In this paper,a new technique is introduced to construct higher-order iterative methods for solving nonlinear systems.The order of convergence of some iterative methods can be improved by three at the cost of introducing only one additional evaluation of the function in each step.Furthermore,some new efficient methods with a higher-order of convergence are obtained by using only a single matrix inversion in each iteration.Analyses of convergence properties and computational efficiency of these new methods are made and testified by several numerical problems.By comparison,the new schemes are more efficient than the corresponding existing ones,particularly for large problem sizes.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12371393,11971150 and 11801143)Natural Science Foundation of Henan Province(Grant No.242300421047).
文摘In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.
基金supported by the National Natural Science Foundation of China(Nos.52401342 and 12572025)the Fundamental Research Funds for the Central Universities of China(Nos.D5000240076 and G2025KY05171)+1 种基金the Natural Science Basic Research Program of Shaanxi Province(No.2025JCYBMS-026)the Basic Research Programs of Taicang(No.TC2024JC36)。
文摘In recent years,scholars around the world have shown increasing interest in elastic support structures,leading to significant progress in dynamic modeling techniques for pipeline systems.Although multiple analytical approaches exist,engineers increasingly prioritize computationally efficient,precise low-order models for practical implementation.In order to address this need,this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities.The proposed solution methodology initiates with global mode extraction using the global mode technique,followed by a detailed implementation procedure.Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions,where strong agreement between the proposed model's predictions and finiteelement benchmark solutions demonstrates its reliability.Subsequently,a comprehensive parametric study investigates the combined effects of foundation stiffness,boundary constraints,excitation intensity,and nonlinear interaction terms on the vibrational response of the cantilever pipe.This systematic approach yields critical insights for practical engineering designs and applications.
基金sponsored by the National Natural Science Foundation of China(Grant Nos.41930971,42330111,and 42405061)the National Key Scientific and Technological Infrastructure project“Earth System Numerical Simulation Facility”(Earth Lab).
文摘Orthogonal conditional nonlinear optimal perturbations(O-CNOPs)have been used to generate ensemble forecasting members for achieving high forecasting skill of high-impact weather and climate events.However,highly efficient calculations for O-CNOPs are still challenging in the field of ensemble forecasting.In this study,we combine a gradient-based iterative idea with the Gram‒Schmidt orthogonalization,and propose an iterative optimization method to compute O-CNOPs.This method is different from the original sequential optimization method,and allows parallel computations of O-CNOPs,thus saving a large amount of computational time.We evaluate this method by using the Lorenz-96 model on the basis of the ensemble forecasting ability achieved and on the time consumed for computing O-CNOPs.The results demonstrate that the parallel iterative method causes O-CNOPs to yield reliable ensemble members and to achieve ensemble forecasting skills similar to or even slightly higher than those produced by the sequential method.Moreover,the parallel method significantly reduces the computational time for O-CNOPs.Therefore,the parallel iterative method provides a highly effective and efficient approach for calculating O-CNOPs for ensemble forecasts.Expectedly,it can play an important role in the application of the O-CNOPs to realistic ensemble forecasts for high-impact weather and climate events.
基金supported by the major advanced research project of Civil Aerospace from State Administration of Science,Technology and Industry of China.
文摘The distribution-free P-box process serves as an effective quantification model for timevarying uncertainties in dynamical systems when only imprecise probabilistic information is available.However,its application to nonlinear systems remains limited due to excessive computation.This work develops an efficient method for propagating distribution-free P-box processes in nonlinear dynamics.First,using the Covariance Analysis Describing Equation Technique(CADET),the dynamic problems with P-box processes are transformed into interval Ordinary Differential Equations(ODEs).These equations provide the Mean-and-Covariance(MAC)bounds of the system responses in relation to the MAC bounds of P-box-process excitations.They also separate the previously coupled P-box analysis and nonlinear-dynamic simulations into two sequential steps,including the MAC bound analysis of excitations and the MAC bounds calculation of responses by solving the interval ODEs.Afterward,a Gaussian assumption of the CADET is extended to the P-box form,i.e.,the responses are approximate parametric Gaussian P-box processes.As a result,the probability bounds of the responses are approximated by using the solutions of the interval ODEs.Moreover,the Chebyshev method is introduced and modified to efficiently solve the interval ODEs.The proposed method is validated based on test cases,including a duffing oscillator,a vehicle ride,and an engineering black-box problem of launch vehicle trajectory.Compared to the reference solutions based on the Monte Carlo method,with relative errors of less than 3%,the proposed method requires less than 0.2% calculation time.The proposed method also possesses the ability to handle complex black-box problems.
基金work is supported by the Fundamental Research Funds for the Central Universities(No.3102019HTQD014)of Northwestern Polytechnical UniversityFunding of National Key Laboratory of Astronautical Flight DynamicsYoung Talent Support Project of Shaanxi State.
文摘Although predictor-corrector methods have been extensively applied,they might not meet the requirements of practical applications and engineering tasks,particularly when high accuracy and efficiency are necessary.A novel class of correctors based on feedback-accelerated Picard iteration(FAPI)is proposed to further enhance computational performance.With optimal feedback terms that do not require inversion of matrices,significantly faster convergence speed and higher numerical accuracy are achieved by these correctors compared with their counterparts;however,the computational complexities are comparably low.These advantages enable nonlinear engineering problems to be solved quickly and accurately,even with rough initial guesses from elementary predictors.The proposed method offers flexibility,enabling the use of the generated correctors for either bulk processing of collocation nodes in a domain or successive corrections of a single node in a finite difference approach.In our method,the functional formulas of FAPI are discretized into numerical forms using the collocation approach.These collocated iteration formulas can directly solve nonlinear problems,but they may require significant computational resources because of the manipulation of high-dimensionalmatrices.To address this,the collocated iteration formulas are further converted into finite difference forms,enabling the design of lightweight predictor-corrector algorithms for real-time computation.The generality of the proposed method is illustrated by deriving new correctors for three commonly employed finite-difference approaches:the modified Euler approach,the Adams-Bashforth-Moulton approach,and the implicit Runge-Kutta approach.Subsequently,the updated approaches are tested in solving strongly nonlinear problems,including the Matthieu equation,the Duffing equation,and the low-earth-orbit tracking problem.The numerical findings confirm the computational accuracy and efficiency of the derived predictor-corrector algorithms.
基金supported by the National Natural Science Foundation of China(No.51965034).
文摘This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NREL),to research the effects of the nonlinear flap-wise vibration characteristics.The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam,and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first.Then,the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force.Lastly,it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method,and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration.The results indicated that the rotational speed of the impeller has a significant impact on blade vibration.When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16.From the amplitude-frequency curve,it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity.Closed phase trajectories in blade nonlinear vibration,exhibiting periodic motion characteristics,are found through phase diagrams and Poincare section diagrams.
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
基金supported by the National Natural Science Foundation of China(Grant No.11672142)support through the Technology Innovation 2025 Program(Grant No.2019B10122)of the Municipality of Ningbo,Zhejiang,China.
文摘Elastic beams resting on an elastic foundation are frequently encountered in civil,mechanical,aeronautical,and other engineering disciplines,and the analysis of static and dynamic deflections is one of the essential requirements related to various applications.The Galerkin method is a classical mathematical method for solving differential equations without a closed-form solution with a wide range of applications in engineering and scientific fields.In this study,a demonstration is presented to solve the nonlinear differential equation by transforming it into a series of nonlinear algebraic equations with the Galerkin method for asymptotic solutions in series,and the nonlinear deformation of beams resting on the nonlinear foundation is successfully solved as an example.The approximate solutions based on trigonometric functions are utilized,and the nonlinear algebraic equations are solved both numerically and iteratively.Although widely used in linear problems,it is worth reminding that the Galerkin method also provides an effective approach in dealing with increasingly complex nonlinear equations in practical applications with the aid of powerful tools for symbolic manipulation of nonlinear algebraic equations.
文摘The current theory in NF EN 1995-1-1/NA of Eurocode 5, which is based on maximum deflection, has been investigated on softwoods. Therefore, this theory is not adapted for slender glulam beam columns made of tropical hardwood species from the Congo Basin. This maximum deflection is caused by a set of loads applied to the structure. However, Eurocode 5 doesn’t provide how to predict this deflection in case of long-term load for such structures. This can be done by studying load-displacement (P-Δ) behaviour of these structures while taking into account second order effects. To reach this goal, a nonlinear analysis has been performed on a three-dimensional beam column embedded on both ends. Since conducting experimental investigations on large span structural products is time-consuming and expensive especially in developing countries, a numerical model has been implemented using the Newton-Raphson method to predict load-displacement (P-Δ) curve on a slender glulam beam column made of tropical hardwood species. On one hand, the beam has been analyzed without wood connection. On the other hand, the beam has been analyzed with a bolted wood connection and a slotted-in steel plate. The load cases considered include self-weight and a uniformly applied long-term load. Combinations of serviceability limit states (SLS) and ultimate limit states (ULS) have also been considered, among other factors. A finite-element software RFEM 5 has been used to implement the model. The results showed that the use of steel can reduce displacement by 20.96%. Additionally, compared to the maximum deflection provided by Eurocode 5 for softwoods, hardwoods can exhibit an increasing rate of 85.63%. By harnessing the plastic resistance of steel, the bending resistance of wood can be increased by 32.94%.
基金supported by the National Key Research and Development Program of China (2019YFB1803905)the National Natural Science Foundation of China (No.62171022)+2 种基金Beijing Natural Science Foundation (4222009)Guangdong Basic and Applied Basic Research Foundation (2021B1515120057)the Scientific and Technological Innovation Foundation of Shunde Graduate School,USTB (No.BK19AF005)。
文摘In this paper,a double-effect DNN-based Digital Back-Propagation(DBP)scheme is proposed and studied to achieve the Integrated Communication and Sensing(ICS)ability,which can not only realize nonlinear damage mitigation but also monitor the optical power and dispersion profile over multi-span links.The link status information can be extracted by the characteristics of the learned optical fiber parameters without any other measuring instruments.The efficiency and feasibility of this method have been investigated in different fiber link conditions,including various launch power,transmission distance,and the location and the amount of the abnormal losses.A good monitoring performance can be obtained while the launch optical power is 2 dBm which does not affect the normal operation of the optical communication system and the step size of DBP is 20 km which can provide a better distance resolution.This scheme successfully detects the location of single or multiple optical attenuators in long-distance multi-span fiber links,including different abnormal losses of 2 dB,4 dB,and 6 dB in 360 km and serval combinations of abnormal losses of(1 dB,5 dB),(3 dB,3 dB),(5 dB,1 dB)in 360 km and 760 km.Meanwhile,the transfer relationship of the estimated coefficient values with different step sizes is further investigated to reduce the complexity of the fiber nonlinear damage compensation.These results provide an attractive approach for precisely sensing the optical fiber link status information and making correct strategies timely to ensure optical communication system operations.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金the financial support from the National Key R&D Program of China(No.2023YFE0125900)National Natural Science Foundation of China(Nos.12372008 and 12102234)+1 种基金Natural Science Foundation of Heilongjiang Province,China(No.YQ2022A008)Taif University,Saudi Arabia,for supporting this work through Project number(TU-DSPP-2024-73).
文摘This paper analyzes the nonlinear dynamic characteristics and stability of Aero-Engine Dual-Rotor(AEDR)systems under high-frequency excitation,based on the Adaptive Harmonic Balance with the Asymptotic Harmonic Selection(AHB-AHS)method.A finite element dynamic equation for the AEDR system is introduced,considering complex nonlinearities of the intershaft bearing,unbalanced excitations,and high-frequency excitation.A solving strategy combining the AHB-AHS method and improved arclength continuation method is proposed to solve highdimensional dynamic equations containing complex nonlinearities and to track periodic solutions with parameter variations.The Floquet theory is used to analyze the types of bifurcation points in the system and the stability of periodic motions.The results indicate that high-frequency excitation can couple high-order and low-order modes,especially when the system undergoes superharmonic resonance.High-frequency excitation leads to more combination frequency harmonics,among which N_(f)ω_(1)-2ω_(2)dominates.Furthermore,changing the parameters(amplitude and frequency)of high-frequency excitation widens or shifts the unstable regions of the system.These findings contribute to understanding the mechanism of high-frequency excitation on aero-engines and demonstrate that the proposed AHB-AHS method is a powerful tool for analyzing highdimensional complex nonlinear dynamic systems under multi-frequency excitation.
基金supported by the China National Funds for Distinguished Young Scholars(Grant No.12025204)the Shanghai Municipal Education Commission(Grant No.2019-01-07-00-09-E00018)。
文摘Suppressing micro-amplitude vibrations is a critical issue in aerospace engineering.While nonlinear energy sinks(NES)are effective for passive vibration damping,their performance diminishes for micro-amplitude vibrations.This paper introduces a motion-amplified NES(MANES)to address this challenge.The system’s governing equations are derived using Hamilton’s principle,and an approximate analytical solution is validated by numerical methods.The effects of various parameters are explored,with higher vibration reduction efficiency achievable through parameter adjustments.Compared to cubic NES,MANES shows superior vibration suppression and a broader reduction bandwidth for micro-amplitude excitations.Additionally,MANES enters the effective vibration reduction range at lower excitation levels,indicating a reduced threshold for vibration suppression.This study provides insight into the vibration suppression mechanism of MANES,offering a theoretical foundation for mitigating micro-amplitude vibrations in engineering applications.
文摘The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.
文摘In this paper, the nonlinear Schr?dinger equation combining quadratic-cubic nonlinearity is considered, which can be represented by an approximate model of relatively dense quasi-one-dimensional Bose-Einstein condensate. Based on the bifurcation theory, we proved the existence of solitary and periodic solutions. The methods we take are the trial equation method and the complete discrimination system for polynomial method. Therefore, we obtain the exact chirped solutions, which are more abundant in type and quantity than the existing results, so that the equation has more profound physical significance. These two methods are rigorously mathematical derivation and calculations, rather than based on certain conditional assumptions. In addition, we give some specific parameters to graphing the motion of the solutions, which helps to understand the propagation of nonlinear waves in fiber optic systems.
基金supported by grants from the National Natural Science Foundation of China (51478130)the Guangzhou Municipal Education Bureau’s Scientific Research Project, China (2024312217)+1 种基金the China Scholarship Council (201808440070)the 111 Project of China (D21021).
文摘This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings.It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading,using geometric nonlinear finite element analysis.A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members.Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation,a novel Lagrange multiplier search method is proposed.Additionally,the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization,accommodating multiple physical field couplings.
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region,China(Grant No.2024D01C44).
文摘A meshless particle method based on the smoothed particle hydrodynamics(SPH)method is first proposed for the numerical prediction of physical phenomena of nonlinear solitary wave propagation and complex phenomena arising from the inelastic interactions of solitary waves.The method is a fully discrete implicit scheme.This method does not rely on a grid,avoids the need to solve for derivatives of kernel functions,and makes the calculation more convenient.Additionally,the unique solvability of the proposed implicit scheme is proved.To verify the effectiveness and flexibility of the proposed method,we apply it to solving various time fractional nonlinear Schrödinger equations(TF-NLSE)on both regular and irregular domains.This mainly includes general or coupled TF-NLSE with or without analytical solutions.Moreover,the proposed method is compared with the existing methods.Through examples,it has been verified that this method can effectively predict complex propagation phenomena generated by the collision of nonlinear solitary waves,such as the collapse phenomenon of solitary waves with increasing fractional-order parameters.Research results indicate that this method provides a new and effective meshless method for predicting the propagation of nonlinear solitary waves,which can better simulate TF-NLSE in complex domains.
文摘Computational modeling plays a vital role in advancing our understanding and application of soliton theory.It allows researchers to both simulate and analyze complex soliton phenomena and discover new types of soliton solutions.In the present study,we computationally derive the bright and dark optical solitons for a Schrödinger equation that contains a specific type of nonlinearity.This nonlinearity in the model is the result of the combination of the parabolic law and the non-local law of self-phase modulation structures.The numerical simulation is accomplished through the application of an algorithm that integrates the classical Adomian method with the Laplace transform.The results obtained have not been previously reported for this type of nonlinearity.Additionally,for the purpose of comparison,the numerical examination has taken into account some scenarios with fixed parameter values.Notably,the numerical derivation of solitons without the assistance of an exact solution is an exceptional take-home lesson fromthis study.Furthermore,the proposed approach is demonstrated to possess optimal computational accuracy in the results presentation,which includes error tables and graphs.It is important tomention that themethodology employed in this study does not involve any form of linearization,discretization,or perturbation.Consequently,the physical nature of the problem to be solved remains unaltered,which is one of the main advantages.
