Existing numerical methods for complex composites, such as multiscale simulation and neural network algorithms, face significant limitations. Multiscale techniques are often prohibitively expensive for large models, w...Existing numerical methods for complex composites, such as multiscale simulation and neural network algorithms, face significant limitations. Multiscale techniques are often prohibitively expensive for large models, while neural networks struggle to represent underlying microscopic material properties. To overcome these challenges, a meso-micro scale numerical method using a virtual node approach is developed in this study. A Wbraid/Al/Epoxy functional structural material is fabricated, and a representative periodic unit cell is identified based on its architecture. The complex structure is then discretized into nodes, and mechanical interactions are governed by pre-defined computation rules. This virtual node method is systematically compared against both multiscale simulation and a neural network algorithm, with validation provided through mechanical experiments. The results demonstrate that the nodal operation strategy significantly reduces computational resource requirements. By quantifying microscopic bonding with coefficients, explicit interface treatment is avoided, granting the method strong adaptability to lattice materials. The method can simulate extremely complex structures using parameters from simple tests and is suited for large systems. Compared to three-point bending experiments, errors for multiscale, virtual node, and neural network methods were 12.4%, 6.9%, and 34.5%, respectively. Under dynamic compression, the errors were 2.7%, 9.3%, and 15.43%. The virtual node method demonstrated superior accuracy under static conditions, enabling efficient prediction and auxiliary development of complex structural materials.展开更多
Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The t...Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.展开更多
As binary geological media,soil-rock mixtures(SRMs)exhibit a distinct gradational composition,leading to their unique mechanical behaviors.To appraise the stability of SRM slopes,it is essential to determine equivalen...As binary geological media,soil-rock mixtures(SRMs)exhibit a distinct gradational composition,leading to their unique mechanical behaviors.To appraise the stability of SRM slopes,it is essential to determine equivalent parameters of SRMs,which are typically obtained through experimental and numerical methods.In contrasted to other numerical methods,the numerical manifold method(NMM)is more effective in addressing SRM problems.This is because the high-precision regular mathematical meshes in NMM can be used without aligning with the soil-rock interfaces and boundaries of SRMs.In the current research,the equivalent strength parameters of SRMs,i.e.the equivalent cohesion ce and internal friction angleϕ_(e),are determined using NMM.Initially,an NMM triaxial numerical model is established and validated based on triaxial experiments.Subsequently,the soil and rock parameters are derived through parameter inversion.Moreover,the impacts of rock content,size,shape and rock blocks'major-axis orientation on ce andϕ_(e) of SRMs are thoroughly examined using the NMM triaxial numerical model.Additionally,a fitting function is proposed to linkϕ_(e) to the rock content and size of SRMs.When other influencing factors are fixed,the above fitting model leads to the following conclusions:(1)the predictedϕ_(e) of SRMs increase with the increase of rock content;and(2)SRM samples with smaller rocks display a higher predictedϕ_(e).展开更多
Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture ...Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H^(2)-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.展开更多
Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implemen...Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implementation,or configuration.To guarantee the durability&robustness of the software,vulnerability identification and fixation have become crucial areas of focus for developers,cybersecurity experts and industries.This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection.To uniquely model these processes,the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function.Furthermore,the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain.The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets,which offers a solid basis for the research conclusions.According to computational research,learning dynamics improves security response and results in more effective vulnerability management.The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment,software maintenance,and cybersecurity.This study helps create more robust software systems by increasing patch management effectiveness,which benefits developers,cybersecurity experts,and sectors looking to reduce security threats in a growing digital world.展开更多
This article reviews the application and progress of deep learning in efficient numerical computing methods.Deep learning,as an important branch of machine learning,provides new ideas for numerical computation by cons...This article reviews the application and progress of deep learning in efficient numerical computing methods.Deep learning,as an important branch of machine learning,provides new ideas for numerical computation by constructing multi-layer neural networks to simulate the learning process of the human brain.The article explores the application of deep learning in solving partial differential equations,optimizing problems,and data-driven modeling,and analyzes its advantages in computational efficiency,accuracy,and adaptability.At the same time,this article also points out the challenges faced by deep learning numerical computation methods in terms of computational efficiency,interpretability,and generalization ability,and proposes strategies and future development directions for integrating with traditional numerical methods.展开更多
This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form c...This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications.The phase-field model,in particular,is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time.In this paper,we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths,limitations,stability,accuracy,and computational efficiency of each method.Traditional approaches such as Fourier spectral methods,finite difference methods and alternating direction explicit methods are reviewed,as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented.In addition,we introduce examples of the phase-field model,which are fingerprint image restoration and 3D printing.These examples demonstrate the extensive applicability of the reviewed methods and models.展开更多
To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solutio...This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.展开更多
In order to predict the long-term rutting of asphalt pavement, the effective temperature for pavement rutting is calculated using the numerical simulation method. The transient temperature field of asphalt pavement wa...In order to predict the long-term rutting of asphalt pavement, the effective temperature for pavement rutting is calculated using the numerical simulation method. The transient temperature field of asphalt pavement was simulated based on actual meteorological data of Nanjing. 24-hour rutting development under a transient temperature field was calculated in each month. The rutting depth accumulated under the static temperature field was also estimated and the relationship between constant temperature parameters was analyzed. Then the effective temperature for pavement rutting was determined based on the rutting equivalence principle. The results show that the monthly effective temperature is above 40 t in July and August, while in June and September it ranges from 30 to 40 Rutting development can be ignored when the monthly effective temperature is less than 30 t. The yearly effective temperature for rutting in Nanjing is around 38. 5 t. The long-term rutting prediction model based on the effective temperature can reflect the influences of meteorological factors and traffic time distribution.展开更多
To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based sim...To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based simulation(NNS)method with higher accuracy and better efficiency was proposed.The NNS method consisted of three main steps.First,the parameters of blast loads,including the peak pressures and impulses of cylindrical charges with different aspect ratios(L/D)at different stand-off distances and incident angles were obtained by two-dimensional numerical simulations.Subsequently,incident shape factors of cylindrical charges with arbitrary aspect ratios were predicted by a neural network.Finally,reflected shape factors were derived and implemented into the subroutine of the ABAQUS code to modify the CONWEP model,including modifications of impulse and overpressure.The reliability of the proposed NNS method was verified by related experimental results.Remarkable accuracy improvement was acquired by the proposed NNS method compared with the unmodified CONWEP model.Moreover,huge efficiency superiority was obtained by the proposed NNS method compared with the CEL method.The proposed NNS method showed good accuracy when the scaled distance was greater than 0.2 m/kg^(1/3).It should be noted that there is no need to generate a new dataset again since the blast loads satisfy the similarity law,and the proposed NNS method can be directly used to simulate the blast loads generated by different cylindrical charges.The proposed NNS method with high efficiency and accuracy can be used as an effective method to analyze the dynamic response of structures under blast loads,and it has significant application prospects in designing protective structures.展开更多
For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional...For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.展开更多
A numerical method based on B-spline is developed to solve the time-dependent Emden-Fow- ler-type equations. We also present a reliable new algorithm based on B-spline to overcome the difficulty of the singular point ...A numerical method based on B-spline is developed to solve the time-dependent Emden-Fow- ler-type equations. We also present a reliable new algorithm based on B-spline to overcome the difficulty of the singular point at x = 0. The error analysis of the method is described. Numerical results are given to illustrate the efficiency of the proposed method.展开更多
We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the...We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.展开更多
The rotating shallow water system is an important physical model,which has been widely used in many scientific areas,such as fluids,hydrodynamics,geophysics,oceanic and atmospheric dynamics.In this paper,we extend the...The rotating shallow water system is an important physical model,which has been widely used in many scientific areas,such as fluids,hydrodynamics,geophysics,oceanic and atmospheric dynamics.In this paper,we extend the application of the Adomian decomposition method from the single equation to the coupled system to investigate the numerical solutions of the rotating shallow water system with an underlying circular paraboloidal basin.By introducing some special initial values,we obtain interesting approximate pulsrodon solutions corresponding to pulsating elliptic warm-core rings,which take the form of realistic series solutions.Numerical results reveal that the numerical pulsrodon solutions can quickly converge to the exact solutions derived by Rogers and An,which fully shows the efficiency and accuracy of the proposed method.Note that the method proposed can be effectively used to construct numerical solutions of many nonlinear mathematical physics equations.The results obtained provide some potential theoretical guidance for experts to study the related phenomena in geography,oceanic and atmospheric science.展开更多
As a pyrometallurgical process,circulating fluidized bed(CFB) roasting has good potential for application in desulfurization of high-sulfur bauxite.The gas-solid distribution and reaction during CFB roasting of high-s...As a pyrometallurgical process,circulating fluidized bed(CFB) roasting has good potential for application in desulfurization of high-sulfur bauxite.The gas-solid distribution and reaction during CFB roasting of high-sulfur bauxite were simulated using the computational particle fluid dynamics(CPFD) method.The effect of primary air flow velocity on particle velocity,particle volume distribution,furnace temperature distribution and pressure distribution were investigated.Under the condition of the same total flow of natural gas,the impact of the number of inlets on the desulfurization efficiency,atmosphere mass fraction distribution and temperature distribution in the furnace was further investigated.展开更多
Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its u...Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions.展开更多
After a long period of water flooding development,the oilfield has entered the middle and high water cut stage.The physical properties of reservoirs are changed by water erosion,which directly impacts reservoir develo...After a long period of water flooding development,the oilfield has entered the middle and high water cut stage.The physical properties of reservoirs are changed by water erosion,which directly impacts reservoir development.Conventional numerical reservoir simulation methodologies typically employ static assumptions for model construction,presuming invariant reservoir geological parameters throughout the development process while neglecting the reservoir’s temporal evolution characteristics.Although such simplifications reduce computational complexity,they introduce substantial descriptive inaccuracies.Therefore,this paper proposes a meshless numerical simulation method for reservoirs that considers time-varying characteristics.This method avoids the meshing in traditional numerical simulation methods.From the fluid flow perspective,the reservoir’s computational domain is discretized into a series of connection units.An influence domain with a certain radius centered on the nodes is selected,and one-dimensional connection units are established between the nodes to achieve the characterization of the flow topology structure of the reservoir.In order to reflect the dynamic evolution of the reservoir’s physical properties during the water injection development process,the time-varying characteristics are incorporated into the formula of the seepage characteristic parameters in the meshless calculation.The change relationship of the permeability under different surface fluxes is considered to update the calculated connection conductivity in real time.By combining with the seepage control equation for solution,a time-varying meshless numerical simulation method is formed.The results show that compared with the numerical simulationmethod of the connection elementmethod(CEM)that only considers static parameters,this method has higher simulation accuracy and can better simulate the real migration and distribution of oil and water in the reservoir.Thismethod improves the accuracy of reservoir numerical simulation and the development effect of oilfields,providing a scientific basis for optimizing the water injection strategy,adjusting the production plan,and extending the effective production cycle of the oilfield.展开更多
Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce f...Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce fatigue failure and even cause unpredictable drilling accidents.Therefore,it is important to study the ViV characteristics of deepwater drilling riser and reveal the main controlling factors for ensuring the safe and efficient operation of deepwater drilling engineering.In this paper,the ViV of deepwater drilling riser is numerically simulated in time domain based on the discrete vortex method(DvM).A hydrodynamic analysis model and governing equation of VIV is proposed with considering the effect of riser motion using DVM and slice method,where the governing equation is solved by Runge-Kutta method.Model validation is performed,which verified the correctness and accuracy of the mechanical model and the solution method.On this basis,the influence of the number of control points,current velocity,riser outer diameter,shear flow and top tension on the ViV characteristics of deepwater drilling risers are discussed in detail.The results show that with the increase of current velocity,the vibration amplitude of deepwater drilling riser decreases obviously,while the vibration frequency increases gradually.However,if the outer diameter of riser increases,the vibration amplitude increases,while the vibration frequency decreases gradually.The top tension also has great influence on the VIV of riser.When the top tension is 1.25 G,the VIV is suppressed to a certain extent.This study has guiding significance for optimal design and engineering control of deepwater drilling riser.展开更多
0 INTRODUCTION In recent years,modern railways have been actively under construction in the complex mountainous area of Southwest China.However,rockfall poses a significant threat to both construction and operation ph...0 INTRODUCTION In recent years,modern railways have been actively under construction in the complex mountainous area of Southwest China.However,rockfall poses a significant threat to both construction and operation phases of railway projects(Yan et al.,2023;Chen et al.,2022;Fanos and Pradhan,2018).展开更多
文摘Existing numerical methods for complex composites, such as multiscale simulation and neural network algorithms, face significant limitations. Multiscale techniques are often prohibitively expensive for large models, while neural networks struggle to represent underlying microscopic material properties. To overcome these challenges, a meso-micro scale numerical method using a virtual node approach is developed in this study. A Wbraid/Al/Epoxy functional structural material is fabricated, and a representative periodic unit cell is identified based on its architecture. The complex structure is then discretized into nodes, and mechanical interactions are governed by pre-defined computation rules. This virtual node method is systematically compared against both multiscale simulation and a neural network algorithm, with validation provided through mechanical experiments. The results demonstrate that the nodal operation strategy significantly reduces computational resource requirements. By quantifying microscopic bonding with coefficients, explicit interface treatment is avoided, granting the method strong adaptability to lattice materials. The method can simulate extremely complex structures using parameters from simple tests and is suited for large systems. Compared to three-point bending experiments, errors for multiscale, virtual node, and neural network methods were 12.4%, 6.9%, and 34.5%, respectively. Under dynamic compression, the errors were 2.7%, 9.3%, and 15.43%. The virtual node method demonstrated superior accuracy under static conditions, enabling efficient prediction and auxiliary development of complex structural materials.
基金Supported by the National Natural Science Foundation of China under Grant No.51975138the High-Tech Ship Scientific Research Project from the Ministry of Industry and Information Technology under Grant No.CJ05N20the National Defense Basic Research Project under Grant No.JCKY2023604C006.
文摘Marine thin plates are susceptible to welding deformation owing to their low structural stiffness.Therefore,the efficient and accurate prediction of welding deformation is essential for improving welding quality.The traditional thermal elastic-plastic finite element method(TEP-FEM)can accurately predict welding deformation.However,its efficiency is low because of the complex nonlinear transient computation,making it difficult to meet the needs of rapid engineering evaluation.To address this challenge,this study proposes an efficient prediction method for welding deformation in marine thin plate butt welds.This method is based on the coupled temperature gradient-thermal strain method(TG-TSM)that integrates inherent strain theory with a shell element finite element model.The proposed method first extracts the distribution pattern and characteristic value of welding-induced inherent strain through TEP-FEM analysis.This strain is then converted into the equivalent thermal load applied to the shell element model for rapid computation.The proposed method-particularly,the gradual temperature gradient-thermal strain method(GTG-TSM)-achieved improved computational efficiency and consistent precision.Furthermore,the proposed method required much less computation time than the traditional TEP-FEM.Thus,this study lays the foundation for future prediction of welding deformation in more complex marine thin plates.
基金supported by the National Natural Science Foundation of China(Grant Nos.12272393 and 52130905).
文摘As binary geological media,soil-rock mixtures(SRMs)exhibit a distinct gradational composition,leading to their unique mechanical behaviors.To appraise the stability of SRM slopes,it is essential to determine equivalent parameters of SRMs,which are typically obtained through experimental and numerical methods.In contrasted to other numerical methods,the numerical manifold method(NMM)is more effective in addressing SRM problems.This is because the high-precision regular mathematical meshes in NMM can be used without aligning with the soil-rock interfaces and boundaries of SRMs.In the current research,the equivalent strength parameters of SRMs,i.e.the equivalent cohesion ce and internal friction angleϕ_(e),are determined using NMM.Initially,an NMM triaxial numerical model is established and validated based on triaxial experiments.Subsequently,the soil and rock parameters are derived through parameter inversion.Moreover,the impacts of rock content,size,shape and rock blocks'major-axis orientation on ce andϕ_(e) of SRMs are thoroughly examined using the NMM triaxial numerical model.Additionally,a fitting function is proposed to linkϕ_(e) to the rock content and size of SRMs.When other influencing factors are fixed,the above fitting model leads to the following conclusions:(1)the predictedϕ_(e) of SRMs increase with the increase of rock content;and(2)SRM samples with smaller rocks display a higher predictedϕ_(e).
基金supported by Beijing Natural Science Foundation(L233025)。
文摘Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H^(2)-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.
基金supported by grants received by the first author and third author from the Institute of Eminence,Delhi University,Delhi,India,as part of the Faculty Research Program via Ref.No./IoE/2024-25/12/FRP.
文摘Software systems are vulnerable to security breaches as they expand in complexity and functionality.The confidentiality,integrity,and availability of data are gravely threatened by flaws in a system’s design,implementation,or configuration.To guarantee the durability&robustness of the software,vulnerability identification and fixation have become crucial areas of focus for developers,cybersecurity experts and industries.This paper presents a thorough multi-phase mathematical model for efficient patch management and vulnerability detection.To uniquely model these processes,the model incorporated the notion of the learning phenomenon in describing vulnerability fixation using a logistic learning function.Furthermore,the authors have used numerical methods to approximate the solution of the proposed framework where an analytical solution is difficult to attain.The suggested systematic architecture has been demonstrated through statistical analysis using patch datasets,which offers a solid basis for the research conclusions.According to computational research,learning dynamics improves security response and results in more effective vulnerability management.The suggested model offers a systematic approach to proactive vulnerability mitigation and has important uses in risk assessment,software maintenance,and cybersecurity.This study helps create more robust software systems by increasing patch management effectiveness,which benefits developers,cybersecurity experts,and sectors looking to reduce security threats in a growing digital world.
文摘This article reviews the application and progress of deep learning in efficient numerical computing methods.Deep learning,as an important branch of machine learning,provides new ideas for numerical computation by constructing multi-layer neural networks to simulate the learning process of the human brain.The article explores the application of deep learning in solving partial differential equations,optimizing problems,and data-driven modeling,and analyzes its advantages in computational efficiency,accuracy,and adaptability.At the same time,this article also points out the challenges faced by deep learning numerical computation methods in terms of computational efficiency,interpretability,and generalization ability,and proposes strategies and future development directions for integrating with traditional numerical methods.
文摘This review paper provides a comprehensive introduction to various numerical methods for the phase-field model used to simulate the phase separation dynamics of diblock copolymer melts.Diblock copolymer systems form complex structures at the nanometer scale and play a significant role in various applications.The phase-field model,in particular,is essential for describing the formation and evolution of these structures and is widely used as a tool to effectively predict the movement of phase boundaries and the distribution of phases over time.In this paper,we discuss the principles and implementations of various numerical methodologies for this model and analyze the strengths,limitations,stability,accuracy,and computational efficiency of each method.Traditional approaches such as Fourier spectral methods,finite difference methods and alternating direction explicit methods are reviewed,as well as recent advancements such as the invariant energy quadratization method and the scalar auxiliary variable scheme are also presented.In addition,we introduce examples of the phase-field model,which are fingerprint image restoration and 3D printing.These examples demonstrate the extensive applicability of the reviewed methods and models.
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
文摘This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤0.where aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.
基金The National Natural Science Foundation of China(No.51378121)the Fok Ying Tung Education Foundation(No.141076)the Scientific Innovation Research of College Graduates in Jiangsu Province(No.KYLX_0164)
文摘In order to predict the long-term rutting of asphalt pavement, the effective temperature for pavement rutting is calculated using the numerical simulation method. The transient temperature field of asphalt pavement was simulated based on actual meteorological data of Nanjing. 24-hour rutting development under a transient temperature field was calculated in each month. The rutting depth accumulated under the static temperature field was also estimated and the relationship between constant temperature parameters was analyzed. Then the effective temperature for pavement rutting was determined based on the rutting equivalence principle. The results show that the monthly effective temperature is above 40 t in July and August, while in June and September it ranges from 30 to 40 Rutting development can be ignored when the monthly effective temperature is less than 30 t. The yearly effective temperature for rutting in Nanjing is around 38. 5 t. The long-term rutting prediction model based on the effective temperature can reflect the influences of meteorological factors and traffic time distribution.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52271317 and 52071149)the Fundamental Research Funds for the Central Universities(HUST:2019kfy XJJS007)。
文摘To address the problems of low accuracy by the CONWEP model and poor efficiency by the Coupled Eulerian-Lagrangian(CEL)method in predicting close-range air blast loads of cylindrical charges,a neural network-based simulation(NNS)method with higher accuracy and better efficiency was proposed.The NNS method consisted of three main steps.First,the parameters of blast loads,including the peak pressures and impulses of cylindrical charges with different aspect ratios(L/D)at different stand-off distances and incident angles were obtained by two-dimensional numerical simulations.Subsequently,incident shape factors of cylindrical charges with arbitrary aspect ratios were predicted by a neural network.Finally,reflected shape factors were derived and implemented into the subroutine of the ABAQUS code to modify the CONWEP model,including modifications of impulse and overpressure.The reliability of the proposed NNS method was verified by related experimental results.Remarkable accuracy improvement was acquired by the proposed NNS method compared with the unmodified CONWEP model.Moreover,huge efficiency superiority was obtained by the proposed NNS method compared with the CEL method.The proposed NNS method showed good accuracy when the scaled distance was greater than 0.2 m/kg^(1/3).It should be noted that there is no need to generate a new dataset again since the blast loads satisfy the similarity law,and the proposed NNS method can be directly used to simulate the blast loads generated by different cylindrical charges.The proposed NNS method with high efficiency and accuracy can be used as an effective method to analyze the dynamic response of structures under blast loads,and it has significant application prospects in designing protective structures.
基金the Natural Science Foundation of CQ CSTC under Grant No. 2007BB2161.
文摘For a general nonlinear fractional-order differential equation, the numerical solution is a good way to approximate the trajectory of such systems. In this paper, a novel algorithm for numerical solution of fractional-order differential equations based on the definition of Grunwald-Letnikov is presented. The results of numerical solution by using the novel method and the frequency-domain method are compared, and the limitations of frequency-domain method are discussed.
文摘A numerical method based on B-spline is developed to solve the time-dependent Emden-Fow- ler-type equations. We also present a reliable new algorithm based on B-spline to overcome the difficulty of the singular point at x = 0. The error analysis of the method is described. Numerical results are given to illustrate the efficiency of the proposed method.
文摘We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.
基金supported by the National Natural Science Foundation of China(Grant No.12371250)the Jiangsu Provincial Natural Science Foundation(Grant Nos.BK20221508,12205154 and 11775116)the Dean’s Research Fund of the Education University of Hong Kong 2023/23(FLASS/DRF/IRS-8)。
文摘The rotating shallow water system is an important physical model,which has been widely used in many scientific areas,such as fluids,hydrodynamics,geophysics,oceanic and atmospheric dynamics.In this paper,we extend the application of the Adomian decomposition method from the single equation to the coupled system to investigate the numerical solutions of the rotating shallow water system with an underlying circular paraboloidal basin.By introducing some special initial values,we obtain interesting approximate pulsrodon solutions corresponding to pulsating elliptic warm-core rings,which take the form of realistic series solutions.Numerical results reveal that the numerical pulsrodon solutions can quickly converge to the exact solutions derived by Rogers and An,which fully shows the efficiency and accuracy of the proposed method.Note that the method proposed can be effectively used to construct numerical solutions of many nonlinear mathematical physics equations.The results obtained provide some potential theoretical guidance for experts to study the related phenomena in geography,oceanic and atmospheric science.
基金supported by the National Key Research and Development Program of China(2022YFC2904400)Guangxi Science and Technology Major Project(Gui Ke AA23023033)。
文摘As a pyrometallurgical process,circulating fluidized bed(CFB) roasting has good potential for application in desulfurization of high-sulfur bauxite.The gas-solid distribution and reaction during CFB roasting of high-sulfur bauxite were simulated using the computational particle fluid dynamics(CPFD) method.The effect of primary air flow velocity on particle velocity,particle volume distribution,furnace temperature distribution and pressure distribution were investigated.Under the condition of the same total flow of natural gas,the impact of the number of inlets on the desulfurization efficiency,atmosphere mass fraction distribution and temperature distribution in the furnace was further investigated.
文摘Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions.
基金funded by the 14th Five-Year Plan Major Science and Technology Project of CNOOC project number KJGG2021-0506.
文摘After a long period of water flooding development,the oilfield has entered the middle and high water cut stage.The physical properties of reservoirs are changed by water erosion,which directly impacts reservoir development.Conventional numerical reservoir simulation methodologies typically employ static assumptions for model construction,presuming invariant reservoir geological parameters throughout the development process while neglecting the reservoir’s temporal evolution characteristics.Although such simplifications reduce computational complexity,they introduce substantial descriptive inaccuracies.Therefore,this paper proposes a meshless numerical simulation method for reservoirs that considers time-varying characteristics.This method avoids the meshing in traditional numerical simulation methods.From the fluid flow perspective,the reservoir’s computational domain is discretized into a series of connection units.An influence domain with a certain radius centered on the nodes is selected,and one-dimensional connection units are established between the nodes to achieve the characterization of the flow topology structure of the reservoir.In order to reflect the dynamic evolution of the reservoir’s physical properties during the water injection development process,the time-varying characteristics are incorporated into the formula of the seepage characteristic parameters in the meshless calculation.The change relationship of the permeability under different surface fluxes is considered to update the calculated connection conductivity in real time.By combining with the seepage control equation for solution,a time-varying meshless numerical simulation method is formed.The results show that compared with the numerical simulationmethod of the connection elementmethod(CEM)that only considers static parameters,this method has higher simulation accuracy and can better simulate the real migration and distribution of oil and water in the reservoir.Thismethod improves the accuracy of reservoir numerical simulation and the development effect of oilfields,providing a scientific basis for optimizing the water injection strategy,adjusting the production plan,and extending the effective production cycle of the oilfield.
基金the financial support from National Key R&D Program of China(Grant number:2024YFC2815100)Natural Science Foundation of China(Grant number:52322110)Beijing Nova Program(Grant number:20230484341).
文摘Deepwater drilling riser is the key equipment connecting the subsea wellhead and floating drilling platform.Due to complex marine environment,vortex-induced vibration(ViV)will be generated on riser,which will induce fatigue failure and even cause unpredictable drilling accidents.Therefore,it is important to study the ViV characteristics of deepwater drilling riser and reveal the main controlling factors for ensuring the safe and efficient operation of deepwater drilling engineering.In this paper,the ViV of deepwater drilling riser is numerically simulated in time domain based on the discrete vortex method(DvM).A hydrodynamic analysis model and governing equation of VIV is proposed with considering the effect of riser motion using DVM and slice method,where the governing equation is solved by Runge-Kutta method.Model validation is performed,which verified the correctness and accuracy of the mechanical model and the solution method.On this basis,the influence of the number of control points,current velocity,riser outer diameter,shear flow and top tension on the ViV characteristics of deepwater drilling risers are discussed in detail.The results show that with the increase of current velocity,the vibration amplitude of deepwater drilling riser decreases obviously,while the vibration frequency increases gradually.However,if the outer diameter of riser increases,the vibration amplitude increases,while the vibration frequency decreases gradually.The top tension also has great influence on the VIV of riser.When the top tension is 1.25 G,the VIV is suppressed to a certain extent.This study has guiding significance for optimal design and engineering control of deepwater drilling riser.
基金supported by the Open Research Fund of Key Laboratory of Geological Hazards on Three Gorges Reservoir Area(China Three Gorges University),Ministry of Education(No.2022KDZ03)the Science and Technology Projects of Yunnan Provincial Science and Technology Department(No.202401AT070328)+1 种基金the Young talents project of“Xingdian Talent Support Program”in Yunnan Province(No.YNWR-QNBJ-2020-019)the Fund Project of China Academy of Railway Sciences Co.,Ltd.(No.2021YJ178)。
文摘0 INTRODUCTION In recent years,modern railways have been actively under construction in the complex mountainous area of Southwest China.However,rockfall poses a significant threat to both construction and operation phases of railway projects(Yan et al.,2023;Chen et al.,2022;Fanos and Pradhan,2018).
