A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Research on entropy weight variation evaluation method for wind power clusters based on dynamic layered sorting

This paper presents an evaluation method for the entropy-weighting of wind power clusters that comprehensively evaluates the allocation problems of wind power clusters by considering the correlation between indicators and the dynamic performance of weight changes.A dynamic layered sorting allocation method is also proposed.The proposed evaluation method considers the power-limiting degree of the last cycle,the adjustment margin,and volatility.It uses the theory of weight variation to update the entropy weight coefficients of each indicator in real time,and then performs a fuzzy evaluation based on the membership function to obtain intuitive comprehensive evaluation results.A case study of a large-scale wind power base in Northwest China was conducted.The proposed evaluation method is compared with fixed-weight entropy and principal component analysis methods.The results show that the three scoring trends are the same,and that the proposed evaluation method is closer to the average level of the latter two,demonstrating higher accuracy.The proposed allocation method can reduce the number of adjustments made to wind farms,which is significant for the allocation and evaluation of wind power clusters.

Dynamic failure process of expanded polystyrene particle lightweight soil under cyclic loading using discrete element method

Expanded polystyrene(EPS)particle-based lightweight soil,which is a type of lightweight filler,is mainly used in road engineering.The stability of subgrades under dynamic loading is attracting increased research attention.The traditional method for studying the dynamic strength characteristics of soils is dynamic triaxial testing,and the discrete element simulation of lightweight soils under cyclic load has rarely been considered.To study the meso-mechanisms of the dynamic failure processes of EPS particle lightweight soils,a discrete element numerical model is established using the particle flow code(PFC)software.The contact force,displacement field,and velocity field of lightweight soil under different cumulative compressive strains are studied.The results show that the hysteresis curves of lightweight soil present characteristics of strain accumulation,which reflect the cyclic effects of the dynamic load.When the confining pressure increases,the contact force of the particles also increases.The confining pressure can restrain the motion of the particle system and increase the dynamic strength of the sample.When the confining pressure is held constant,an increase in compressive strain causes minimal change in the contact force between soil particles.However,the contact force between the EPS particles decreases,and their displacement direction points vertically toward the center of the sample.Under an increase in compressive strain,the velocity direction of the particle system changes from a random distribution and points vertically toward the center of the sample.When the compressive strain is 5%,the number of particles deflected in the particle velocity direction increases significantly,and the cumulative rate of deformation in the lightweight soil accelerates.Therefore,it is feasible to use 5%compressive strain as the dynamic strength standard for lightweight soil.Discrete element methods provide a new approach toward the dynamic performance evaluation of lightweight soil subgrades.

Dynamic Location Method for Shallow Ocean Bottom Nodes Using the Levenberg-Marquart Algorithm

Ocean bottom node(OBN)data acquisition is the main development direction of marine seismic exploration;it is widely promoted,especially in shallow sea environments.However,the OBN receivers may move several times because they are easily affected by tides,currents,and other factors in the shallow sea environment during long-term acquisition.If uncorrected,then the imaging quality of subsequent processing will be affected.The conventional secondary positioning does not consider the case of multiple movements of the receivers,and the accuracy of secondary positioning is insufficient.The first arrival wave of OBN seismic data in shallow ocean mainly comprises refracted waves.In this study,a nonlinear model is established in accordance with the propagation mechanism of a refracted wave and its relationship with the time interval curve to realize the accurate location of multiple receiver movements.In addition,the Levenberg-Marquart algorithm is used to reduce the influence of the first arrival pickup error and to automatically detect the receiver movements,identifying the accurate dynamic relocation of the receivers.The simulation and field data show that the proposed method can realize the dynamic location of multiple receiver movements,thereby improving the accuracy of seismic imaging and achieving high practical value.

Comparative study of nudged elastic band and molecular dynamics methods for diffusion kinetics in solid-state electrolytes

Considerable efforts are being made to transition current lithium-ion and sodium-ion batteries towards the use of solid-state electrolytes.Computational methods,specifically nudged elastic band(NEB)and molecular dynamics(MD)methods,provide powerful tools for the design of solid-state electrolytes.The MD method is usually the choice for studying the materials involving complex multiple diffusion paths or having disordered structures.However,it relies on simulations at temperatures much higher than working temperature.This paper studies the reliability of the MD method using the system of Na diffusion in MgO as a benchmark.We carefully study the convergence behavior of the MD method and demonstrate that total effective simulation time of 12 ns can converge the calculated diffusion barrier to about 0.01 eV.The calculated diffusion barrier is 0.31 eV from both methods.The diffusion coefficients at room temperature are 4.3×10^(-9) cm^(2)⋅s^(−1) and 2.2×10^(-9) cm^(2)⋅s^(−1),respectively,from the NEB and MD methods.Our results justify the reliability of the MD method,even though high temperature simulations have to be employed to overcome the limitation on simulation time.

Dynamic Characteristics of Functionally Graded Timoshenko Beams by Improved Differential Quadrature Method

This study proposes an effective method to enhance the accuracy of the Differential Quadrature Method(DQM)for calculating the dynamic characteristics of functionally graded beams by improving the form of discrete node distribution.Firstly,based on the first-order shear deformation theory,the governing equation of free vibration of a functionally graded beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam axial displacement,transverse displacement,and cross-sectional rotation angle by considering the effects of shear deformation and rotational inertia of the beam cross-section.Then,ignoring the shear deformation of the beam section and only considering the effect of the rotational inertia of the section,the governing equation of the beam is transformed into the eigenvalue problem of ordinary differential equations with respect to beam transverse displacement.Based on the differential quadrature method theory,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations.Finally,the first several natural frequencies of the beam can be calculated.The feasibility and accuracy of the improved DQM are verified using the finite element method(FEM)and combined with the results of relevant literature.

Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.

EFFICIENT NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FLEXIBLE ROD HIT BY RIGID BALL

Impact dynamics of flexible solids is important in engineering practice. Obtaining its dynamic response is a challenging task and usually achieved by numerical methods. The objectives of the study are twofold. Firstly, the discrete singular convolution （DSC） is used for the first time to analyze the impact dynamics. Secondly, the efficiency of various numerical methods for dynamic analysis is explored via an example of a flexible rod hit by a rigid ball. Three numerical methods, including the conventional finite element （FE） method, the DSC algorithm, and the spectral finite element （SFE） method, and one proposed modeling strategy, the improved spectral finite element （ISFE） method, are involved. Numerical results are compared with the known analytical solutions to show their efficiency. It is demonstrated that the proposed ISFE modeling strategy with a proper length of con- ventional FE yields the most accurate contact stress among the four investigated models. It is also found that the DSC algorithm is an alternative method for collision problems.

DETERMINING CRITICAL TIME OF ROCK DYNAMIC FRACTURE BY DYNAMIC MOIRE METHOD

An effective Dynamic Moire method was presented to determine the critical time of crack instable propagation in rock dynamic fracture. Two pieces of grating were installed near the notch of Short Rod specimen to form the Moire fringes, then the COD versus time could be monitored from the movement of the Moire fringes, and finally the critical time could be determined from the velocity of COD. This method was also compared with another one.It could be concluded that the critical time determined by Dynamic Moire method corresponds with that of the Transmitted Wave method at the loading rates from 103 to 104 MPa·m(1/2)·S(-1).

Analysis of mesoscopic mechanical dynamic characteristics of ballast bed with under sleeper pads

The meso-dynamical behaviour of a high-speed rail ballast bed with under sleeper pads(USPs)was studied.The geometrically irregular refined discrete element model of the ballast particles was constructed using 3D scanning techniques,and the 3D dynamic model of the rail-sleeper-ballast bed was constructed using the coupled discrete element method-multiflexible-body dynamics(DEM-MFBD)approach.We analyse the meso-mechanical dynamics of the ballast bed with USPs under dynamic load on a train and verify the correctness of the model in laboratory tests.It is shown that the deformation of the USPs increases the contact area between the sleeper and the ballast particles,and subsequently the number of contacts between them.As the depth of the granular ballast bed increases,the contact area becomes larger,and the contact force between the ballast particles gradually decreases.Under the action of the elastic USPs,the contact forces between ballast particles are reduced and the overall vibration level of the ballast bed can be reduced.The settlement of the granular ballast bed occurs mainly at the shallow position of the sleeper bottom,and the installation of the elastic USPs can be effective in reducing the stress on the ballast particles and the settlement of the ballast bed.

Seismic wave input method for three-dimensional soil-structure dynamic interaction analysis based on the substructure of artificial boundaries

The method of inputting the seismic wave determines the accuracy of the simulation of soil-structure dynamic interaction. The wave method is a commonly used approach for seismic wave input, which converts the incident wave into equivalent loads on the cutoff boundaries. The wave method has high precision, but the implementation is complicated, especially for three-dimensional models. By deducing another form of equivalent input seismic loads in the fi nite element model, a new seismic wave input method is proposed. In the new method, by imposing the displacements of the free wave fi eld on the nodes of the substructure composed of elements that contain artifi cial boundaries, the equivalent input seismic loads are obtained through dynamic analysis of the substructure. Subsequently, the equivalent input seismic loads are imposed on the artifi cial boundary nodes to complete the seismic wave input and perform seismic analysis of the soil-structure dynamic interaction model. Compared with the wave method, the new method is simplifi ed by avoiding the complex processes of calculating the equivalent input seismic loads. The validity of the new method is verifi ed by the dynamic analysis numerical examples of the homogeneous and layered half space under vertical and oblique incident seismic waves.

A Correction Method Suitable for Dynamical Seasonal Prediction

Based on the hindcast results of summer rainfall anomalies over China for the period 1981-2000 by the Dynamical Climate Prediction System （IAP-DCP） developed by the Institute of Atmospheric Physics, a correction method that can account for the dependence of model＇s systematic biases on SST anomalies is proposed. It is shown that this correction method can improve the hindcast skill of the IAP-DCP for summer rainfall anomalies over China, especially in western China and southeast China, which may imply its potential application to real-time seasonal prediction.

Partition method for impact dynamics of flexible multibody systems based on contact constraint

The impact dynamics of a flexible multibody system is investigated. By using a partition method, the system is divided into two parts, the local impact region and the region away from the impact. The two parts are connected by specific boundary conditions, and the system after partition is equivalent to the original system. According to the rigid-flexible coupling dynamic theory of multibody system, system＇s rigid-flexible coupling dynamic equations without impact are derived. A local impulse method for establishing the initial impact conditions is proposed. It satisfies the compatibility con- ditions for contact constraints and the actual physical situation of the impact process of flexible bodies. Based on the contact constraint method, system＇s impact dynamic equa- tions are derived in a differential-algebraic form. The contact/separation criterion and the algorithm are given. An impact dynamic simulation is given. The results show that system＇s dynamic behaviors including the energy, the deformations, the displacements, and the impact force during the impact process change dramatically. The impact makes great effects on the global dynamics of the system during and after impact.

Distributed Collaborative Response Surface Method for Mechanical Dynamic Assembly Reliability Design

Because of the randomness of many impact factors influencing the dynamic assembly relationship of complex machinery, the reliability analysis of dynamic assembly relationship needs to be accomplished considering the randomness from a probabilistic perspective. To improve the accuracy and efficiency of dynamic assembly relationship reliability analysis, the mechanical dynamic assembly reliability（MDAR） theory and a distributed collaborative response surface method（DCRSM） are proposed. The mathematic model of DCRSM is established based on the quadratic response surface function, and verified by the assembly relationship reliability analysis of aeroengine high pressure turbine（HPT） blade-tip radial running clearance（BTRRC）. Through the comparison of the DCRSM, traditional response surface method（RSM） and Monte Carlo Method（MCM）, the results show that the DCRSM is not able to accomplish the computational task which is impossible for the other methods when the number of simulation is more than 100 000 times, but also the computational precision for the DCRSM is basically consistent with the MCM and improved by 0.40-4.63% to the RSM, furthermore, the computational efficiency of DCRSM is up to about 188 times of the MCM and 55 times of the RSM under 10000 times simulations. The DCRSM is demonstrated to be a feasible and effective approach for markedly improving the computational efficiency and accuracy of MDAR analysis. Thus, the proposed research provides the promising theory and method for the MDAR design and optimization, and opens a novel research direction of probabilistic analysis for developing the high-performance and high-reliability of aeroengine.

A Flexible-Segment-Model-Based Dynamics Calculation Method for Free Hanging Marine Risers in Re-Entry

In re-entry, the drilling riser hanging to the holding vessel takes on a free hanging state, waiting to be moved from the initial random position to the wellhead. For the re-entry, dynamics calculation is often done to predict the riser motion or evaluate the structural safety. A dynamics calculation method based on Flexible Segment Model （FSM） is proposed for free hanging marine risers. In FSM, a riser is discretized into a series of flexible segments. For each flexible segment, its deflection feature and external forces are analyzed independently. For the whole riser, the nonlinear governing equations are listed according to the moment equilibrium at nodes. For the solution of the nonlinear equations, a linearization iteration scheme is provided in the paper. Owing to its flexibility, each segment can match a long part of the riser body, which enables that good results can be obtained even with a small number of segments. Moreover, the linearization iteration scheme can avoid widely used Newton-Rapson iteration scheme in which the calculation stability is influenced by the initial points. The FSM-based dynamics calculation is timesaving and stable, so suitable for the shape prediction or real-time control of free hanging marine risers.

Simulation of Dynamic Recrystallization Using Cellular Automaton Method

A new modeling approach that couples fundamental metallurgical principles of dynamical recrystallization with the cellular automaton method was developed to simulate the microstructural evolution linking with the plastic flow behavior during thermomechanical processing.The driving force for the nucleation and growth of dynamically recrystallized grain is the volume free energy due to the stored dislocation density of a deformation matrix.The growth terminates the impingement.The model is capable of simulating kinetics,microstructure and texture evolution during recrystallization.The predictions of microstructural evolution agree with the experimental results.

Modified precise time step integration method of structural dynamic analysis

The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.

THE APPLICATION OF DISCRETE ELEMENT METHOD IN SOLVING THREE-DIMENTIONAL IMPACT DYNAMICS PROBLEMS

A three-dimensional discrete element model of the connective type is presented. Moreover,a three-dimensional numerical analysis code,which can carry out the transitional pro- cess from connective model(for continuum)to contact model(for non-continuum),is developed for simulating the mechanical process from continuum to non-continuum.The wave propagation process in a concrete block(as continuum)made of cement grout under impact loading is numer- ically simulated with this code.By comparing its numerical results with those by LS-DYNA,the calculation accuracy of the model and algorithm is proved.Furthermore,the failure process of the concrete block under quasi-static loading is demonstrated,showing the basic dynamic tran- sitional process from continuum to non-continuum.The results of calculation can be displayed by animation.The damage modes are similar to the experimental results.The two numerical examples above prove that our model and its code are powerful and efficient in simulating the dynamic failure problems accompanying the transition from continuum to non-continuum.It also shows that the discrete element method(DEM)will have broad prospects for development and application.

Quasi-static and dynamical analyses of a thermoviscoelastic Timoshenko beam using the differential quadrature method

The quasi-static and dynamic responses of a thermoviscoelastic Timoshenko beam subject to thermal loads are analyzed. First, based on the small geometric deformation assumption and Boltzmann constitutive relation, the governing equations for the beam are presented. Second, an extended differential quadrature method(DQM)in the spatial domain and a differential method in the temporal domain are combined to transform the integro-partial-differential governing equations into the ordinary differential equations. Third, the accuracy of the present discrete method is verified by elastic/viscoelastic examples, and the effects of thermal load parameters, material and geometrical parameters on the quasi-static and dynamic responses of the beam are discussed. Numerical results show that the thermal function parameter has a great effect on quasi-static and dynamic responses of the beam. Compared with the thermal relaxation time, the initial vibrational responses of the beam are more sensitive to the mechanical relaxation time of the thermoviscoelastic material.