基于DEM-FEM耦合方法的碎屑流对桥墩最大冲击力的影响因素研究

碎屑流是我国山区最危险的地质灾害之一,山区桥墩常受到碎屑流冲击而开裂、倾斜甚至倒塌,给山区桥梁建设、运营带来严重的安全隐患。采用离散元方法(discrete element method,DEM)和有限元方法(finite element method,FEM)耦合的三维数值模拟方法模拟了碎屑流对双柱式桥墩的冲击效应,并结合斜槽试验,验证了耦合方法的准确性,进一步分析了碎屑流冲击坡度、距离和体积密度对桥墩冲击力的影响规律。结果表明,最大冲击力与碎屑流冲击坡度、距离和体积密度分别呈幂函数(指数大于1)、幂函数(指数小于1)和线性正相关。冲击坡度、距离和体积密度对最大冲击力的敏感度值分别为3.012、0.202、0.804,在桥梁碎屑流灾害防治时需重视冲击坡度和体积密度的影响。将冲击力的数值模拟值与流体动力学模型预测值对比分析表明,流体动力学模型理论公式能较好地预测桥墩所受的最大冲击力,最大预测误差低于23.6%。相关研究结果可为山区桥梁碎屑流灾害防治与设计提供一定的参考依据。

考虑强度速率衰减效应的地震滑坡SPH-FEM模拟

基于SPH和FEM耦合的数值计算方法,引入滑动面摩擦强度的速率衰减模型,提出了一种能够模拟地震诱发滑坡破坏过程的数值模拟方法。基于所提数值方法模拟了唐家山地震滑坡,模拟结果与现场勘查结果及室内试验现象较为一致。基于模拟的滑动面上摩擦系数的演化过程,将唐家山滑坡的发生分为4个阶段:启动阶段、摩擦衰减阶段、低摩擦滑移阶段和逐步稳定阶段。模拟结果表明速度增加和摩擦强度衰减的相互促进,是触发滑体的高速运动的根本原因。提出采用滑体上作用的动摩擦力fd和动下滑力Td的比值R作为判别指标用于判断大型滑坡的启动,当首次出现R小于1时认为滑动面发生整体贯通并出现失稳启动。基于滑动面不同位置摩擦系数的演化,揭示了滑坡启动中滑动面摩擦强度衰减和滑动面的渐进贯通过程,解释了地震作用与滑动面摩擦参数速率衰减效应共同作用触发大型滑坡发生破坏的内在机理。

Acoustic reflection well logging modeling using the frequency-domain finite-element method with a hybrid PML

In this paper, we propose a hybrid PML （H-PML） combining the normal absorption factor of convolutional PML （C-PML） with tangential absorption factor of Mutiaxial PML （M-PML）. The H-PML boundary conditions can better suppress the numerical instability in some extreme models, and the computational speed of finite-element method and the dynamic range are greatly increased using this HPML. We use the finite-element method with a hybrid PML to model the acoustic reflection of the interface when wireline and well logging while drilling （LWD）, in a formation with a reflector outside the borehole. The simulation results suggests that the PS- and SP- reflected waves arrive at the same time when the inclination between the well and the outer interface is zero, and the difference in arrival times increases with increasing dip angle. When there are fractures outside the well, the reflection signal is clearer in the subsequent reflection waves and may be used to identify the fractured zone. The difference between the dominant wavelength and the model scale shows that LWD reflection logging data are of higher resolution and quality than wireline acoustic reflection logging.

基于SPH-FEM耦合方法的泥石流冲击输电塔基础的动力分析

泥石流是我国西南山区常见的地质灾害。架空输电杆塔在泥石流的冲击下往往发生基础破坏甚至会造成杆塔倒塌。首先采用光滑粒子流体动力学(smoothed particle hydrodynamics,简称SPH)方法和有限元方法(finite element method,简称FEM)相耦合的三维数值方法模拟了泥石流对杆塔基础的冲击作用;在与相关模型试验结果验证的基础上,开展了不同泥石流密度、黏度系数及初始速度条件下对输电塔基础的冲击力作用的参数分析;研究结果表明:随着泥石流初始速度的增加,冲击力峰值会随之增大;前排基础的冲击力峰值均大于后排基础;泥石流冲击过程特性受到泥石流密度和黏度系数影响。与稀性泥石流相比:黏性泥石流冲击基础后,基础下游真空区相对要小;此外,将数值模拟结果与Kwan冲击力公式及铁二院推荐的冲击压力设计公式预测值进行对比分析可以发现:Kwan冲击力公式能较好地预测出基础所受泥石流冲击力的平均趋势,最大预测误差低于30%,铁二院公式预测的稀性和黏性泥石流的冲击压力平均偏低分别约17%和28%。相关研究结果有望为泥石流频发区域输电塔基础的设计和风险评估提供一定的参考依据。

Solution of shallow-water equations using least-squares finite-element method

A least-squares finite-element method （LSFEM） for the non-conservative shallow-water equations is presented. The model is capable of handling complex topography, steady and unsteady flows, subcritical and supercritical flows, and flows with smooth and sharp gradient changes. Advantages of the model include： （1） sources terms, such as the bottom slope, surface stresses and bed frictions, can be treated easily without any special treatment; （2） upwind scheme is no needed; （3） a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi （LBB） condition; and （4） the resulting system of equations is symmetric and positive-definite （SPD） which can be solved efficiently with the preconditioned conjugate gradient method. The model is verified with flow over a bump, tide induced flow, and dam-break. Computed results are compared with analytic solutions or other numerical results, and show the model is conservative and accurate. The model is then used to simulate flow past a circular cylinder. Important flow charac-teristics, such as variation of water surface around the cylinder and vortex shedding behind the cylinder are investigated. Computed results compare well with experiment data and other numerical results.

Three-dimensional land FD-CSEM forward modeling using edge finite-element method

A modeling tool for simulating three-dimensional land frequency-domain controlled-source electromagnetic surveys,based on a finite-element discretization of the Helmholtz equation for the electric fields,has been developed.The main difference between our modeling method and those previous works is edge finite-element approach applied to solving the three-dimensional land frequency-domain electromagnetic responses generated by horizontal electric dipole source.Firstly,the edge finite-element equation is formulated through the Galerkin method based on Helmholtz equation of the electric fields.Secondly,in order to check the validity of the modeling code,the numerical results are compared with the analytical solutions for a homogeneous half-space model.Finally,other three models are simulated with three-dimensional electromagnetic responses.The results indicate that the method can be applied for solving three-dimensional electromagnetic responses.The algorithm has been demonstrated,which can be effective to modeling the complex geo-electrical structures.This efficient algorithm will help to study the distribution laws of3-D land frequency-domain controlled-source electromagnetic responses and to setup basis for research of three-dimensional inversion.

Least-squares finite-element method for shallow-water equations with source terms

Numerical solution of shallow-water equations （SWE） has been a challenging task because of its nonlinear hyperbolic nature, admitting discontinuous solution, and the need to satisfy the C-property. The presence of source terms in momentum equations, such as the bottom slope and friction of bed, compounds the difficulties further. In this paper, a least-squares finite-element method for the space discretization and θ-method for the time integration is developed for the 2D non-conservative SWE including the source terms. Advantages of the method include： the source terms can be approximated easily with interpolation functions, no upwind scheme is needed, as well as the resulting system equations is symmetric and positive-definite, therefore, can be solved efficiently with the conjugate gradient method. The method is applied to steady and unsteady flows, subcritical and transcritical flow over a bump, 1D and 2D circular dam-break, wave past a circular cylinder, as well as wave past a hump. Computed results show good C-property, conservation property and compare well with exact solutions and other numerical results for flows with weak and mild gradient changes, but lead to inaccurate predictions for flows with strong gradient changes and discontinuities.

Mesomechanics Finite-element Method for Determining the Shear Strength of Mudded Intercalation Materials

A new method regarding mesomechanics finite-element research is proposed to predict the peak shear strength of mudded intercalation materials on a mesoscopic scale. Based on geometric and mechanical parameters, along with the strain failure criteria obtained by sample＇s deformation characteristics, uniaxial compression tests on the sample were simulated through a finite-element model, which yielded values consistent with the data from the laboratory uniaxial compression tests, implying that the method is reasonable. Based on this model, a shear test was performed to calculate the peak shear strength of the mudded intercalation, consistent with values reported in the literature, thereby providing a new approach for investigating the mechanical properties of mudded intercalation materials.

基于FEM-MEI和正余弦算法的二维电磁成像方法

针对二维介质目标的电磁成像问题,将正余弦算法(Sine Cosine Algorithm,SCA)与有限元方法(Finite Element Method,FEM)和不变性测试方程(Measured Equation of Invariance,MEI)进行结合提出一种新的成像方法。将FEM与MEI进行结合求解二维介质目标的电磁散射正问题,即求解Helmholtz方程。其中,MEI保证边界截断的精度,FEM适用于复杂介质目标的准确模拟。对于电磁散射逆问题,引入SCA并加以改进提出一种新的重构方法。该方法采用等效原理与格林函数的渐近式求得远区散射场,以测量的散射场和计算的散射场最大偏差为目标函数,采用改进的SCA优化介质参数,使目标函数达到最小值,以此重构散射体。为提高计算效率,采用MPI算法进行并行计算。文中采用基准函数展示了改进的SCA算法的快速收敛性,并采用非规则的均匀介质柱目标验证了成像方法的正确性。

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

TWO-GRID METHOD FOR CHARACTERISTICS FINITE-ELEMENT SOLUTION OF 2D NONLINEAR CONVECTION-DOMINATED DIFFUSION PROBLEM

For two-dimension nonlinear convection diffusion equation, a two-grid method of characteristics finite-element solution was constructed. In this method the nonlinear iterations is only to execute on the coarse grid and the fine-grid solution can be obtained in a single linear step. For the nonlinear convection-dominated diffusion equation, this method can not only stabilize the numerical oscillation but also accelerate the convergence and improve the computational efficiency. The error analysis demonstrates if the mesh sizes between coarse-grid and fine-grid satisfy the certain relationship, the two-grid solution and the characteristics finite-element solution have the same order of accuracy. The numerical is more efficient than that of characteristics example confirms that the two-grid method finite-element method.

Big Model Strategy for Bridge Structural Health Monitoring Based on Data-Driven, Adaptive Method and Convolutional Neural Network (CNN) Group

This study introduces an innovative“Big Model”strategy to enhance Bridge Structural Health Monitoring(SHM)using a Convolutional Neural Network(CNN),time-frequency analysis,and fine element analysis.Leveraging ensemble methods,collaborative learning,and distributed computing,the approach effectively manages the complexity and scale of large-scale bridge data.The CNN employs transfer learning,fine-tuning,and continuous monitoring to optimize models for adaptive and accurate structural health assessments,focusing on extracting meaningful features through time-frequency analysis.By integrating Finite Element Analysis,time-frequency analysis,and CNNs,the strategy provides a comprehensive understanding of bridge health.Utilizing diverse sensor data,sophisticated feature extraction,and advanced CNN architecture,the model is optimized through rigorous preprocessing and hyperparameter tuning.This approach significantly enhances the ability to make accurate predictions,monitor structural health,and support proactive maintenance practices,thereby ensuring the safety and longevity of critical infrastructure.

Study on spline wavelet finite-element method in multi-scale analysis for foundation

A new finite element method （FEM） of B-spline wavelet on the interval （BSWI） is proposed. Through analyzing the scaling functions of BSWI in one dimension, the basic formula for 2D FEM of BSWI is deduced. The 2D FEM of 7 nodes and 10 nodes are constructed based on the basic formula. Using these proposed elements, the multiscale numerical model for foundation subjected to harmonic periodic load, the foundation model excited by external and internal dynamic load are studied. The results show the pro- posed finite elements have higher precision than the tradi- tional elements with 4 nodes. The proposed finite elements can describe the propagation of stress waves well whenever the foundation model excited by extemal or intemal dynamic load. The proposed finite elements can be also used to con- nect the multi-scale elements. And the proposed finite elements also have high precision to make multi-scale analysis for structure.

A Mixed Finite-Element Method on Polytopal Mesh

In this paper,we introduce new stable mixed finite elements of any order on polytopal mesh for solving second-order elliptic problem.We establish optimal order error estimates for velocity and super convergence for pressure.Numerical experiments are conducted for our mixed elements of different orders on 2D and 3D spaces that confirm the theory.

基于SPH-FEM方法的舷侧与冰山碰撞结构响应

传统的有限元数值仿真对于研究高速碰撞大变形等问题具有一定的局限性,建立一套基于光滑粒子流体动力学(SPH)的水介质中小型冰山与船舶舷侧碰撞数值模拟方法,验证SPH模拟冰材料与船-水-冰耦合的合理性,对不同舷侧部位与不同冰山碰撞工况进行数值模拟,分析碰撞形状、面积和速度等对舷侧结构的应力、应变、结构损伤等的影响规律。研究表明,提出的冰山与舷侧碰撞数值模拟方法具有较高的计算精度,对冰山-船舶碰撞的研究具有重要的参考价值。

基于SPH-FEM方法的地下结构侵彻爆炸数值模拟研究

为了提高地下防护工程生存能力,需准确考虑侵彻和爆炸连续作用对结构的毁伤。通过SPH-FEM耦合数值模拟方法,模拟分析了地下结构侵彻爆炸全过程,有效解决了传统有限元方法侵爆近区高烈度、大变形模拟难题。根据经验公式验证了模型的有效性。研究结果表明:侵彻弹体对岩体具有封堵作用,增强了毁伤效应,SPH算法弥补了侵蚀算法对侵彻爆炸过程的侵彻孔卸荷缺陷,更准确模拟了侵彻爆炸的联合作用;结构中地板与直墙分离浇筑,可以减少结构损伤;拱顶、拱肩和拱脚为侵彻爆炸作用下直墙拱结构的薄弱部位。

基于BIM精细设计模型融合FEM的铁路高边坡稳定性分析

为拓展BIM技术全生命周期的应用、提高铁路高边坡稳定性分析精度以及实现精细化设计,基于BIM对边坡稳定性分析流程与方法进行优化。通过理论分析、软件开发、数值计算分析等手段开展研究,对比分析边坡三维模型在BIM软件及有限元软件中的表达特征,使用Revit Api及Dynamo.dll进行高边坡三维设计及模型转换程序开发,提出一套基于ACIS内核以及模型关键信息提取相融合的BIM模型与有限元模型转换方法;进一步总结出基于精细化BIM模型融合有限元强度折减法的边坡工程三维设计模型创建与稳定性检算方法,并针对怀化西编组站高边坡进行实例研究,基于强度折减法进行高边坡三维与二维稳定性计算。结果表明,上述方法实现了基于BIM与FEM的边坡稳定性融合分析,三维计算结果相比与二维计算偏安全,高边坡各阶段稳定性系数均大于1.30,边坡处于稳定状态。研究结论:基于ACIS内核以及模型关键信息提取相融合的方法可实现BIM模型向有限元模型的精确转换;基于BIM模型的边坡三维稳定性检算,可有效减少有限元分析前处理时间,并提升有限元分析模型的准确性。

FFT-Based Numerical Method for Nonlinear Elastic

In theoretical research pertaining to sealing, a contact model must be used to obtain the leakage channel. However, for elastoplastic contact, current numerical methods require a long calculation time. Hyperelastic contact is typically simplifed to a linear elastic contact problem, which must be improved in terms of calculation accuracy. Based on the fast Fourier transform, a numerical method suitable for elastoplastic and hyperelastic frictionless contact that can be used for solving two-dimensional and three-dimensional (3D) contact problems is proposed herein. The nonlinear elastic contact problem is converted into a linear elastic contact problem considering residual deformation (or the equivalent residual deformation). Results from numerical simulations for elastic, elastoplastic, and hyperelastic contact between a hemisphere and a rigid plane are compared with those obtained using the fnite element method to verify the accuracy of the numerical method. Compared with the existing elastoplastic contact numerical methods, the proposed method achieves a higher calculation efciency while ensuring a certain calculation accuracy (i.e., the pressure error does not exceed 15%, whereas the calculation time does not exceed 10 min in a 64 × 64 grid). For hyperelastic contact, the proposed method reduces the dependence of the approximation result on the load, as in a linear elastic approximation. Finally, using the sealing application as an example, the contact and leakage rates between complicated 3D rough surfaces are calculated. Despite a certain error, the simplifed numerical method yields a better approximation result than the linear elastic contact approximation. Additionally, the result can be used as fast solutions in engineering applications.

MPS-FEM Coupled Method for Study of Wave-Structure Interaction

Nowadays,an increasing number of ships and marine structures are manufactured and inevitably operated in rough sea.As a result,some phenomena related to the violent fluid-elastic structure interactions(e.g.,hydrodynamic slamming on marine vessels,tsunami impact on onshore structures,and sloshing in liquid containers)have aroused huge challenges to ocean engineering fields.In this paper,the moving particle semi-implicit(MPS)method and finite element method(FEM)coupled method is proposed for use in numerical investigations of the interaction between a regular wave and a horizontal suspended structure.The fluid domain calculated by the MPS method is dispersed into fluid particles,and the structure domain solved by the FEM method is dispersed into beam elements.The generation of the 2D regular wave is firstly conducted,and convergence verification is performed to determine appropriate particle spacing for the simulation.Next,the regular wave interacting with a rigid structure is initially performed and verified through the comparison with the laboratory experiments.By verification,the MPS-FEM coupled method can be applied to fluid-structure interaction(FSI)problems with waves.On this basis,taking the flexibility of structure into consideration,the elastic dynamic response of the structure subjected to the wave slamming is investigated,including the evolutions of the free surface,the variation of the wave impact pressures,the velocity distribution,and the structural deformation response.By comparison with the rigid case,the effects of the structural flexibility on wave-elastic structure interaction can be obtained.

Tensile reliability analysis for gravity dam foundation surface based on FEM and response surface method

In this study, the limit state equation for tensile reliability analysis of the foundation surface of a gravity dam was established. The possible crack length was set as the action effect and allowable crack length was set as the resistance in the limit state. The nonlinear FEM was used to obtain the crack length of the foundation surface of the gravity dam, and the linear response surface method based on the orthogonal test design method was used to calculate the reliability, providing a reasonable and simple method for calculating the reliability of the serviceability limit state. The Longtan RCC gravity dam was chosen as an example. An orthogonal test, including eleven factors and two levels, was conducted, and the tensile reliability was calculated. The analysis shows that this method is reasonable.