自然元与无限元耦合方法在岩土工程粘弹性分析中的应用

自然单元法是一种新的偏微分方程数值解法,由于其位移插值函数采用无网格的方式构造且形函数满足插值性质,从而克服传统有限元方法对单元网格信息的依赖,大大简化数值计算的前处理过程,同时又能像有限元那样准确施加边界条件,在岩土工程中具有广阔的应用前景;介绍了自然元与无限元的基本原理,针对在处理岩土工程无限域或半无限域问题时需要人为确定边界条件而带来计算误差的问题,引入无限元模拟无穷远处边界条件,与自然元相结合形成耦合分析方法;并根据粘弹性理论,采用Laplace插值,编制了基于自然元与无限元耦合方法的二维粘弹性分析程序,通过算例验证了算法的正确性,结果也表明相对于纯自然单元法,耦合方法能够显著提高分析结果的精度,在此基础上拓展了自然单元法在岩土工程中的应用范围.     

基于多边形比例边界有限元的复合材料裂纹扩展模拟

该文采用近年提出的多边形比例边界有限元(Polygon Scaled Boundary Finite Elements,PSBFE),结合基于拓扑的局部网格重剖分方法,首次模拟了层状复合材料交界面、不同弹性模量的圆形夹杂对复合材料裂纹扩展的影响。结果表明,该文方法可以有效模拟复合材料的裂纹扩展,算例的结果同现有文献的实验数据和数值模拟结果吻合良好,采用不同网格密度和不同裂纹扩展步长对计算结果影响不大。基于SBFEM的PSBFE可以半解析求解裂纹尖端应力奇异性,具有比FEM更高的精度。另一方面,同现有基于SBFEM的裂纹扩展方法相比,基于拓扑的局部网格重剖分的PSBFE可以处理任意复杂的二维模型,具有更好的通用性。     

岩土软化行为的网格依赖性问题研究

岩土工程中常出现软化行为,传统的弹塑性有限元计算软化行为的剪切带问题会出现网格依赖性。该文引入偶应力弹塑性理论,详细推导了Drucker-Prager屈服准则下的偶应力增量有限元框架,采用可通过C0―1分片检验的RCT9+RT9单元,并通过UEL用户子程序将该单元加入到大型有限元软件ABAQUS中。算例表明:偶应力理论可以消除网格依赖性,为解决岩土软化问题提供了一条有效的途径。     

基于六面体单元的流线可视化点定位研究

流线是CFD矢量场可视化的重要技术。针对不规则结构化网格的三维定常矢量场数据，对流线可视化技术进行研究。重点针对基于六面体单元网格的数值积分方法生成流线技术中的一个难点——点定位问题，分析了影响算法精度的两个重要原因——对单元Jacobian矩阵的近似，以及网格单元几何结构与拓扑结构的不一致性。最后，提出了基于六面体单元的改进方法。     

基于谱单元方法的平板冲击流固耦合研究

假设流体无粘且无旋,计及流体中的气穴现象,采用谱单元方法建立水下爆炸瞬态流固耦合的三维数值模型,探讨了水下爆炸瞬态流固耦合作用的机理,用经典的平板冲击问题对数值模型进行验证,数值结果与解析解吻合良好,并根据数值结果绘制了流体中的气穴区域,对气穴效应进行分析,分析显示,气穴效应会对结构响应产生很大影响,在计算中应予以考虑。基于本文建立的数值模型,在不同网格细化的条件下,分别采用谱单元方法和有限元方法对弹簧——平板模型进行水下爆炸瞬态流固耦合问题的求解,并在此基础上对谱单元方法和有限元方法进行对比研究,研究发现,谱单元方法在提高精度的同时能大量节省计算时间,可较好地应用于水下爆炸流固耦合问题的求解中。本文旨在为相关水下爆炸瞬态流固耦合的研究提供参考。     

六面体单元体积坐标方法

基于二维问题四边形单元面积坐标法的成功思路,建立了三维六面体单元体积坐标的系统方法,包括:1)六面体单元特征参数的定义及单元退化模式研究;2)六面体单元体积坐标定义;3)六面体单元的体积坐标与直角坐标、等参坐标之间的关系;4)六面体体积坐标的微分公式。可以看到,六面体体积坐标保持了局部自然坐标的优点,并且与直角坐标始终保持线性关系。它为构造对网格畸变不敏感的新型六面体有限元模型提供了新工具。     

预报振动噪声的径向基点插值无网格与无限元耦合方法

为克服传统的有限元耦合无限元方法中的单元匹配问题,研究了径向基点插值法和无限元法的耦合规律,提出了一种预报无限域结构振动噪声的径向基点插值无网格与可变阶无限声波包络单元耦合方法,推导了预报声压的计算公式。为提高声场预报精度和满足声波在无限域的自由衰减,结构外部无限声场分为使用无网格表示的近场和可变阶声波包络单元离散的远场。在该耦合方法中,通过在近场与远场之间的交界面上配置虚拟网格来构造具有连续性的声压形函数,确保了声压的连续与一致性。采用数值仿真和试验对该耦合方法进行了验证,结果表明该耦合方法拥有无网格法的高精度和可变阶声波包络单元法满足声波自由衰减的特点,具有良好的精度和收敛性,可用于实际噪声预报。     

连续—非连续结构应力分析现状与进展

对工程结构应力分析中采用的连续介质模型、非连续介质模型、连续——非连续介质力学模型作了系统介绍。三种模型物理数值模拟的各种理论及数值方法,代表了当今结构应力分析的主流及发展方向。随着工程建设中高、大、精、新结构的出现,表明这个古老而又崭新的命题仍有无限广泛的发展前景。从七个方面论述了它的现状及发展特征:从过时观到现代新观念;从连续到非连续;从精确到数值近似;从有限元到无单元;从单一到统一;从标量无网格到复变量无网格;从独立到耦合,全面介绍了其内容和方法。     

有限元新型自然坐标方法研究进展

网格畸变敏感问题一直是当前有限元法难以解决的问题,而新型自然坐标方法的诞生可以在一定程度上对解决这个难题有所帮助。该文介绍了有限元新型自然坐标方法研究的新近进展。包括第一类四边形面积坐标及其应用(单元构造,解析刚度矩阵的建立,以及在几何非线性问题中的应用等);第二类四边形面积坐标及其应用;六面体体积坐标及其应用。数值算例表明:无论网格如何扭曲畸变,这些基于新型自然坐标方法的有限元模型仍然保持高精度,对网格畸变不敏感。这显示了新型自然坐标方法是构造高性能单元模型的有效工具。     

基于黏聚单元法的冰-柱碰撞流固耦合计算方法研究

在采用黏聚单元法模拟海洋结构物与海冰的相互作用过程中，大多未考虑水的作用，与实际应用场景不符。基于LS-DYNA有限元软件，构建两种不同厚度的黏聚单元冰模型，采用S-ALE流固耦合方法，对圆柱体直立结构与层冰碰撞进行了数值模拟，研究了碰撞过程中层冰的破坏模式及柱体所受冰载荷，数值模拟结果与实际观测现象相吻合。随后分析了流场网格大小对耦合效果及冰载荷的影响。结果表明：柱体所受冰载荷与流场网格呈正相关，当流场网格为冰体单元的2倍时，计算时间及耦合效果最佳。     

Dynamic soil–structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/scaled boundary finite element model

In this paper, a coupled model based on finite element method (FEM), boundary element method (BEM) and scaled boundary FEM (SBFEM) (also referred to as the consistent infinitesimal finite element cell method) for dynamic response of 2D structures resting on layered soil media is presented. The SBFEM proposed by Wolf and Song (Finite‐element Modelling of Unbounded Media. Wiley: England, 1996) and BEM are used for modelling the dynamic response of the unbounded media (far‐field). The standard FEM is used for modelling the finite region (near‐field) and the structure. In SBFEM, which is a semi‐analytical technique, the radiation condition at infinity is satisfied exactly without requiring the fundamental solution. This method, also eliminates the need for the discretization of interfaces between different layers. In both SBFEM and BEM, the spatial dimension is decreased by one. The objective of the development of this coupled model is to combine advantages of above‐mentioned three numerical models to solve various soil–structure interaction (SSI) problems efficiently and effectively. These three methods are coupled (FE–BE–SBFEM) via substructuring method, and a computer programme is developed for the harmonic analyses of SSI systems. The coupled model is established in such a way that, depending upon the problem and far‐field properties, one can choose BEM and/or SBFEM in modelling related far‐field region(s). Thus, BEM and/or SBFEM can be used efficiently in modelling the far‐field. The proposed model is applied to investigate dynamic response of rigid and elastic structures resting on layered soil media. To assess the proposed SSI model, several problems existing in the literature are chosen and analysed. The results of the proposed model agree with the results presented in the literature for the chosen problems. The advantages of the model are demonstrated through these comparisons. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling cohesive crack growth using a two-step finite element-scaled boundary finite element coupled method

A two-step method, coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM), is developed in this paper for modelling cohesive crack growth in quasi-brittle normal-sized structures such as concrete beams. In the first step, the crack trajectory is fully automatically predicted by a recently-developed simple remeshing procedure using the SBFEM based on the linear elastic fracture mechanics theory. In the second step, interfacial finite elements with tension-softening constitutive laws are inserted into the crack path to model gradual energy dissipation in the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the proposed method. The numerical results demonstrate that this two-step SBFEM-FEM coupled method can predict both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for crack growth problems with strong snap-back phenomenon. The effects of the tensile strength, the mode-I and mode-II fracture energies on the predicted load-displacement relations are also discussed.     

SPH and FEM Investigation of Hydrodynamic Impact Problems

Simulation of hydrodynamic impact problems and its effect on surrounding structures, can be considered as a fluid structure coupling problem. The application is mainly used in automotive and aerospace engineering and also in civil engineering. Classical FEM and Finite Volume methods were the main formulations used by engineers to solve these problems. For the last decades, new formulations have been developed for fluid structure coupling applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic) and DEM (Discrete Element Method). Up to these days very little has been done to compare different methods and assess which one would be more suitable. In this paper the mathematical and numerical implementation of the FEM and SPH formulations for hydrodynamic problem are described. From different simulations, it has been observed that for the SPH method to provide similar results as FEM Lagrangian formulations, the SPH meshing, or SPH particle spacing needs to be finer than FEM mesh. To validate the statement, we perform a simulation of a hydrodynamic impact on an elasto-plastic plate structure. For this simple, the particle spacing of SPH method needs to be at least two times finer than FEM mesh. A contact algorithm is performed at the fluid structure interface for both SPH and FEM formulations. In the paper the efficiency and usefulness of two methods, often used in numerical simulations, are compared.     

An elastostatic FEM/BEM analysis of vertically loaded raft and piled raft foundation

In this paper, a static analysis of vertically loaded raft and piled raft foundations in smooth and continuous contact with the supporting soil is presented. In this approach the finite element method (FEM) and the boundary element method (BEM) are coupled: the bending plate is assumed to have linear elastic properties and is modelled by FEM while the soil is considered as an elastic half-space in the BEM. The pile is represented by a single element and the shear force along the shaft is interpolated by a quadratic function. The plate–soil interface is divided into triangular boundary elements (soil) also called cells and finite elements (plate) and the subgrade reaction is linearly interpolated across each cell. The subgrade tractions are eliminated from the FEM and BEM algebraic systems of equations, resulting in the governing system of equations for plate–pile–soil interaction problems. Numerical results are presented and they are close to those resulting from much more elaborate analyses.     

A coupled FEM-MFS method for the vibro-acoustic simulation of laminated poro-elastic shells

A new simulation method for the vibro-acoustic simulation of poro-elastic shells is presented. The proposed methods can be used to investigate arbitrary curved layered panels, as well as their interaction with the surrounding air. We employ a high-order finite element method (FEM) for the discretization of the shell structure. We assume that the shell geometry is given parametrically or implicitly. For both cases the exact geometry is used in the simulation. In order to discretize the fluid surrounding the structure, a variational variant of the method of fundamental solutions (MFS) is developed. Thus, the meshing of the fluid domain can be avoided and in the case of unbounded domains the Sommerfeld radiation condition is fulfilled. In order to simulate coupled fluid-structure interaction problems, the FEM and the MFS are combined to a coupled method. The implementation of the uncoupled FEM for the shell and the uncoupled MFS is verified against numerical examples based on the method of manufactured solutions. For the verification of the coupled method an example with a known exact solution is considered. In order to show the potential of the method sound transmission from cavities to exterior half-spaces is simulated.     

高温后HSC粘结滑移基础参数测量与3D有限元数值模拟

通过自行设计的装置测量了高温后粘结问题中的化学胶结力和摩擦系数,得出了它们随温度经历的变化规律。利用测得的基础参数定义了钢筋与混凝土界面的弹塑性库仑摩擦准则并将其植入有限元模型;采用面-面接触的接触单元模拟混凝土与钢筋界面的力学行为。模型通过对钢筋肋的显式离散实现了钢筋肋与混凝土间机械咬合作用的模拟。数值结果和试验数据的对比表明,该文提出的模型可以较好的模拟高温后带肋钢筋和混凝土之间的粘结滑移。最后,利用有限元模型对400℃温度经历拔出过程中的应力分布及裂缝的扩展进行了细致的研究。     

A coupled analysis method for structures with independently modelled finite element subdomains

A new method for analysing plate and shell structures with two or more independently modelled finite element subdomains is presented, assessed, and demonstrated. This method provides a means of coupling local and global finite element models whose nodes do not coincide along their common interface. In general, the method provides a means of coupling structural components (e.g., wing and fuselage) which may have been modelled by different analysts. In both cases, the need for transition modelling, which is often tedious and complicated, is eliminated. The coupling is accomplished through an interface for which three formulations are considered and presented. These formulations are: collocation, discrete least-squares, and hybrid variational. Several benchmark problems are analysed and it is shown that the hybrid variational formulation provides the most accurate solutions.     

A mesh-free approach for fracture modelling of gravity dams under earthquake

Fracture is a major cause of failure for concrete gravity dams. This can result in the large-scale loss of human lives and enormous economic consequences. Numerical modelling can play a crucial role in understanding and predicting complex fracture processes, providing useful input to fracture-resistant designs. In this paper, the use of a mesh-free particle method called smoothed particle hydrodynamics (SPH) for modelling of gravity dam failure subject to fluctuating dynamic earthquake loads is explored. The structural response of the Koyna dam is analysed with the base of the dam being subjected to high-intensity periodic ground excitations. The SPH prediction of the crack initiation location and propagation pattern is found to be consistent with existing FEM predictions and experimental results from physical models. The transient stress field and the resulting damage evolution in the dam structure were monitored. The amplitude and frequency of the ground excitation is shown to have considerable influence on the fracture pattern and the associated energy dissipation. The fluctuations in the kinetic energy of the dam wall and its fragments are found to vary with different frequencies and amplitudes as the structure undergoes progressive fracture. The dynamic responses and the fracture patterns predicted establish the strong potential of SPH for fracture modelling of dams and similar large structures.     

Adaptive modeling of damage growth using a coupled FEM/BEM approach

We propose a coupled boundary element method (BEM) and a finite element method (FEM) for modelling localized damage growth in structures. BEM offers the flexibility of modelling large domains efficiently, while the non‐linear damage growth is accurately accounted by a local FEM mesh. An integral‐type nonlocal continuum damage mechanics with adapting FEM mesh is used to model multiple damage zones and follow their propagation in the structure. Strong form coupling, BEM hosted, is achieved using Lagrange multipliers. Because the non‐linearity is isolated in the FEM part of the system of equations, the system size is reduced using Schur complement approach, then the solution is obtained by a monolithic Newton method that is used to solve both domains simultaneously. The coupled BEM/FEM approach is verified by a set of convergence studies, where the reference solution is obtained by a fine FEM. In addition, the method is applied to multiple fractures growth benchmark problems and shows good agreement with the literature. Copyright © 2015 John Wiley & Sons, Ltd.