率相关饱和多孔介质动力响应的数值分析

在基于混合物理论的多孔介质模型的基础上,将固体相视为弹粘塑性体,建立了饱和多孔介质的弹粘塑性模型。模型的基本思想是在无粘弹塑性本构关系中引入-时间参数,使固体骨架具备了粘性效应。利用Galerkin加权残值法推导得到了罚有限元格式,并采用Newmark预估校正法求解率相关饱和多孔介质的非线性有限元动力方程,此算法可以很...     

刚／粘塑性梁的强迫振动

本文依据粘塑性梁强迫振动的非齐次方程与非线性本构方程,提出采用分离变量的位移方法求解,获得该问题的应力和位移解.     

非结构网格上多介质可压缩流模拟的RKDG方法

针对一般方法模拟具有运动界面的多介质可压缩流动问题计算量大、实施复杂的缺点,本文发展了一种基于非结构网格的数值模拟方法.该方法采用RKDG(RungeKutta Discontinuous Galerkin)方法的弱形式求解Euler方程,用强形式求解可压缩流场模拟中的Level Set方程,并用Simple Fix方法耦合两套方程的数值求解.二维多介质可压缩流的模拟表明:该方法成功地抑制了界面附近的非物理振荡,计算量小、实施简单,并可有效求解具有运动界面的多介质可压缩流动问题.     

非等温粘弹流体平板收缩流的数值模拟

基于线性PTT本构模型对非等温粘弹流体4∶1平板收缩流进行了模拟,其中分子松弛时间、聚合物黏度与温度的依赖关系通过WLF公式描述。控制方程采用同位网格有限体积法求解,速度-压力以及速度-应力间的耦合采用动量插值技术处理。文中给出了不同We数下粘弹流体等温和非等温情况下流场和应力场的变化情况,分析了温度对流场和应力场的影响,考察了Pe数、We数以及能量方程中参数k对温度场的影响。     

基于不可逆内变量热力学的岩石材料粘弹-粘塑性本构方程

岩石材料的粘弹性和粘塑性变形是与时间相关的能量耗散行为。在Rice不可逆内变量热力学框架下,引入两组内变量分别用来描述在粘弹性和粘塑性变形过程中材料的内部结构调整。通过给定比余能的具体形式和内变量的演化方程,推导出内变量粘弹-粘塑性本构方程。粘弹性本构方程具有普遍性,能涵盖Kelvin-Voigt和Poynting-Thomson在内的经典粘弹性模型的本构方程。并指出热力学力与应力呈线性关系是组合元件模型为线性模型的根本原因。粘塑性本构方程能较好地刻画岩石材料在粘塑性变形过程中的硬化现象。对模拟岩石的模型相似材料进行单轴加卸载蠕变试验,将蠕变过程中的粘弹性和粘塑性变形分离并根据试验数据对本构方程的材料参数进行辨识。试验数据和理论曲线对比结果表明该文提出的本构方程能很好地模拟材料的蠕变行为。该类型的本构方程能为岩石工程的长期稳定性的预测、评价以及加固分析提供基础。     

平板收缩流的对数构象模拟?

本文采用对数构象方法,结合同位网格有限体积离散,对由 Oldroyd-B 本构模型描述的粘弹性流体流动的高 We 数问题(High Weissenberg Number Problem, HWNP)进行了研究,对等温不可压条件下的平面 Poiseuille 流和4:1平板收缩流进行了数值模拟.平面 Poiseuille 流在不同 We 数时的数值结果验证了对数构象方法在简单流动中的有效性.在4:1粘弹性收缩流的数值模拟中,对数构象方法和传统方法在低 We 数时流场中的流线、应力等的对比结果验证了对数构象方法在复杂流动中的有效性.高 We 数时的数值结果表明:对于 Oldroyd-B 模型,对数构象方法可提高求解时的稳定性,并可将临界 We 数由传统方法的2.5提高到5.0.     

层叠流道流场粒子示踪的数值模拟

采用Bird-Carreau本构方程,建立了层叠流道聚合物熔体流动的三维粘弹数值模型,运用有限元法,对示踪粒子在层叠流道中的运动轨迹进行数值模拟,分析工艺参数和流道结构参数对示踪粒子在层叠流道中运动轨迹的影响。并根据分析结果对工艺参数和流道结构参数进行了优化。模拟结果表明,示踪粒子的运动轨迹与理想运动轨迹的偏移值随着入口体积流率(Q)的增大而增大,随着流道水平流程长(L)和流道入口面长宽比(K)的增大而减小。此外,与优化前的层叠流道模型相比,示踪粒子在优化后的层叠流道中流动时产生的偏移值更小。     

非线性Burgers方程求解的自适应Euler-Lagrange无单元Galerkin方法

建立了求解非线性Burgers方程的自适应Euler-Lagrange无单元Galerkin(adaptiveEuler-Lagrange element-free Galerkin,AELEFG)方法.该方法将Euler形式的非线性Burgers方程转化成Lagrange形式的纯扩散方程,使用节点自适应无单元Galerkin(element-free Galerkin,EFG)方法求解该扩散方程,并沿特征路径反向追踪对对流项进行处理.数值结果表明,运用AELEFG方法求解非线性Burgers方程具有较高的精度及稳定性.     

粘弹-塑性海冰动力学本构模型中的Drucker-Prager屈服准则

针对中小尺度下海冰动力作用过程中的漂移和堆积特征,在粘弹-塑性海冰动力学本构模型中引入了Drucker-Prager(D-P)屈服准则。该模型在海冰屈服前采用Kelvin-Vogit粘弹模型,屈服后采用相关联的正则流动法则。采用该模型对规则海区内的海冰堆积过程进行了数值试验,计算的海冰堆积高度与其解析解一致。另外,在对渤海海冰动力过程中的海冰厚度、密集度、速度以及冰内应力进行的48小时数值模拟中,计算的冰厚分布与卫星遥感资料相符合。基于D-P准则的计算结果与Mohr-Coulomb(M-C)准则的结果相一致,但D-P准则克服了M-C准则计算塑性应力时的奇异现象,进而简化了计算过程。在以上数值模拟中,均采用了光滑质点动力学计算方法。以上数值计算均验证了基于D-P屈服准则的粘弹-塑性本构模型在海冰动力学中的可靠性。     

对流-扩散-反应方程的变分多尺度解法

根据变分多尺度的思想求解了对流项和反应项占优的对流-扩散-反应方程.在变分多尺度思想的理论框架内,推导了附加于Galerkin变分弱形式的稳定化结构和具体的稳定化系数;阐述了这种稳定化结构和经典的SUPG稳定化结构之间的关系;数值算例表明,该稳定化系数可以适应均匀和非均匀的计算网格.通过网格的恰当加密,变分多尺度方法消除了算例中的数值伪振荡.     

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

A Mixed Finite Element (MFE) method for 3D non-steady flow of a viscoelastic compressible fluid is presented. It was used to compute polymer injection flows in a complex mold cavity, which involves moving free surfaces. The flow equations were derived from the Navier-Stokes incompressible equations, and we extended a mixed finite element method for incompressible viscous flow to account for compressibility (using the Tait model) and viscoelasticity (using a Pom-Pom like model). The flow solver uses tetrahedral elements and a mixed velocity/pressure/extra-stress/density formulation, where elastic terms are solved by decoupling our system and density variation is implicitly considered. A new DEVSS-like method is also introduced naturally from the MINI-element formulation. This method has the great advantage of a low memory requirement. At each time slab, once the velocity has been calculated, all evolution equations (free surface and material evolution) are solved by a space-time finite element method. This method is a generalization of the discontinuous Galerkin method, that shows a strong robustness with respect to both re-entrant corners and flow front singularities. Validation tests of the viscoelastic and free surface models implementation are shown, using literature benchmark examples. Results obtained in industrial 3D geometries underline the robustness and the efficiency of the proposed methods.     

An element‐free method for in‐plane notch problems with anisotropic materials

This study developed an element‐free Galerkin method (EFGM) to simulate notched anisotropic plates containing stress singularities at the notch tip. Two‐dimensional theoretical complex displacement functions are first deduced into the moving least‐squares interpolation. The interpolation functions and their derivatives are then determined to calculate the nodal stiffness using the Galerkin method. In the numerical validation, an interface layer of the EFGM is used to combine the mesh between the traditional finite elements and the proposed singular notch EFGM. The H‐integral determined from finite element analyses with a very fine mesh is used to validate the numerical results of the proposed method. The comparisons indicate that the proposed method obtains more accurate results for the displacement, stress, and energy fields than those determined from the standard finite element method. Copyright © 2013 John Wiley & Sons, Ltd.     

An explicit finite volume method for viscoelastic fluid flows

We discuss a finite volume method for computing solutions of steady incompressible viscoelastic fluid flows. A fourth-order Runge-Kutta method is used in the explicit time-stepping scheme. The computations are carried out mainly on unstructured grids on Newtonian, inelastic and differential-type constitutive equations, which include the Oldroyd-B and the upper-convected Maxwell models. The performance of the scheme on unstructured grids is investigated, with particular reference to the stick-slip problem for the modified upper-convected Maxwell fluid. The results are compared with those obtained by using the finite element method whenever possible.This research was supported by the Australian Research Council (ARC).     

Finite elements in space and time for generalized viscoelastic maxwell model

 The generalization of a new numerical approach with simultaneous space–time finite element discretization for viscoelastic problems developed in the papers by Buch et al. (1999) and Idesman et al. (2000) is presented for the case of the generalized viscoelastic Maxwell model. New non-symmetric variational and discretized formulations are derived using the continuous Galerkin method (CGM) and discontinuous Galerkin method (DGM). Viscoelastic behaviour described by the generalized Maxwell model is represented by means of internal variables. It allows to use only differential equations for the constitutive equations instead of integrodifferential ones. The variational formulation reduces to two types of equations with total displacements and internal displacements (internal variables) as unknowns, namely to the equilibrium equation and the evolution equations for the internal displacements which are fulfilled in the weak form. Using continuous test functions in space and time, a continuous space–time finite element formulation is obtained with simultaneous discretization in space and time. Subdividing the total observation time interval into appropriate time slabs and introducing discontinuous trial functions, being continuous within time slabs and allowing jumps across time interfaces, a more general discontinuous finite element formulation is obtained. The difference between these two formulations for one time slab consists in the satisfaction of initial conditions which are fulfilled exactly for the continuous formulation and in a weak form for the discontinuous case. The proposed approach has some very attractive advantages with respect to semidiscretization methods, regarding the possibility of adaptive space–time refinements and efficient parallel processing on MIMD-parallel computers. The considered numerical examples show the effectiveness of simultaneous space–time finite element calculations and a high convergence rate for adaptive refinement. Numerical efficiency is an advantage of DGM in comparison with CGM for discontinuously changing (e.g. piecewise constant) boundary conditions in time and for solutions with high gradients. Received 7 February 2000     

A numerical integration approach for fractional-order viscoelastic analysis of hereditary-aging structures

In this paper, a novel numerical integration scheme is proposed for fractional-order viscoelastic analysis of hereditary-aging structures. More precisely, the idea of aging is first introduced through a new phenomenological viscoelastic model characterized by variable-order fractional operators. Then, the presented fractional-order viscoelastic model is included in a variational formulation, conceived for any viscous kernel and discretized in time by employing a discontinuous Galerkin method. The accuracy of the resulting finite element (FE) scheme is analyzed through a model problem, whose exact solution is known; and the most significant variables affecting the solution quality, such as the number of Gaussian quadrature points and time subintervals, are then investigated in terms of error and computational cost. Moreover, the proposed FE integration scheme is applied to study the short- and long-term behavior of concrete structures, which, due to the severe aging exhibited during their service life, represents one of the most challenging time-dependent behavior to be investigated. Eventually, also the Euler implicit method, commonly used in commercial software, is compared.     

A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non‐linear solids and saturated porous media

A time‐discontinuous Galerkin finite element method (DGFEM) for dynamics and wave propagation in non‐linear solids and saturated porous media is presented. The main distinct characteristic of the proposed DGFEM is that the specific P3–P1 interpolation approximation, which uses piecewise cubic (Hermite's polynomial) and linear interpolations for both displacements and velocities, in the time domain is particularly proposed. Consequently, continuity of the displacement vector at each discrete time instant is exactly ensured, whereas discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously saved, particularly in the materially non‐linear problems, as compared with that required for the existing DGFEM. Both the implicit and explicit algorithms are developed to solve the derived formulations for linear and materially non‐linear problems. Numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and in providing much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain. Copyright © 2003 John Wiley & Sons, Ltd.     

A temporal stable node-based smoothed finite element method for three-dimensional elasticity problems

A stabilized node-based smoothed finite element method (sNS-FEM) is formulated for three-dimensional (3-D) elastic-static analysis and free vibration analysis. In this method, shape functions are generated using finite element method by adopting four-node tetrahedron element. The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are used to perform the smoothing operation and the numerical integration. The stabilization term for 3-D problems is worked out, and then propose a strain energy based empirical rule to confirm the stabilization parameter in the formula. The accuracy and stability of the sNS-FEM solution are studied through detailed analyses of benchmark cases and actual elastic problems. In elastic-static analysis, it is found that sNS-FEM can provide higher accuracy in displacement and reach smoother stress results than the reference approaches do. And in free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that sNS-FEM solution strengths the original relatively soft node-based smoothed finite element method (NS-FEM), and the natural frequency values provided by sNS-FEM are confirmed to be far more accurate than results given by traditional methods. Thus, the feasibility, accuracy and stability of sNS-FEM applied on 3-D solid are well represented and clarified.     

On the computation of steady‐state compressible flows using a discontinuous Galerkin method

Computation of compressible steady‐state flows using a high‐order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics‐based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low‐storage p‐multigrid method is used for solving the governing compressible Euler equations to obtain steady‐state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady‐state flows. Copyright © 2007 John Wiley & Sons, Ltd.     

Phase‐field modelling of solidification microstructure formation using the discontinuous finite element method

This paper presents a discontinuous Galerkin finite element computational methodology for solving the coupled phase‐field and heat diffusion equations to predict the microstructure evolution during solidification. The phase‐field modelling of microstructure formation is briefly discussed. The discontinuous Galerkin finite element formulation for the phase‐field model systems for solidification microstructure formation is described in detail. Numerical stability is performed using the Neumann method. The accuracy of the discontinuous model is verified by the analytic solution of a simple 1‐D solidification problem. Numerical calculations using the discontinuous finite element phase‐field model have been performed for simulating the complex 2‐D and 3‐D dendrite structures formed in supercooled melts and the results are compared well with those in literature using the finite difference methods. Parallel computing algorithm is presented and results show that the minimization of the intercommunication between microprocessors is the key to increase the effectiveness in parallel computing with the discontinuous finite element phase‐field model for solidification microstructure formation. Copyright © 2006 John Wiley & Sons, Ltd.     

A general discontinuous Galerkin method for finite hyperelasticity. Formulation and numerical applications

A discontinuous Galerkin formulation of the boundary value problem of finite‐deformation elasticity is presented. The primary purpose is to establish a discontinuous Galerkin framework for large deformations of solids in the context of statics and simple material behaviour with a view toward further developments involving behaviour or models where the DG concept can show its superiority compared to the continuous formulation. The method is based on a general Hu–Washizu–de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. It is shown that this approach naturally leads to the formulation of average stress fluxes at interelement boundaries in a finite element implementation. The consistency and linearized stability of the method in the non‐linear range as well as its convergence rate are proven. An implementation in three dimensions is developed, showing that the proposed method can be integrated into conventional finite element codes in a straightforward manner. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Copyright © 2006 John Wiley & Sons, Ltd.