不同波纹板核的波纹夹层板抗弯刚度比较

采用无网格伽辽金法对两种不同波纹板核的波纹夹层板抗弯刚度进行比较.基于Mindlin平板理论,采用移动最小二乘近似构造各板近似位移,通过位移协调条件将各板刚度方程叠加,以得到复合结构的整体刚度方程,位移边界采用完全变换法处理.算例结果表明:在同等条件下,梯形式波纹夹层板的抗弯刚度要高于正弦式波纹夹层板.     

A coupled SDPH–FVM method for gas‐particle multiphase flow: Methodology

This paper describes a novel methodology that combines smoothed discrete particle hydrodynamics (SDPH) and finite volume method (FVM) to enhance the effective performance in solving the problems of gas‐particle multiphase flow. To describe the collision and fluctuation of particles, this method also increases a new parameter, namely, granular temperature, according to the kinetic theory of granular flow. The coupled framework of SDPH–FVM has been established, in which the drag force and pressure gradient act on the SDPH particles and the momentum sources of drag force are added back onto the FVM mesh. The proposed technique is a coupled discrete‐continuum method based on the two‐fluid model. To compute for the discrete phase, its SDPH is developed from smoothed particle hydrodynamics (SPH), in which the properties of SPH are redefined with some new physical quantities added into the traditional SPH parameters, so that it is more beneficial for SDPH in representing the particle characteristics. For the continuum phase, FVM is employed to discretize the continuum flow field on a stationary grid by capturing fluid characteristics. The coupled method exhibits strong efficiency and accuracy in several two‐dimensional numerical simulations. Copyright © 2016 John Wiley & Sons, Ltd.     

Evaluation of effective elastic properties of 3D printable interpenetrating phase composites using the meshfree radial point interpolation method

ABSTRACT

Interpenetrating phase composites (IPCs) have recently been fabricated using three-dimensional (3D) printing methods. In a two-phase IPC, the two phases are topologically interconnected and mutually reinforced in the three dimensions. As a result, such IPCs exhibit higher stiffness, strength, and toughness than particle- or fiber-reinforced composites. In the current study, three unit cell models for the IPCs with the simple cubic (SC), face-centered cubic (FCC), and body-centered cubic (BCC) microstructures are developed using the meshfree radial point interpolation method. Radial basis functions with polynomial reproduction are applied to construct shape functions, and the Galerkin method is employed to formulate discretized equations. These unit cell-based meshfree models are used to evaluate effective elastic properties of 3D printable IPCs. The simulation results are compared with those based on the finite element (FE) method and various analytical bounding techniques in micromechanics, including the Voigt–Reuss, Hashin–Shtrikman, and Tuchinskii bounds. It is found that all of the simulation results for the effective Young's modulus and shear modulus fall between the Voigt–Reuss upper and lower bounds for each IPC considered, with the FE models predicting higher values than the meshfree models. In addition, it is seen that the SC microstructure leads to higher effective Young's modulus than the BCC and FCC microstructures. Furthermore, the numerical results reveal that the IPCs with the SC, BCC, and FCC microstructures can be approximated as isotropic materials (with the Zener anisotropic ratio varying between 0.9 and 1.0), with the BCC IPC being the most isotropic one, and the SC IPC being the least isotropic one among the three types of IPCs.     

A superconvergent point interpolation method (SC‐PIM) with piecewise linear strain field using triangular mesh

A superconvergent point interpolation method (SC‐PIM) is developed for mechanics problems by combining techniques of finite element method (FEM) and linearly conforming point interpolation method (LC‐PIM) using triangular mesh. In the SC‐PIM, point interpolation methods (PIM) are used for shape functions construction; and a strain field with a parameter α is assumed to be a linear combination of compatible stains and smoothed strains from LC‐PIM. We prove theoretically that SC‐PIM has a very nice bound property: the strain energy obtained from the SC‐PIM solution lies in between those from the compatible FEM solution and the LC‐PIM solution when the same mesh is used. We further provide a criterion for SC‐PIM to obtain upper and lower bound solutions. Intensive numerical studies are conducted to verify these theoretical results and show that (1) the upper and lower bound solutions can always be obtained using the present SC‐PIM; (2) there exists an α_exact∈(0, 1) at which the SC‐PIM can produce the exact solution in the energy norm; (3) for any α∈(0, 1) the SC‐PIM solution is of superconvergence, and α=0 is an easy way to obtain a very accurate and superconvergent solution in both energy and displacement norms; (4) a procedure is devised to find a α_prefer∈(0, 1) that produces a solution very close to the exact solution. Copyright © 2008 John Wiley & Sons, Ltd.     

基于SPH的射流成形机理研究

光滑粒子流体动力学是一种纯 Lagrangian 的无网格数值计算方法,可以很好地处理动态载荷下材料大变形问题。采用SPH方法对射流成形和拉伸进行初步研究,给出求解爆炸和射流成形的力学模型和离散格式,针对一定锥角药型罩射流成形进行数值研究。结果表明,对爆炸、射流成形等瞬态动力学问题,SPH方法是行之有效的,但在计算过程中也存在数值断裂和应力不稳定等问题。     

两种SPH算法在模拟不可压缩流中的比较

基于二维腔剪切流模型,对弱可压缩光滑粒子流体动力学（WCSPH）和不可压缩光滑粒子流体动力学（ISPH）两种SPH算法进行了对比分析。分别使用了排斥力方法与静态粒子法来设置边界。结果显示：ISPH算法在计算速度场和压力场时,计算精度均较WCSPH算法高;时间步长不像WCSPH算法受声速的限制,计算效率更高。     

On the optimum support size in meshfree methods: A variational adaptivity approach with maximum‐entropy approximants

We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum‐entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non‐linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright © 2009 John Wiley & Sons, Ltd.     

二维大地电磁正演中无网格算法研究

无网格法是近几年来发展的一种新的基于变分原理的数值计算方法,由于在计算形函数中不需要划分网格,在力学、电磁学等领域得到了广泛的研究。基于无网格法在大地电磁勘探正演中的应用进行了研究,首先对无网格法的基本原理进行了阐述,并利用广义变分原理推导出了相应的离散方程,编制了相应的程序。最后通过理论模型的计算结果检验了该算法的正确性。     

A meshfree‐enriched finite element method for compressible and near‐incompressible elasticity

In this paper, a two‐dimensional displacement‐based meshfree‐enriched FEM (ME‐FEM) is presented for the linear analysis of compressible and near‐incompressible planar elasticity. The ME‐FEM element is established by injecting a first‐order convex meshfree approximation into a low‐order finite element with an additional node. The convex meshfree approximation is constructed using the generalized meshfree approximation method and it possesses the Kronecker‐delta property on the element boundaries. The gradient matrix of ME‐FEM element satisfies the integration constraint for nodal integration and the resultant ME‐FEM formulation is shown to pass the constant stress test for the compressible media. The ME‐FEM interpolation is an element‐wise meshfree interpolation and is proven to be discrete divergence‐free in the incompressible limit. To prevent possible pressure oscillation in the near‐incompressible problems, an area‐weighted strain smoothing scheme incorporated with the divergence‐free ME‐FEM interpolation is introduced to provide the smoothing on strains and pressure. With this smoothed strain field, the discrete equations are derived based on a modified Hu–Washizu variational principle. Several numerical examples are presented to demonstrate the effectiveness of the proposed method for the compressible and near‐incompressible problems. Copyright © 2012 John Wiley & Sons, Ltd.     

A thin plate formulation without rotation DOFs based on the radial point interpolation method and triangular cells

A formulation for thin plates with only the deflection as nodal variables has been proposed using the generalized gradient smoothing technique and the radial point interpolation method (RPIM). The deflection fields are approximated using the RPIM shape functions which possess the Kronecker Delta property for easy impositions of essential boundary conditions. Three types of smoothing domains, which are also serving as the numerical integrations domains, are constructed based on the background three‐node triangular cells and the generalized gradient smoothing operation is performed over each of them to obtain the smoothed curvatures. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. The essential boundary conditions of rotations are imposed in the process of constructing the curvature field, and the translation boundary conditions are imposed as in the standard FEM. A number of numerical examples, including both static and free vibration analysis, are studied using the present methods and the numerical results are compared with the analytical ones and those in the open literatures. The results show that the present formulation can obtain very stable and accurate solutions, even for the extremely irregular background cells. Copyright © 2010 John Wiley & Sons, Ltd.