等腰三角形空间桁架自由扭转理论分析和试验研究

为研究腹杆对称布置的等腰三角形空间桁架的抗扭性能,以经典的自由扭转理论为基础,根据自由扭转变形的特点对桁架扭转变形关系进行了简化。给出了桁架的扭心位置、弹性抗扭刚度和屈服扭矩的计算方法,并分析了桁架破坏的机理。为验证桁架抗扭性能的计算方法,进行了桁架的扭转试验,试验构件弹性抗扭刚度和屈服扭矩的计算值和试验值的误差均小于10%。运用有限元方法对试验构件和计算方法进行了模拟和验证。结果表明:该文方法的计算值、试验值和有限元分析数值符合良好,该文的研究为等腰三角形空间桁架自由扭转提供了一种实用计算方法。     

Mechanical modeling of incompressible particle-reinforced neo-Hookean composites based on numerical homogenization

In this paper, the mechanical response of incompressible particle-reinforced neo-Hookean composites (IPRNC) under general finite deformations is investigated numerically. Three-dimensional Representative Volume Element (RVE) models containing 27 non-overlapping identical randomly distributed spheres are created to represent neo-Hookean composites consisting of incompressible neo-Hookean elastomeric spheres embedded within another incompressible neo-Hookean elastomeric matrix. Four types of finite deformation (i.e., uniaxial tension, uniaxial compression, simple shear and general biaxial deformation) are simulated using the finite element method (FEM) and the RVE models with periodic boundary condition (PBC) enforced. The simulation results show that the overall mechanical response of the IPRNC can be well-predicted by another simple incompressible neo-Hookean model up to the deformation the FEM simulation can reach. It is also shown that the effective shear modulus of the IPRNC can be well-predicted as a function of both particle volume fraction and particle/matrix stiffness ratio, using the classical linear elastic estimation within the limit of current FEM software.     

A novel methodology for the rapid identification of the water diffusion coefficients of composite materials

The paper presents a novel methodology for the rapid identification of the water diffusion coefficients of composite materials. The methodology consists in employing a numerical parametric Proper Generalized Decomposition (PGD) method allowing incorporating the diffusion coefficients among the number of degrees of freedom. Compared to classical identification schemes, often based on Finite Element Method (FEM) iterations, the proposed method allows achieving consistent CPU time gain. The method is general and can be applied when diffusion anomalies take place or when diffusion–reaction coupling must be taken into account, moreover can deal with anisotropic materials. However, for the scope of illustration, in the present case, it is applied to the simple case of “classical diffusion” (Fick’s model with constant boundary conditions) and concerns isotropic materials.     

Four-parameter functionally graded cracked plates of arbitrary shape: A GDQFEM solution for free vibrations

The dynamic behavior of moderately thick FGM plates with geometric discontinuities and arbitrarily curved boundaries is investigated. The Generalized Differential Quadrature Finite Element Method (GDQFEM) is proposed as a numerical approach. The irregular physical domain in Cartesian coordinates is transformed into a regular domain in natural coordinates. Several types of cracked FGM plates are investigated. It appears that GDQFEM is analogous to the well-known Finite Element Method (FEM). With reference to the proposed technique the governing FSDT equations are solved in their strong form and the connections between the elements are imposed with the inter-element compatibility conditions. The results show excellent agreement with other numerical solutions obtained by FEM.     

Embedded interfaces by polytope FEM

In this paper, the Polytope Finite Element Method is employed to model an embedded interface through the body, independent of the background FEM mesh. The elements that are crossed by the embedded interface are decomposed into new polytope elements which have some nodes on the interface line. The interface introduces discontinuity into the primary variable (strong) or into its derivatives (weak). Both strong and weak discontinuities are studied by the proposed method through different numerical examples including fracture problems with traction‐free and cohesive cracks, and heat conduction problems with Dirichlet and Dirichlet–Neumann types of boundary conditions on the embedded interface. For traction‐free cracks which have tip singularity, the nodes near the crack tip are enriched with the singular functions through the eXtended Finite Element Method. The concept of Natural Element Coordinates (NECs) is invoked to drive shape functions for the produced polytopes. A simple treatment is proposed for concave polytopes produced by a kinked interface and also for locating crack tip inside an element prior to using the singularity enrichment. The proposed method pursues some implementational details of eXtended/Generalized Finite Element Methods for interfaces. But here the additional DOFs are constructed on the interface lines in contrast to X/G‐FEM, which attach enriched DOFs to the previously existed nodes. Copyright © 2011 John Wiley & Sons, Ltd.     

拆除爆破研究中数值分析方法的比较与选择

概述了数值分析法的分类。介绍了平面杆系有限元法、离散元法、数值流形法和不连续变形分析等几种数值分析方法。简单地讨论了平面杆系有限元法的分析步骤以及在拆除爆破中适于解决的问题 ;同时叙述了流形分析中采用的有限覆盖技术。通过分析和比较这几种方法在拆除爆破研究中的应用 ,作者认为 ,当前应用传统的有限元法进行爆破理论研究或拆除爆破模拟存在一些困难 ;离散元法用于拆除爆破理论的研究是可行的 ;不连续变形分析法对于拆除爆破模拟研究是一种具有良好前景的数值方法     

拆除爆破研究中数值分析方法的比较与选择

概述了数值分析法的分类。介绍了平面杆系有限元法、离散元法、数值流形法和不连续变形分析等几种数值分析方法。简单地讨论了平面杆系有限元法的分析步骤以及在拆除爆破中适于解决的问题 ;同时叙述了流形分析中采用的有限覆盖技术。通过分析和比较这几种方法在拆除爆破研究中的应用 ,作者认为 ,当前应用传统的有限元法进行爆破理论研究或拆除爆破模拟存在一些困难 ;离散元法用于拆除爆破理论的研究是可行的 ;不连续变形分析法对于拆除爆破模拟研究是一种具有良好前景的数值方法     

Overcoming element quality dependence of finite elements with adaptive extended stencil FEM (AES‐FEM)

The finite element methods (FEMs) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES‐FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial basis functions, which we construct using local weighted least‐squares approximations. The method preserves the theoretical framework of FEM and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES‐FEM can use higher‐degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES‐FEM and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poisson equation and a time‐independent convection–diffusion equation. The numerical results demonstrate that AES‐FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor‐quality meshes. Copyright © 2016 John Wiley & Sons, Ltd.     

A Coupling Algorithm of Finite Element Method and Smoothed Particle Hydrodynamics for Impact Computations

For impact computations, it is efficient to model small and large deformation regions by Finite Element Method (FEM) and Smoothed Particle Hydrodynamics (SPH), respectively. However, it requires an effective algorithm to couple FEM and SPH calculations. To fulfill this requirement, an alternative coupling algorithm is presented in this paper. In the algorithm, the coupling between element and particle regions are achieved by treating elements as imaginary particles and applying equivalent tractions to element sides on coupling interfaces. In addition, an adaptive coupling technique is proposed based on the algorithm to improve the computational efficiency of FEM-SPH coupling further. For this technique, the initial model can totally consist of elements. During the deformation process distorted elements are converted to particles automatically and the generated particles are linked to adjacent elements with the present coupling algorithm. Several examples are included to demonstrate the accuracy and utility of the present coupling algorithm and adaptive coupling technique.     

The Discontinuity‐Enriched Finite Element Method

We introduce a new methodology for modeling problems with both weak and strong discontinuities independently of the finite element discretization. At variance with the eXtended/Generalized Finite Element Method (X/GFEM), the new method, named the Discontinuity‐Enriched Finite Element Method (DE‐FEM), adds enriched degrees of freedom only to nodes created at the intersection between a discontinuity and edges of elements in the mesh. Although general, the method is demonstrated in the context of fracture mechanics, and its versatility is illustrated with a set of traction‐free and cohesive crack examples. We show that DE‐FEM recovers the same rate of convergence as the standard FEM with matching meshes, and we also compare the new approach to X/GFEM.     

Nodal sensitivities as error estimates in computational mechanics

Summary This paper proposes the use of special sensitivities, called nodal sensitivities, as error indicators and estimators for numerical analysis in mechanics. Nodal sensitivities are defined as rates of change of response quantities with respect to nodal positions. Direct analytical differentiation is used to obtain the sensitivities, and the infinitesimal perturbations of the nodes are forced to lie along the elements. The idea proposed here can be used in conjunction with general purpose computational methods such as the Finite Element Method (FEM), the Boundary Element Method (BEM) or the Finite Difference Method (FDM); however, the BEM is the method of choice in this paper. The performance of the error indicators is evaluated through two numerical examples in linear elasticity.     

Tsallis entropy in dual homogenization of random composites using the stochastic finite element method

This work concerns an application of the Tsallis entropy to homogenization problem of the fiber‐reinforced and also of the particle‐filled composites with random material and geometrical characteristics. Calculation of the effective material parameters is done with two alternative homogenization methods—the first is based upon the deformation energy of the Representative Volume Element (RVE) subjected to the few specific deformations, while the second uses explicitly the so‐called homogenization functions determined under periodic boundary conditions imposed on this RVE. Probabilistic homogenization is made with the use of three concurrent non‐deterministic methods, namely Monte‐Carlo simulation, iterative generalized stochastic perturbation technique as well as the semi‐analytical approach. The last two approaches are based on the Least Squares Method with polynomial basis of the statistically optimized order— this basis serves for further differentiation in the 10th‐order stochastic perturbation technique, while semi‐analytical method uses it in probabilistic integrals. These three approaches are implemented all as the extensions of the traditional Finite Element Method (FEM) with contrastively different mesh sizes, and they serve in computations of Tsallis entropies of the homogenized tensor components as the functions of input coefficient of variation.     

一维Ritz有限元超收敛计算的EEP法简约格式的误差估计

该文对一维问题Ritz有限元后处理超收敛计算的EEP(单元能量投影)法简约格式给出误差估计的数学证明,即对足够光滑问题的(>1)次单元的有限元解答,采用EEP法简约格式计算得到的单元内任一点位移和应力(导数)超收敛解均可以达到的收敛阶,即位移比常规有限元解的收敛阶至少高一阶,而应力则至少高二阶。     

具有最佳超收敛阶的Galerkin有限元EEP法计算格式

对二阶非自伴问题的一维Galerkin有限元法提出其后处理超收敛计算的EEP(单元能量投影)法改进的最佳超收敛计算格式,即用m次单元对足够光滑问题的Galerkin有限元解答,采用该格式计算的任一点的位移和应力都可以达到h2m阶的最佳超收敛结果。该文首先针对高次单元提出了凝聚试探形函数和凝聚检验形函数的概念,证明了相关的逼近定理和等价定理,然后给出了具体的算法公式。最后给出了一系列典型的数值算例用以验证这种最新的EEP法改进格式确实能够使位移和导数逐点达到最佳收敛阶。     

波浪入射角及地形对浮体水动力学特性影响的有限元分析

利用有限元方法分析了二维情况下波浪入射角及地形对浮体水动力学特性的影响，计算了不同情况下浮体的水动力学系数；通过与简单地形情况下解析解的比较，验证了数值方法的正确性；并在分析中采用了BiCGStab算法，高效地求解离散形成的线性方程组，大大地提高了分析的效率。研究结果为海上结构物的设计提供了关键的水动力学数据。     

A multiscale DEM-FEM approach to investigate the tire–pavement friction

Abstract

Fundamental understandings of the pavement-tire friction are vital to improve the design of asphalt pavements. Most of the current research on pavement-tire friction is based on Finite Element Method (FEM), which is relatively complex and difficult to simulate the discontinuity during friction. To overcome the limitations, in this paper, the pavement–tire friction process is investigated using a coupled Multi-scale Discrete Element Method (DEM) – FEM approach. The benefit of such a multiscale method is that DEM has the advantage of simulating the discontinuity behaviour during friction, and FEM is good at simulating the continuum material with low computation consumption. The multi-scale approach provides an innovative and promising approach to simulate the tire-pavement friction behaviour.     

An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems

Strain smoothing operation has been recently adopted to soften the stiffness of the model created using tetrahedron mesh, such as the Face-based Smoothed Finite Element Method (FS-FEM), with the aim to improve solution accuracy and the applicability of low order tetrahedral elements. In this paper, a new method with strain smoothing operation based on the edge of four-node tetrahedron mesh is proposed, and the edge-based smoothing domain of tetrahedron mesh is serving as the assembly unit for computing the 3D stiffness matrix. Numerical results demonstrate that the proposed method possesses a close-to-exact stiffness of the continuous system and gives better results than both the FEM and FS-FEM using tetrahedron mesh or even the FEM using hexahedral mesh in the static and dynamic analysis. In addition, a novel domain-based selective scheme is proposed leading to a combined ES-T-/NS-FEM model that is immune from volumetric locking and hence works well for nearly incompressible materials. The proposed method is an innovative and unique numerical method with its distinct features, which possesses strong potentials in the successful applications for static and dynamics problems.     

带紧度涡轮盘鼓结构的有限元应力分析

本文应用有限元素法分析带紧度轴对称组合旋转体的热弹性应力问题,具体做法是首先应用有限元素法分别计算在自由状态下各个轴对称旋转体的热弹性应力,然后应用图解法,画出位移——载荷图,求得组合体各个配合面的变形协调点,最后加上予定的紧度,求得在真正画出实际状态下的带紧度轴对称旋转体的热弹性应力。通过对某型航空发动机的带紧度低压涡轮盘鼓结构的实例计算,取得比较满意的结果。值得指示:带紧度与左自由状态下的轴对称旋转体,它们的应力状态是截然不同的,有时会导致很大的差异,由此,决不可忽视紧度。应用有限元法与图解法结合计算,原理简单明瞭,易于掌握,说明这个方法在实践中是可行的,已为实际工程所采用。     

Capability of iterative learning control and influence of the material properties on the improvement of the geometrical accuracy in incremental sheet forming process

Incremental Sheet Forming (ISF) is a flexible technology that allows the deformation of blank sheets without the need of complex and high cost tools or equipments. One of the main lacks of ISF is the geometrical accuracy which is not comparable with the one achieved by using traditional sheet stamping processes. There are several approaches proposed to enhance this aspect and among them the Authors have developed a method based on an Iterative Learning Control (ILC). ILC consists of a cyclic and progressive error compensation method that improves the quality of the manufactured parts. ILC has been proved to be capable for optimising the production of parts with tight tolerances when dealing with ductile materials (aluminium and steel alloys) and small deformations. In this paper, the method was tested to investigate its capability in a virtual environment. The suggested compensations were checked with Finite Element Method (FEM) so to reduce the number of parts to be manufactured saving time and costs. Moreover, the algorithm was tested considering both a difficult to form material (titanium alloy) and high deformation conditions. The results demonstrated how the precision of ISF processes depends on the blank material properties. Moreover, the capabilities of ILC are shown and discussed.