A topological optimization approach for structural design of a high‐speed low‐load mechanism using the equivalent static loads method

In high‐speed low‐load mechanisms, the principal loads are the inertial forces caused by the high accelerations and velocities. Hence, mechanical design should consider lightweight structures to minimize such loads. In this paper, a topological optimization method is presented on the basis of the equivalent static loads method. Finite element (FE) models of the mechanism in different positions are constructed, and the equivalent loads are obtained using flexible multibody dynamics simulation. Kinetic DOFs are used to simulate the motion joints, and a quasi‐static analysis is performed to obtain the structural responses. The element sensitivity is calculated according to the static‐load‐equivalent equilibrium, in such a way that the influence on the inertial force is considered. A dimensionless component sensitivity factor (strain energy caused by unit load divided by kinetic energy from unit velocity) is used, which quantifies the significance of each element. Finally, the topological optimization approach is presented on the basis of the evolutionary structural optimization method, where the objective is to find the maximum ratio of strain energy to kinetic energy. In order to show the efficiency of the presented method, we presented two numerical cases. The results of these analyses show that the presented method is more efficient and can be easily implemented in commercial FE analysis software. Copyright © 2011 John Wiley & Sons, Ltd.     

基于小波有限元法的连续梁移动荷载识别

将待识别车载简化为移动荷载投影到小波空间;车载所作用的连续梁模型以小波尺度函数为插值函数,以小波有限元法为建模方法,并通过单元转换矩阵实现了小波空间向物理空间的变换;采用部分加速度信号作为测得动响应数据,据此积分求出速度与位移响应并用于识别移动荷载。识别方法则借助了动态规划法与正则化法,避免了时程分析中的振荡现象。仿真算例验证了小波有限元用于连续梁模型移动荷载识别的可行性,且单元数较少;识别过程中所用一阶Tikhonov正则化法具有平滑去噪能力。     

基于有限元-向量式有限元的斜拉桥非线性振动计算方法

向量式有限元(VFFE)法本质上是考虑几何非线性的有限元(FE)显式动力时程积分方法。阐述了向量式有限元的基本原理,对比了向量式有限元与基于单元随动坐标系的非线性有限元动力计算方法的相同点与差别,开发了使用杆、梁单元的有限元-向量式有限元统一算法框架的计算程序。使用该程序建立了大跨度斜拉桥计算模型,首先,使用非线性有限元法计算了斜拉桥的静力状态与动力特性,计算了列车-桥梁耦合动力作用下桥梁的振动;然后,使用向量式有限元法计算了斜拉桥在拉索突然断裂状态下的非线性振动;最后,计算了在列车-桥梁耦合动力作用下,拉索发生断裂时,桥梁与列车的振动状态。结果表明:使用向量式有限元可以简单可靠地直接模拟斜拉桥在破坏状态下的非线性振动状态;列车运行至跨中附近时,若斜拉桥跨中最长拉索突然发生断裂,对其他拉索的安全性影响不大,离断裂拉索越远的拉索受到的影响越小,但拉索突然断裂会对桥上行驶中列车的安全性造成威胁。该研究为大跨度斜拉桥在破坏状态下的非线性振动分析提供了新的解决方案。     

On the use of the extended finite element method with quadtree/octree meshes

This paper describes the use of the extended finite element method in the context of quadtree/octree meshes. Particular attention is paid to the enrichment of hanging nodes that inevitably arise with these meshes. An approach for enforcing displacement continuity along hanging edges and faces is proposed and validated on various numerical examples (holes, material interfaces, and singularities) in both 2D and 3D. Copyright © 2010 John Wiley & Sons, Ltd.     

On the essence and the evaluation of the shape functions for the smoothed finite element method (SFEM)

This paper is written in response to the recently published paper (Int. J. Numer. Meth. Engng 2008; 76 :1285–1295) at IJNME entitled ‘On the smoothed finite element method’ (SFEM) by Zhang HH, Liu SJ, Li LX. In this paper we

• (1) repeat briefly the important essence of the original SFEM presented in (Comp. Mech. 2007; 39 : 859–877; Int. J. Numer. Meth. Engng 2007; 71 :902–930; Int. J. Numer. Meth. Engng 2008; 74 :175–208; Finite Elem. Anal. Des. 2007; 43 :847–860; J. Sound Vib. 2007; 301 :803–820), and
• (2) examine further issues in the evaluation of the shape functions used in the SFEM.

It will be shown that the ‘SFEM’ presented in paper (Int. J. Numer. Meth. Engng 2008; 76 :1285–1295) is not at all our original SFEM presented in (Comp. Mech. 2007; 39 :859–877; Int. J. Numer. Meth. Engng 2007; 71 :902–930; Int. J. Numer. Meth. Engng 2008; 74 :175–208; Finite Elem. Anal. Des. 2007; 43 :847–860; J. Sound Vib. 2007; 301 :803–820). Therefore, all these ‘Theorems’, ‘Corollaries’ and ‘Remarks’ presented in paper (Int. J. Numer. Meth. Engng 2008; 76 :1285–1295) have nothing to do with our original SFEM. The properties of the original SFEM stand as they were presented in our original papers (Comp. Mech. 2007; 39 :859–877; Int. J. Numer. Meth. Engng 2007; 71 :902–930; Int. J. Numer. Meth. Engng 2008; 74 :175–208; Finite Elem. Anal. Des. 2007; 43 :847–860; J. Sound Vib. 2007; 301 :803–820). Finally, we brief on our advancements made far beyond our original SFEM and our visions on future numerical methods. Copyright © 2009 John Wiley & Sons, Ltd.     

A locking‐free selective smoothed finite element method using tetrahedral and triangular elements with adaptive mesh rezoning for large deformation problems

A novel finite element (FE) formulation with adaptive mesh rezoning for large deformation problems is proposed. The proposed method takes the advantage of the selective smoothed FE method (S‐FEM), which has been recently developed as a locking‐free FE formulation with strain smoothing technique. We adopt the selective face‐based smoothed/node‐based smoothed FEM (FS/NS‐FEM‐T4) and edge‐based smoothed/node‐based smoothed FEM (ES/NS‐FEM‐T3) basically but modify them partly so that our method can handle any kind of material constitutive models other than elastic models. We also present an adaptive mesh rezoning method specialized for our S‐FEM formulation with material constitutive models in total form. Because of the modification of the selective S‐FEMs and specialization of adaptive mesh rezoning, our method is locking‐free for severely large deformation problems even with the use of tetrahedral and triangular meshes. The formulation details for static implicit analysis and several examples of analysis of the proposed method are presented in this paper to demonstrate its efficiency. Copyright © 2014 John Wiley & Sons, Ltd.     

Rapid evaluation of notch stress intensity factors using the peak stress method: Comparison of commercial finite element codes for a range of mesh patterns

The peak stress method (PSM) is an engineering, finite element (FE)‐oriented method to rapidly estimate the notch stress intensity factors by using the singular linear elastic peak stresses calculated from coarse FE analyses. The average element size adopted to generate the mesh pattern can be chosen arbitrarily within a given range. Originally, the PSM has been calibrated under pure mode I and pure mode II loadings by means of Ansys FE software. In the present contribution, a round robin between 10 Italian universities has been carried out to calibrate the PSM with 7 different commercial FE codes. To this aim, several two‐dimensional mode I and mode II problems have been analysed independently by the participants. The obtained results have been used to calibrate the PSM for given stress analysis conditions in (i) FE software, (ii) element type and element formulation, (iii) mesh pattern, and (iv) criteria for stress extrapolation and principal stress analysis at FE nodes.     

Use of equivalent mass method for free vibration analyses of a beam carrying multiple two‐dof spring–mass systems with inertia effect of the helical springs considered

This paper investigates the free vibration characteristics of a beam carrying multiple two‐degree‐of‐freedom (two‐dof) spring–mass systems (i.e. the loaded beam). Unlike the existing literature to neglect the inertia effect of the helical springs of each spring–mass system, this paper takes the last inertia effect into consideration. To this end, a technique to replace each two‐dof spring–mass system by a set of rigidly attached equivalent masses is presented, so that the free vibration characteristics of a loaded beam can be predicted from those of the same beam carrying multiple rigidly attached equivalent masses. In which, the equation of motion of the loaded beam is derived analytically by means of the expansion theorem (or the mode superposition method) incorporated with the natural frequencies and the mode shapes of the bare beam (i.e. the beam carrying nothing). In addition, the mass and stiffness matrices including the inertia effect of the helical springs of a two‐dof spring–mass system, required by the conventional finite element method (FEM), are also derived. All the numerical results obtained from the presented equivalent mass method (EMM) are compared with those obtained from FEM and satisfactory agreement is achieved. Because the equivalent masses of each two‐dof spring–mass system are dependent on the magnitudes of its lumped mass, spring constant and spring mass, the presented EMM provides an effective technique for evaluating the overall inertia effect of the two‐dof spring–mass systems attached to the beam. Furthermore, if the total number of two‐dof spring–mass systems attached to the beam is large, then the order of the overall property matrices for the equation of motion of the loaded beam in EMM is much less than that in FEM and the computer storage memory required by the former is also much less than that required by the latter. Copyright © 2005 John Wiley & Sons, Ltd.