Discrete element response of beams with traveling mass

This article extends a procedure that has been used to discretize the static physical system following the assumption that a continuous flexible beam can be replaced by a system of rigid bars and joints which resists relative rotation of the attached bars. We call this procedure the “discrete element response of beams”. The object of this article is to present and formulate a new simple, practical and inexpensive approximate technique for determining the time response of beams, with different boundary conditions, carrying a moving mass. To verify the results, other solutions are obtained by continuous simulation systems, CSMP, and dynamic finite element, PAFEC. This algorithm is shown to be much more efficient computationally.     

FEM and BEM in the context of information retrieval

Numerical techniques such as, first of all, the finite element and boundary element methods are frequently used today in research as well as in many industry applications. The output of finite element and boundary element literature and development of software, has been growing during last three decades. Today, it is almost impossible to be up-to-date with all the relevant information. At present, we have an excess of information––the term “information fatigue syndrome” will soon be a recognized medical condition. The author presents, by means of information from his database, the progress of both numerical techniques in their theoretical developments and practical usage for the period of last 30 years. The topics included: finite element and boundary element literature and software with emphasis on structural and solid mechanics. Some pointers for classical, printed, and for modern, on-line, information retrieval are given.     

燃油箱吊座焊缝的强度和疲劳有限元分析

对某内燃机车燃油箱吊座中T型焊接接头部位焊缝强度和疲劳进行有限元分析.在焊缝熔深为2,3和5 mm(全熔透)时,将吊座有焊缝和无焊缝时应力有限元计算结果与传统方法计算结果进行比较,结果表明:在焊缝全熔透时吊座整体最大应力小于传统方法计算的无焊缝时的最大应力,说明全熔透结构具有更好的连接性能.焊缝全熔透时焊缝处节点应力分布表明几何截面突变明显处的节点应力较大.疲劳计算结果表明该燃油箱吊座满足疲劳强度要求.     

An automated procedure for fatigue crack growth analysis

An automated procedure is developed to determine the influence of a crack detected in a structural element subjected to cyclic combined axial and bending loadings with constant amplitude. A theoretical formulation for fatigue crack growth analysis is presented and the results obtained are compared with the experimental data of the Wöhler curves. The critical crack configurations for which the fatigue failure occurs after a given number of loading cycles can be obtained from the above-mentioned comparison. Finally, an example is shown in order to illustrate the use of a computer program, which translates the proposed procedure.     

Evaluation of thermo-mechanical damage and fatigue life of solar cell solder interconnections

The soldering process of interconnecting crystalline silicon solar cells to form photovoltaic (PV) module is a key manufacturing process. However, during the soldering process, stress is induced in the solar cell solder joints and remains in the joint as residual stress after soldering. Furthermore, during the module service life time, thermo-mechanical degradation of the solder joints occurs due to thermal cycling of the joints which induce stress, creep strain and strain energy. The resultant effect of damage on the solder joint is premature failure, hence shortened fatigue life. This study seeks to determine accumulated thermo-mechanical damage and fatigue life of solder interconnection in solar cell assembly under thermo-mechanical cycling conditions. In this investigation, finite element modelling (FEM) and simulations are carried out in order to determine nonlinear degradation of SnAgCu solder joints. The degradation of the solder material is simulated using Garofalo-Arrhenius creep model. A three dimensional (3D) geometric model is subjected to six accelerated thermal cycles (ATCs) utilising IEC 61215 standard for photovoltaic panels. The results demonstrate that induced stress, strain and strain energy impacts the solder joints during operations. Furthermore, the larger the accumulated creep strain and creep strain energy in the joints, the shorter the fatigue life. This indicates that creep strain and creep strain energy in the solder joints significantly impacts the thermo-mechanical reliability of the assembly joints. Regions of solder joint with critical stress, strain and strain energy values including their distribution are determined. Analysis of results demonstrates that creep energy density is a better parameter than creep strain in predicting interconnection fatigue life. The use of six ATCs yields significant data which enable better understanding of the response of the solder joints to the induced loads. Moreover, information obtained from this study can be used for improved design and better-quality fabrication of solder interconnections in solar cell assembly for enhanced thermo-mechanical reliability.     

Human-like behavior of robot arms: general considerations and the handwriting task—Part I: mathematical description of human-like motion: distributed positioning and virtual fatigue

This two-part paper is concerned with the analysis and achievement of human-like behavior by robot arms (manipulators). The analysis involves three issues: (i) the resolution of the inverse kinematics problem of redundant robots, (ii) the separation of the end-effector's motion into two components, i.e. the smooth (low accelerated) component and the fast (accelerated) component, and (iii) the fatigue of the motors (actuators) of the robot joints. In the absence of the fatigue, the human-like performance is achieved by using the partitioning of the robot joints into “smooth” and “accelerated” ones (called distributed positioning—DP). The actuator fatigue is represented by the so-called “virtual fatigue” (VF) concept. When fatigue starts, the human-like performance is achieved by engaging more the joints (motors) that are less fatigued, as does the human arm. Part I of the paper provides the theoretical issues of the above approach, while Part II applies it to the handwriting task and provides extensive simulation results that support the theoretical expectations.     

基于道路载荷谱的车身焊点疲劳寿命分析

针对目前汽车焊点疲劳分析方法精度低、建模复杂等问题,以某自主SUV车身焊点为研究对象,采集道路载荷谱,通过载荷虚拟迭代得到底盘与车身连接点的载荷.研究结果表明,对车身焊点分别使用基于力(载荷)和应力的疲劳分析,可以准确预测试验样车焊点开裂位置,缩短焊点疲劳分析周期.改进后的样车顺利通过耐久试验场验证.     

基于FBG的半潜式平台关键节点疲劳响应监测试验研究

半潜式平台在深海服役期间其关键部位的疲劳响应监测和超载预警是至关重要的。基于光纤布拉格光栅(FBG)监测原理,对半潜式平台结构关键节点进行了疲劳响应监测试验研究和疲劳损伤后的极限强度监测试验研究,通过FBG与应变计监测结果对比,分析了节点应变和位移变化规律,探讨了平台结构节点疲劳响应和疲劳剩余极限强度的监测方法。试验结果表明,FBG的疲劳响应监测值与应变计的监测值接近,曲线变化趋势一致,应变变化规律与位移变化规律比较吻合。FBG传感器能够监测到结构节点的疲劳响应和疲劳剩余极限强度的变化,可以为半潜式平台结构的安全评估和运行维护提供参考。     

Boundary formulations for sensitivities of three-dimensional stress invariants

The direct, singular, boundary element analysis (BEA) formulation has been shown to provide a basis for a computationally efficient and accurate shape structural design sensitivity analysis (DSA) approach for three-dimensional solid objects. Within the boundary element analysis context, the theoretical formulation for sensitivities of important stress-related quantities including principal and deviatoric stresses, von Mises, maximum shear, and other stress invariants are presented, both for the surface as well as the interior of a continuum structure. Numerical results are given to demonstrate the accuracy of this approach.     

On the viscoelastic beam subjected to moving mass

In this paper two methods are presented that can be used to determine the dynamic behavior of viscoelastic beams with different boundary conditions, carrying a moving mass. An analytical–numerical formulation that transforms the governing differential equation in viscoelastic media into a set of ordinary differential equations and thereafter a discrete element model based on assumption that continuous viscoelastic beam can be replaced by a system of rigid bars and joints which resist relative rotation of attached bars. The physical properties of the joints can be found through considering the viscoelastic model of beams material. Correctness of results has been ascertained by a comparison, made between the above two techniques and good agreements has been achieved.     

Analysis of 3D frame problems by DQEM using EDQ

The differential quadrature element method (DQEM) and extended differential quadrature (EDQ) have been proposed by the author. The development of a differential quadrature element analysis model of three-dimensional shear-undeformable frame problems adopting the EDQ is carried out. The element can be a nonprismatic beam. The EDQ technique is used to discretize the element-based governing differential equations, the transition conditions at joints and the boundary conditions on domain boundaries. An overall algebraic system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the overall algebraic system. Mathematical formulations for the EDQ-based DQEM frame analysis are carried out. By using this DQEM model, accurate results of frame problems can efficiently be obtained. Numerical results demonstrate this DQEM model.     

Design study of hole positions and hole shapes for crack tip stress releasing

The method of hole drilling near or at the crack tip is often used in fatigue damage repair. From a design optimization point of view, two questions are posed: Where should the hole(s) be drilled? And is there a better shape of the hole than a circular one? For the first question, we extend earlier results for isotropic material and in general study the influence of having orthotropic material. Optimal shapes are by no means circular, and we focus on the shape of a single hole centered at (or in front of) the crack tip. It is shown that the stress field at the crack boundary can be significantly improved by noncircular shapes. As a byproduct, an alternative method for extracting the stress intensity factor from a finite element analysis is presented.     

基于主S-N曲线法的地铁制动箱焊接疲劳分析

为研究地铁车辆制动箱焊接接头的疲劳寿命,根据实际结构建立4节点壳单元有限元模型,给出搭接焊和T型焊的焊缝建模方法.在3种振动工况下,运用主S N曲线法计算焊缝的等效结构应力和对应损伤比.结果表明：该地铁车辆制动箱焊接结构设计合理可靠;通过与实体单元模型计算结果进行对比证明壳单元模拟焊缝的合理性;在不同尺寸单元下对比2种疲劳评估方法,结果表明名义应力法预测疲劳寿命的准确性较低.     

Rotational fluid flow using a least squares collocation technique

A potential theory approach for incompressible viscous flow which leads to the biharmonic equation is first developed. A numerical least squares collocation technique using fundamental singular solutions of the biharmonic equation is then applied to a rotational flow problem with moving boundaries that produce discontinuous boundary conditions associated with the biharmonic. It is shown that the least squares technique smoothes out local disturbances in boundary data of the type which are likely to present difficulties to the more commonly used boundary element method. A compact computer program for the method and the results for the problem of a rectangular channel with one moving boundary are included along with an experimental verification of the results using the thin plate bending analogy.     

Penalty resolution of the babuska circle paradox

If the solution for a simply-supported circular plate is approximated by a sequence of finite element solutions on successively refined polygonal domains the finite element approximations converge to the solution of a different problem. In the present study we present a finite element formulation with boundary penalty that produces valid approximations to the simply-supported plate. The penalty term is shown to require the use of reduced integration. The dependence of the penalty parameter on mesh size h is also examined. Numerical experiments confirm the validity of the method and determine rates of convergence. A second approach involving a modified corner condition is also considered and error estimates determined. This scheme is implemented also using a discrete penalty technique. The results and rates are compared with the boundary penalty method and their relative merits discussed.     

Effective approach for the identification of boundary conditions in distributed-parameter systems

This paper is concerned with the identification of boundary conditions in parabolic-type distributed systems with boundaries of irregular shape. In the present approach, finite element discretization in the spatial domain and orthogonal functions expansion in the time domain are adopted to reduce the partial differential equation to a set of algebraic equations. The boundary conditions are then estimated by the method of least squares using state observations taken at a few interior points. The present approach is very straightforward and, at least as shown in illustrative examples, the results are in excellent agreement with exact results.     

An analysis of,and remedies for,kinematic modes in hybrid-stress finite elements: selection of stable,invariant stress fields

In this paper a study of the existence of spurious kinematic modes in hybrid-stress finite elements, based on assumed equilibrated stresses and compatible boundary displacements, and the resulting rank-deficiency of the element stiffness matrix, is presented. A method of selection of least-order, stable, invariant, stress fields is developed so as to ensure the prevention of kinematic modes. A 20-node cubic element, a 8-node cubic element and a 4-node square, based on assumed equilibrated stresses within the element and compatible displacements at the boundary of the element, are discussed for purposes of illustration. Comments are made on the generality of the present method, which is based on group theoretical arguments.     

h-p Spectral Element Method for Elliptic Problems on Non-smooth Domains Using Parallel Computers

We propose a new h-p spectral element method to solve elliptic boundary value problems with mixed Neumann and Dirichlet boundary conditions on non-smooth domains. The method is shown to be exponentially accurate and asymptotically faster than the standard h-p finite element method. The spectral element functions are fully non-conforming for pure Dirichlet problems and conforming only at the vertices of the elements for mixed problems, and hence, the dimension of the resulting Schur complement matrix is quite small. The method is a least-squares collocation method and the resulting normal equations are solved using preconditioned conjugate gradient method with an almost optimal preconditioner. The algorithm is suitable for a distributed memory parallel computer. The numerical results of a number of model problems are presented, which confirm the theoretical estimates.     

Finite element analysis of residual stress induced by shot peening process

The aircraft industry has only recently begun to explore possible application of welding as an alternative joining method for the design of future large civil airliner wing. One of the main obstacles, encountered in the past years, to welding application within the aircraft industries were due to failure in the weldments, caused by high tensile residual stresses present in the region of the weld, reducing drastically fatigue strength of welded joints. Improvement in the fatigue life of the welded joint can be obtained if compressive residual stresses are introduced at the weld region.Shot peening is a manufacturing process intended to give aircraft structures the final shape and to introduce a compressive residual state of stress inside the material in order to increase fatigue life. This paper presents the modeling and simulation of the residual stress field resulting from the shot peening process. The results achieved show that a significant decrease of welding induced tensile residual stress magnitude can be obtained. Good agreement between experimental and numerical results was achieved.