Stiffness Evaluation of the Welded Connection between Guide Thimbles and the Spacer Grids for 16 × 16 Fuel Assemblies Types, Using the Finite Element Method

The present work aims to evaluate the increase in the number of spot welds in the 16 × 16 type fuel assembly structure that connects guide thimbles and spacer grids, in order to provide a proper joint for this connection. This new and improved process can provide more stiffness to the whole structure, since the number of spots raised from four to eight. A 3-D geometric model of a guide thimble section was generated in a CAD （computer aided design） program （SolidWorks）. After that, the geometric model was imported to a CAE （computer aided engineering） program （ANSYS Mechanical APDL, Release 14.0）, where the finite element model was built, considering the guide thimble geometry assembled with the spacer grid through the welded connections. Boundaries conditions were implemented in the model in order to simulate the correct physical behavior due to the operation of the fuel assembly inside the reactor. The analysis covered specific loads and displacements acting on the entire structure. The method used to solve this finite element analysis was a linear static simulation in order to perform the connection between a spacer grid cell and a guide thimble section. Hence, four models was evaluated, differing on the spot weld number in the spacer grid and guide thimble connection. The rotational stiffness results of each model were compared. The results acquired from four and eight spot weld were validated with physical test results. The behavior of the structure under the acting force/displacement and the related results of the analysis, mainly the stiffness, were satisfied. The results of this analysis were used to prove that the increasing spot welds number is an improvement in the dimensional stability when submitted to loads and displacements required on the fuel assembly design. This analysis aid to get more information of extreme importance such as, the pursuance to develop better manufacturing process and to improve the fuel assembly performance due to the increasing of the bum-up.

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.

A Finite Element Method for Cracked Components of Structures

In this paper, a method is developed for determining the effective stiffness of the cracked component. The stiffness matrix of the cracked component is integrated into the global stiffness matrix of the finite element model of the global platform for the FE calculation of the structure in any environmental conditions. The stiffness matrix equation of the cracked component is derived by use of the finite variation principle and fracture mechanics. The equivalent parameters defining the element that simulates the cracked component are mathematically presented, and can be easily used for the FE calculation of large scale cracked structures together with any finite element program. The theories developed are validated by both lab tests and numerical calculations, and applied to the evaluation of crack effect on the strength of a fixed platform and a self-elevating drilling rig.

Numerical Analysis on the Static Performance of Gas Journal Bearing by Using Finite Element Method

In this paper,finite element method is used to calculate the static performance of gas journal bearing,in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed.The results indicate that the average gas film thicknesses corresponding to the maximum load capac-ity and stiffness,and the minimum attitude angle increase with the growth of orifice diameter.Load capacity and stiffness significantly improved with the increase of rotation speed,eccentricity ratio and supply pressure when the bearing has thin average gas film thickness.Attitude angle increases with the growth of rotation speed,while the growth rate slows down or even decreases at high speed.The most effective way of reducing attitude angle is to increase supply pressure.It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices,while other parameters have the same effect by changing gas pressure at orifice outlet.

Finite element model for arch bridge vibration dynamics considering effect of suspender length adjustment on geometry stiffness matrix

In this paper, we established a finite element (FEM) model to analyze the dynamic characteristics of arch bridges. In this model, the effects of adjustment to the length of a suspender on its geometry stiffness matrix are stressed. The FEM equations of mechanics characteristics, natural frequency and main mode are set up based on the first order matrix perturbation theory. Applicantion of the proposed model to analyze a real arch bridge proved the improvement in the simulation precision of dynamical characteristics of the arch bridge by considering the effects of suspender length variation.

THE DYNAMIC STIFFNESS MATRIX OF THE FINITE ANNULAR PLATE ELEMENT

The dynamic deformation of harmonic vibration is used as the shape functions of the finite annular plate element, and sonic integration difficulties related to the Bessel's functions are solved in this paper. Then the dynamic stiffness matrix of the finite annular plate element is established in closed form and checked by the direct stiffness method. The paper has given wide convcrage for decomposing the dynamic matrix into the power series of frequency square. By utilizing the axial symmetry of annular elements, the modes with different numbers of nodal diameters at s separately treated. Thus some terse and complete results are obtained as the foundation of structural characteristic analysis and dynamic response compulation.

Damage prediction for magnesium matrix composites formed by liquid-solid extrusion process based on finite element simulation

A damage prediction method based on FE simulation was proposed to predict the occurrence of hot shortness crocks and surface cracks in liquid-solid extrusion process. This method integrated the critical temperature criterion and Cockcroft ＆ Latham ductile damage model, which were used to predict the initiation of hot shortness cracks and surface cracks of products, respectively. A coupling simulation of deformation with heat transfer as well as ductile damage was carried out to investigate the effect of extrusion temperature and extrusion speed on the damage behavior of Csf/AZ91D composites. It is concluded that the semisolid zone moves gradually toward deformation zone with the punch descending. The amplitude of the temperature rise at the exit of die from the initial billet temperature increases with the increase of extrusion speed during steady-state extrusion at a given punch displacement. In order to prevent the surface temperature of products beyond the incipient melting temperature of composites, the critical extrusion speed is decreased with the increase of extrusion temperature, otherwise the hot shortness cracks will occur. The maximum damage values increase with increasing extrusion speed or extrusion temperature. Theoretical results obtained by the Deform^TM-2D simulation agree well with the experiments.

THE STRESS SUBSPACE OF HYBRID STRESS ELEMENT AND THE DIAGONALIZATION METHOD FOR FLEXIBILITY MATRIX H

The following is proved: 1) The linear independence of assumed stress modes is the necessary and sufficient condition for the nonsingular flexibility matrix; 2) The equivalent assumed stress modes lead to the identical hybrid element. The Hilbert stress subspace of the assumed stress modes is established. So, it is easy to derive the equivalent orthogonal normal stress modes by Schmidt's method. Because of the resulting diagonal flexibility matrix, the identical hybrid element is free from the complex matrix inversion so that the hybrid efficiency, is improved greatly. The numerical examples show that the method is effective.

Finite Element Analysis of Push-Out Test of SiC Fiber Reinforced Titanium Matrix Composites

Based on the interphase layer model and the spring layer model, an improved interface model was developed to evaluate the interfacial shear strength of Titanium matrix composites(TMCs) and to analyze the effects of various parameters on the interfacial properties. The results showed that the improved interface model is more suitable for calculating the interfacial properties of SiC fiber reinforced titanium matrix composites. The interfacial shear strength of SiC/Timetal-834 predicted is 500 MPa. In addition, in order to better understand the interfacial properties of composites, some push out phenomenon were analyzed.

Finite Element Calculation of the Flexural Stiffness of Corroded RC Eccentric Compressive Members

A finite element calculation model of corroded RC eccentric compressive members was build using finite element software ANSYS. The model considers the decline of mechanical properties and the effective section of a corroded steel bar,as well as the deterioration of bond character between corroded reinforcement and concrete. The reliability of the finite element model was evaluated by comparing the results of the finite element calculation with the data from experiments. Based on the finite element analysis results,the influence of corrosion degree,the diameter change of the longitudinal reinforcing bars and the spacing change of stirrups on the flexural stiffness were calculated and analyzed.

GEOMETRICALLY NONLINEAR FINITE ELEMENT MODEL OF SPATIAL THIN-WALLED BEAMS WITH GENERAL OPEN CROSS SECTION

Based on the theory of Timoshenko and thin-walled beams, a new finite element model of spatial thin-walled beams with general open cross sections is presented in the paper, in which several factors are included such as lateral shear deformation, warp generated by nonuni- form torsion and second-order shear stress, coupling of flexure and torsion, and large displacement with small strain. With an additional internal node in the element, the element stiffness matrix is deduced by incremental virtual work in updated Lagrangian （UL） formulation. Numerical examples demonstrate that the presented model well describes the geometrically nonlinear property of spatial thin-walled beams.

Method to analyze wrinkled membranes with zero shear modulus and equivalent stiffness

To solve the problems of divergence,low accuracy and project application of membrane wrinkling analysis,an analysis method of zero shear modulus and equivalent stiffness was proposed.This method is an improvement to the previous method (Method I) of local coordinate transposition and stiffness equivalence.The new method is derived and the feasibility is theoretically proved.A small-scale membrane structure is analyzed by the two methods,and the results show that the computational efficiency of the new method (Method II) is approximately 23 times that of Method I.When Method II is applied to a large-scale membrane stadium structure,it is found that this new method can quickly make the second principal stress of one way wrinkled elements zero,and make the two principal stresses of two-way wrinkled elements zero as well.It could attain the correct load responses right after the appearance of wrinkled elements,which indicates that Method II can be applied to wrinkling analysis of large-scale membrane structures.

Optimal design of automotive body B-pillar using simplified finite element model of body-in-prime combined with an optimization procedure

Optimization of an automotive body structure faces the difficulty of having too many design variables and a too large design search space. A simplified model of body-in-prime(BIP) can solve this difficulty by reducing the number of design variables. In this study, to achieve lighter weight and higher stiffness, the simplified model of BIP was developed and combined with an optimization procedure;consequently, optimal designs of automotive body B-pillar were produced. B-pillar was divided into four quarters and each quarter was modelled by one simplified beam. In the optimization procedure, depth, width, and thickness of the simplified beams were considered as the design variables.Weight, bending and torsional stiffness were also considered as objective functions. The optimization procedure is composed of six stages: designing the experiments, calculating grey relational grade, calculating signal-to noise ratio,finding an optimum design using Taguchi grey relational analysis, performing sensitivity analysis using analysis of variance(ANOVA) and performing non-dominated sorting and multi-criteria decision making. The results show that the width of lower B-pillar has the highest effect(about 55%) and the obtained optimum design point could reduce the weight of B-pillar by about 40% without reducing the BIP stiffness by more than 1.47%.

Gershgorin and Rayleigh Bounds on the Eigenvalues of the Finite-Element Global Matrices via Optimal Similarity Transformations

The large finite element global stiffness matrix is an algebraic, discreet, even-order, differential operator of zero row sums. Direct application of the, practically convenient, readily applied, Gershgorin’s eigenvalue bounding theorem to this matrix inherently fails to foresee its positive definiteness, predictably, and routinely failing to produce a nontrivial lower bound on the least eigenvalue of this, theoretically assured to be positive definite, matrix. Considered here are practical methods for producing an optimal similarity transformation for the finite-elements global stiffness matrix, following which non trivial, realistic, lower bounds on the least eigenvalue can be located, then further improved. The technique is restricted here to the common case of a global stiffness matrix having only non-positive off-diagonal entries. For such a matrix application of the Gershgorin bounding method may be carried out by a mere matrix vector multiplication.

New Formula for Geometric Stiffness Matrix Calculation

The standard formula for geometric stiffness matrix calculation, which is convenient for most engineering applications, is seen to be unsatisfactory for large strains because of poor accuracy, low convergence rate, and stability. For very large compressions, the tangent stiffness in the direction of the compression can even become negative, which can be regarded as physical nonsense. So in many cases rubber materials exposed to great compression cannot be analyzed, or the analysis could lead to very poor convergence. Problems with the standard geometric stiffness matrix can even occur with a small strain in the case of plastic yielding, which eventuates even greater practical problems. The authors demonstrate that amore precisional approach would not lead to such strange and theoretically unjustified results. An improved formula that would eliminate the disadvantages mentioned above and leads to higher convergence rate and more robust computations is suggested in this paper. The new formula can be derived from the principle of virtual work using a modified Green-Lagrange strain tensor, or from equilibrium conditions where in the choice of a specific strain measure is not needed for the geometric stiffness derivation (which can also be used for derivation of geometric stiffness of a rigid truss member). The new formula has been verified in practice with many calculations and implemented in the RFEM and SCIA Engineer programs. The advantages of the new formula in comparison with the standard formula are shown using several examples.

Diamond Rib: A Mechanical Design Method for Improving the Stiffness of a Structure

It is necessary to decrease the weight of space satellites, while maintaining their stiffness. To achieve this weight reduction, many structures, such as honeycomb and isogrid, have been reported in the literature. In this paper, the diamond rib method, a mechanical design method for improving the stiffness of structures, is introduced. By applying this method to a small space satellite, we propose a new structure called the “Diamond Rib Structure”. This structure significantly improves the ability to withstand the vibrational disturbances in a rocket fairing.

扣件刚度非线性对波磨区轮轨瞬态滚动接触行为的影响

WJ-8型扣件橡胶垫板刚度在长期服役过程中表现出非线性特征,静刚度随荷载增加而降低,为提高三维瞬态滚动接触有限元模型计算精确性,本文以LMA踏面车轮及CHN60型钢轨为基础,基于显式积分算法,将以往研究中线弹性扣件转化为非线性扣件,建立考虑扣件刚度非线性特征的三维轮轨瞬态滚动接触有限元模型,研究刚度非线性对车轮与钢轨波磨间高频动态响应及瞬态接触行为的影响,并重点分析了波磨工况下时频域内轮轨接触力、轴箱加速度的变化信息.结果表明:扣件非线性对轮轨接触力变化影响明显,主要表现为车轮行驶至扣件前端时强振动导致橡胶垫板表现为柔软特性使轮轨接触力减小,车轮行驶至扣件上方时在轴重作用下振动减弱表现为刚硬特性使轮轨接触力增大,轮轨力变化差异最大达到13.1%.

燃气轮机拉杆转子抗弯刚度分析

为提高计算效率,发展了一种计算抗弯刚度的简便算法。该算法利用接触压力在接触面上近似线性分布的特点,在给定的总体预紧力及弯矩情况下,计算得到接触面上法向应力及分布,结合轮盘的结构特点采用平截面假设,求出抗弯刚度的修正系数,再乘以连续模型的抗弯刚度就可得到界面分离时的抗弯刚度。采用简化算法得到的抗弯刚度与三维有限元接触算法计算结果相差在5.8%以内,计算所需时间为后者的1%,证明了本算法的高效性;以某F级重型燃气轮机转子为例,综合考虑了界面局部分离和粗糙度对转子整体刚度的影响,并研究了预紧松弛对转子固有频率的影响。

基于有限元法的空间探测器复合材料结构安全裕度分析

针对复合材料结构强度和安全性评估问题,提出一种基于有限元法的复合材料层压板结构安全裕度(MS)分析方法。使用ABAQUS软件和Python二次开发前后处理程序,对火星环绕器复合材料结构进行安全裕度分析。通过与试验结果对比,验证了安全裕度分析方法的准确性和可靠性。根据分析结果,对火星环绕器主承力结构局部补强后,提高了结构刚度、强度和安全裕度。

考虑结合面特性影响的机床整机有限元静力学分析模型

针对机床数字化设计中典型结合面建模精度误差较大的问题,提出了一种采用虚拟材料等效结合面静力学特性的方法,建立了考虑结合面特性影响的机床整机有限元静力学分析模型,并完成了相应的静刚度测试实验。首先,综合考虑了弹塑性变形机制和摩擦力的影响,提出了一种新的结合面法向和切向刚度的分析模型;其次,根据不同类型结合面的特点,采用虚拟材料模拟结合面的刚度特性,建立了刚度特性与虚拟材料弹性模量和泊松比的关系,并将其应用于精密数控机床整机的静刚度分析;最后,开展了整机工艺系统的静刚度测试实验,得到了主轴末端X、Y、Z三个方向的刚度分别为26.60 N/μm、41.87 N/μm和40.17 N/μm,并将其与仿真数据进行了对比。研究结果表明:不考虑结合面影响的模型相对误差将近17%,而考虑结合面影响的模型相对误差在5%以内,验证了考虑结合面特性影响的机床整机有限元静力学分析模型的有效性;采用虚拟材料等效结合面静力学特性的方法可作为机床数字化设计的一种可行的方法。