Efficient frequency response and its direct sensitivity analyses for large-size finite element models using Krylov subspace-based model order reduction

In this paper, we examine an efficient calculation of the approximate frequency response (FR) for large-size finite element (FE) models using the Krylov subspace-based model order reduction (MOR) and its direct design sensitivity analysis with respect to design variables for sizing. Information about both the FR and its design sensitivity is necessary for typical gradient-based optimization iterations; therefore, the problem of high computational cost may occur when FRs of a large-size FE models are involved in the optimization problem. In the method suggested in this paper, reduced order models, generated from the original full-order FE models through the Arnoldi process, are used to calculate both the FR and FR sensitivity. This maximizes the speed of numerical computation of the FR and its design sensitivity. Assuming that the Krylov basis vectors remain constant with respect to the perturbation of a design variable, the FR sensitivity analysis is performed in a more efficient manner. As numerical examples, a car body with 535,992 degrees of freedom (DOF) and a 6 × 6 micro-resonator array with 368,424 DOF are adopted to demonstrate the numerical accuracy and efficiency of the suggested approach. Using the reduced-order models, we found that the FR and FR sensitivity are in a good agreement with those using the fullorder FE model. The reduction in computation time is also found to be significant because of the use of Krylov subspace-based reduced models.     

A Comparative Study of Fractional Order Models on State of Charge Estimation for Lithium Ion Batteries

State of charge(SOC) estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles. Battery fractional order models(FOMs) which come from frequency-domain modelling have provided a distinct insight into SOC estimation. In this article, we compare five state-of-the-art FOMs in terms of SOC estimation. To this end, firstly, characterisation tests on lithium ion batteries are conducted, and the experimental results are used to identify FOM parameters. Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy. The model R(RQ)W shows superior identification accuracy than the other four FOMs. Secondly, the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under di erent profiles, memory lengths, ambient temperatures, cells and voltage/current drifts. The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs. Although more complex models can have better robustness against temperature variation, R(RQ), the simplest FOM, can overall provide satisfactory accuracy. Validation results on di erent cells demonstrate the generalisation ability of FOMs, and R(RQ) outperforms other models. Moreover, R(RQ) shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.     

Finite element analysis on global and local estimation for thermo-mechanical response of EPL wafer heating

In this paper, an approach is presented for the computation of the in-plane pattern placement error (PPE) caused by the wafer heating during exposure of electron projection lithography (EPL) using the finite element method (FEM), which is one of candidates in the next-generation lithography (NGL) exposure tools. The PPE is the global and local distortion, and is the thermo-mechanical response due to the thermal deformation of the wafer in the lithography process. The prediction of PPE requires high accuracy for NGL exposure tools. The simultaneous estimation of the global and local PPE to the whole wafer of a full three-dimensional FE model using a solid element requires excessive computation time. A novel technique of numerical simulation is developed and proposed, which is the employment of a shell element combined with previously proposed the dynamic meshing technique (DMT), being possible to predict PPE in realistic computation time with high accuracy. Simulations are performed for the wafer heating of EPL effectively using three techniques, that is the equivalent average heating technique and two proposed techniques. The simulation results agree closely with the result of a full three-dimensional FE analysis, and the required computation time becomes 1/16 or much less of that.     

A computationally efficient finite element model of wire and arc additive manufacture

Wire and arc additive manufacturing (WAAM) is an emerging technology which has the potential to significantly reduce material usage and manufacturing time through the production of near net-shape components with high deposition rates. One of the main problems of this process is the residual stresses and distortions of the deposited workpiece. To help understand and optimise the process, finite element (FE) models are commonly used; however, the conventional transient models are not efficient for simulating a large-scale WAAM process. In this paper, the stress evolution during the thermal cycles of the WAAM process was investigated with the help of a transient thermomechanical FE model. It was found that the peak temperatures experienced during the thermal cycles of the WAAM process determine the residual stress of that point. Based on this finding, an efficient “engineering” FE model was developed. Compared to the conventional transient thermomechanical approach, this model can save the computational time by 99 %. This new model produced distortion and residual stress predictions that were nearly identical to the original transient model and the experimental results.     

汽车座椅安全带固定点强度试验仿真模型改进

通过对比分析有限元理论中显式积分和隐式积分两种方法的优劣,针对汽车座椅安全带拉伸试验这一准静态过程,选用LS-DYNA显式有限元程序建立国产某车型汽车安全带分析模型,通过对传统模型中单元类型、计算时间、加载曲线等关键参数进行优化,逐步提高计算仿真结果与实车安全带拉伸试验的吻合度。研究结果为优化建模精度,提高预测准确度,并进一步优化车身结构提供了较好的思路。     

Optimization of contact forces in tailor-welded blanks forming process

To attain the objective of minimizing the harmful movement of the weld joint in tailor-welded blanks (TWBs) forming, a novel optimization methodology based on dynamic explicit finite element simulation is presented to determine optimum contact forces. In this methodology, forming limit diagram (FLD) models developed for different types of TWBs are treated as a criterion of constraint in optimizations. Due to the highly nonlinear nature of the forming process, response surface methodology (RSM) is utilized to construct sequential response surfaces to approximately describe the objective the constraint functions and the optimum contact forces of TWBs stamping are obtained with some successive iterations. However, a large number of numerical simulation runs are needed for optimization with higher-order approximate models or many design variables. To improve the efficiency of optimization, the space mapping (SM) technique utilizing surrogate models is integrated with RSM. Two examples are used to validate this algorithm: one optimization for TWBs stamping with the same thickness but different materials, and the other optimization for TWBs stamping with the same material but different thicknesses. The results demonstrate that the method is efficient and effective in solving contact forces optimization problems.     

Frequency response similarity-based bolt clamping force prediction method using convolutional neural networks

This paper proposes a convolutional neural network (CNN)-based method with which to predict bolt clamping force using the frequency response of bolted structures. The dynamic characteristics of the bolted structure change with the bolt clamping force, which is predicted using a CNN trained with massive frequency response data. Big data required for training the CNN is constructed using prestressed frequency response analysis according to the clamping force of individual bolts. The numerical efficiency is increased using the Krylov subspace-based model order reduction (MOR) method. The frequency response for each set of bolt clamping forces calculated from the MOR method is converted into form of the magnitude and shape (MS) similarity spectrum by using the MS similarity function. Finally, an MS similarity map is generated by stacking the MS similarity spectrum at several output points. A CNN that is trained using massive MS similarity maps as training data, is used to predict the clamping force of bolted structures. To validate the efficiency and accuracy of a trained CNN in practical applications, the prediction results of the trained network in terms of computation time and accuracy were compared according to the size of the training input data.

     

有限元逆算法与板料成形工艺的评价

依据理想形变理论，研究开发了冲压成形过程模拟的有限元逆算法，根据变形体的整体塑性功取相对极值的条件，导出了塑算法有限元方程。提出了求逆算法初始解以及求解与给定形状的毛坯相对应的冲压件形状的迭代计算方法。采用有限元塑算法预测了与冲压件形状相对应的冲压件毛坯的展开形状，根据给定的板坯形状计算了冲压件最终构形及应变分布。分析计算实例表明，逆算法可用于对板料成形工艺方案进行快速评价，对冲压工艺参数进行优化。     

运用模块化方法建立口腔修复有限元模型

以工程领域中的模块化方法为核心建立了牙颌组织的有限元模型库。对标本进行CT扫描、数据提取、和三维重建技术建立牙颌组织的实体模型。对实体模型切分模块 ,得到一套正常牙列的模块化模型库 ,并在其基础上派生一系列反映上下颌牙生理、病理情况的模型库。上述方法可建成正常牙、牙槽骨不同程度吸收、牙周不同程度松动、缺牙区牙槽骨、固定桥修复体、可摘局部义齿修复体等有限元模型。将模块化设计与有限元方法相结合 ,可高效地生成适用于口腔修复学设计和分析的有限元模型库。     

基于中国人体特征的正面碰撞假人的开发策略探讨

采用计算机仿真方法探讨了在现有Hybrid Ⅲ假人基础上通过较少的改变来开发符合中国人体特征的假人的可行性。根据比例缩放方法建立了整体符合中国50百分位人体的假人有限元模型。考虑到中美两国人体最大差异在于四肢,且躯干全部缩放后加工难度较大,故建立了以美国人体特征为基础仅缩放假人四肢和调整部分躯干部件的假人模型,同时,改变假人的材料参数得到了另外一个假人模型。对以上三个假人模型进行碰撞仿真,结果表明,改变假人的材料参数对其碰撞响应的影响很小,而缩放假人外形尺寸对其碰撞响应影响较大,且结果显示缩放假人四肢并调整部分躯干部件的假人与缩放全体段假人的动态响应基本吻合。因此,采用部分缩放的方法来开发中国假人是可行的。     

某星载电子设备有限元分析及设计改进

文中利用ANSYS建立了某星载电子设备的有限元分析模型,对其进行模态分析,并在此基础上进行了随机振动响应分析,结果表明设备的刚强度满足系统要求.获得了某型器件安装处的加速度响应情况,结合有限元分析结果对结构进行局部设计改进,改进后最大加速度响应值降低了19.4％,并顺利通过了振动试验考核.研究表明,在设计初期采用有限元方法对设备结构性能进行仿真分析可以缩短研制周期,降低后续试验风险.     

跌落碰撞下球栅阵列无铅焊点寿命分析

基于跌落试验与有限元模拟结果进行球栅阵列(ball grid array,BGA)无铅焊点的跌落碰撞寿命分析。首先用统计学的方法,建立跌落碰撞下不同脉冲幅值与脉冲时间的BGA封装无铅焊点寿命预测模型,并通过其寿命预测模型定量评估BGA无铅焊点的跌落碰撞寿命;接着用Power原理建立一个将焊点最大拉应力与焊点失效时跌落次数联系起来的焊点寿命预测模型。无铅焊点寿命预测模型的研究对封装的设计及其可靠性提高具有一定的指导意义。     

考虑模型偏差的结构动力学模型修正

针对结构有限元模型修正后仍可能存在模型偏差的问题,提出用待修正参数的不确定性来表征模型偏差的有限元模型修正方法。首先,基于响应面方法识别得到待修正参数的最优值,并通过计算结果与试验结果比较获得模型偏差;然后,基于响应面模型并结合灵敏度分析计算得到模型偏差对待修正参数的影响,从而得到考虑模型偏差后待修正参数的区间;最后,通过一个悬臂梁工程实例的模型修正,验证了笔者所提出方法的可行性。结果表明,考虑模型偏差的修正可以提高模型可靠性。     

弹性-粘弹性复合结构动力学模型验证

研究了弹性-粘弹性复合结构的动力学有限元模型的验证问题,提出了基于频率响应的模型验证方法。以粘弹材料夹芯复合板为研究对象,分别利用Matlab软件和Msc.Patran/Nastran软件进行有限元建模和频率响应分析,结果发现两种有限元模型的频率响应曲线非常吻合。这即验证了用Matlab软件建立的有限元模型的正确性,又表明该模型验证方法是可行的。     

基于DYNAFORM的汽车覆盖件冲压仿真研究

简要介绍了汽车覆盖件冲压成形有限元模拟的动力显式求解算法和采用冲压仿真软件DYNAFORM进行汽车覆盖件冲压成形有限元仿真的步骤,并以典型覆盖件(某型号轿车的行李箱内板)为例,阐述了成形仿真的过程.实践表明,采用有限元数值仿真技术对汽车覆盖件成形过程进行模拟,并根据仿真结果进行冲压工艺规划和模具的设计,可以降低成本,缩短生产周期,提高车身质量.     

Multi-objective optimization of oblique turning operations using finite element model and genetic algorithm

Multi-objective optimization of oblique turning operations while machining AISI H13 tool steel has been carried out using developed finite element (FE) model and multi-objective genetic algorithm (MOGA-II). The turning operation is optimized in terms of cutting force and temperature with constraints on required material removal rate and cutting power. The developed FE model is capable to simulate cutting forces, temperature and stress distributions, and chip morphology. The tool is modeled as a rigid body, whereas the workpiece is considered as elastic–thermoplastic with strain rate sensitivity and thermal softening effect. The effects of cutting speed, feed rate, rake angle, and inclination angle are modeled and compared with experimental findings. FE model is run with different parameters with central composite design used to develop a response surface model (RSM). The developed RSM is used as a solver for the MOGA-II. The optimal processing parameters are validated using FE model and experiments.     

面向对象的微机电系统结构设计方法

为了解决微机电系统模型重复利用性差以及其仿真精度与计算时间的矛盾,针对微机电系统结构工作原理相似的特点,提出了面向对象的微机电系统结构设计方法.将大自由度微机电系统结构按其工作原理划分为参数化的小自由度对象,对象互相联系实现器件功能.相比于传统有限元方法,对象底层数学模型着重基于对象的功能建模和工作环境中状态的迁移原则,对象模型计算速度快且易于修改,可自由搭配重复使用.以1种音叉式微陀螺为例构造其对象模型,基于Simulink进行了时域和频域的仿真,实现了较好的解析精度和速度.     

刚塑性成形模拟中有限元和无网格迦辽金法的自动耦合算法

利用有限元法分析金属的刚塑性问题时,在变形的高梯度区域单元容易严重畸变,这极大地降低了分析精度.在刚塑性有限元方法的框架中,文中根据计算增量步的网格质量,提出金属刚塑性有限元和无网格迦辽金法的自动耦合算法,在单元严重畸变的区域转换为无网格迦辽金法进行计算.数值实例表明:算法在很大程度上既保持了有限元法的计算效率,又能够...     

薄壁覆盖件的结构优化设计

研究了薄壁覆盖件结构优化设计中的一些关键技术，包括薄壁覆盖件的结构有限分析、优化方法选择、敏度结构重分析，选择了序列二次规划法用于结构优化问题，睡敛效果较好 。以汽车车身为例，对其进行了结构优化设计，计算结果适用，所编制的软件（ＯＰＴＳＨＥＥＴ）使用方便可靠。     

减振器节流阀非线性特性的有限元模拟分析

探讨汽车筒式液阻减振器节流阀非线性动态特性的有限元分析方法。利用ADINA有限元分析软件分别建立板阀型节流阀的结构动力学模型和流体动力学模型,并利用其液一固耦合分析模块,对此耦合模型进行瞬态响应分析,得到阀的非线性节流特性、阀板的动态运动响应以及节流阀内流场特性。模拟计算结果与实验结果具有较好的一致性,节流阀在工作时开度很小,液体压力场具有强不均匀性,液体对阀板的作用力也具有不均匀性,板阀型预载阀的节流特性接近于线性,节流通道在大流量下对节流阀的特性有较大影响,