Viscoelastic and geometrically nonlinear behavior of laminated cylindrical shells

A viscoelastic and geometrically nonlinear finite element analysis is performed to investigate the stress relaxation and deflection of a laminated cylindrical shell under thermal loading. Incremental viscoelastic constitutive equations are derived to predict the stress relaxation. The finite element program is developed using a 3-D degenerated shell element, the first order shear deformation theory and the updated Lagrangian formulation. The viscoelastic and geometrically nonlinear analysis is executed for laminated shells with cross-ply and angle-ply stacking sequences, and its results are compared with those obtained from geometrically linear and viscoelastic analyses. The numerical results show that viscoelasticity and geometrical nonlinearity affect on the deflections and stresses of laminated cylindrical shells.     

Curing induced residual stresses in laminated cylindrical shells

A viscoelastic finite element analysis is presented to investigate residual stresses occurred in a laminated cylindrical shell during cure. An incremental viscoelastic constitutive equation that can describe stress relaxation during the cure is derived as a recursive formula which can be used conveniently for a numerical analysis. The finite element analysis program is developed on the basis of a 3-D degenerated shell element and the first order shear deformation theory, and is verified by comparing with an one dimensional exact solution. Viscoelastic effect on the residual stresses in the laminated shell during the cure is investigated by performing both the viscoelastic and linear elastic analyses considering thermal deformation and chemical shrinkage simultaneously. The results show that there is big difference between viscoelastic stresses and linear elastic stresses. The effect of cooling rates and cooling paths on the residual stresses is also examined.     

An optimization strategy for die design in the low-density polyethylene annular extrusion process based on FES/BPNN/NSGA-II

An optimization strategy for die design in the polymer extrusion process is proposed in the study based on the finite element simulation, the back-propagation neural network, and the non-dominated sorting genetic algorithm II (NSGA-II). The three-dimensional simulation of polymer melts flow in the extrusion process is conducted using the penalty finite element method. The model for predicting the flow patterns in the extrusion process is established with the artificial neural network based on the simulated results. The non-dominated sorting genetic algorithm II is performed for the search of globally optimal design variables with its objective functions evaluated by the established neural network model. The proposed optimization strategy is successfully applied to the die design in low-density polyethylene (LDPE) annular extrusion process. A constrained multi-objective optimization model is established according to the characteristics of annular extrusion process. The minimum of velocity relative difference, δu, and the minimum of swell ratio, S _w, that, respectively, ensure the extrinsic feature, mechanical property, and dimensional precision of the final products are taken as optimization objectives with a constrained condition on the maximum shear stress. Three important die structure parameters, including the die contraction angle α, the ratio of parallel length to inner radius L/R _i, and the ratio of outer to inner radius R _o /R _i, are taken as design variables. The Phan-Thien–Tanner constitutive model is adopted to describe the viscoelastic rheological characteristics of LDPE whose parameters are fitted by the distributions of material functions detected on the strain-controlled rheometer. The penalty finite element model of polymer melts flowing through out of the extrusion die is derived. A decoupled method is employed to solve the viscoelastic flow problem with the discrete elastic-viscous split-stress algorithm. The simulated results are selected and extracted to constitute the learning samples according to the orthogonal experimental design method. The back propagation algorithm is adopted for the training and the establishment of the predicting model for the optimization objective. A Pareto-optimal set for the constrained multi-objective optimization is obtained using the constrained NSGA-II, and the optimal solution is extracted based on the fuzzy set theory. The optimization for die parameters in the annular extrusion process of low-density polyethylene is performed and the optimization objective is successfully achieved.     

Residual stresses in a laminated shell during cure

In this paper, a viscoelastic finite element analysis was performed to investigate residual stresses occurred in a laminated shell during cure. A viscoelastic constitutive equation that can describe stress relaxation during the cure was defined as functions of degree of cure and temperature, and derived as a recursive formula used conveniently for numerical analyses. The finite element program was developed on the basis of 3-D degenerated shell element and the first order shear deformation theory, and was verified by comparing with an exact solution of the one dimensional problem. Effects of chemical shrinkage and stacking sequence on the residual stresses in the laminated shell during the cure were investigated. The results showed that there were big differences between viscoelastic stresses and linear elastic stresses calculated by considering thermal deformation and the chemical shrinkage induced by the degree of cure.     

断裂力学和有限元法在疲劳磨损研究中的应用

综述了近年来国外应用断裂力学和有限元法研究疲劳磨损的进展和现状。主要评述了以线弹性断裂力学和弹塑性断裂力学理论为基础,借助于有限元法分析疲劳裂纹的萌生、裂纹的扩展方向和扩展速率,以及疲劳磨损机理的热一机械耦合应力分析方法,目前疲劳磨损的研究主要集中于应用断裂力学建立恰当的磨损模型,用有限元法进行参数定量计算和疲劳裂纹行为的数值模拟,但关键问题在于确定合理的有限元分析模型,最后探讨了今后研究的方向。     

Vibration response and harmonic wave propagation of ultrasonic arc drivers

A piezoelectric curvilinear arc driver designed for an ultrasonic curvilinear motor is evaluated in this study. A design of piezoelectric curvilinear arc driver is proposed and its governing equations, vibration behaviour and wave propagation are investigated. Then, analysis of forced vibration response or driving characteristics to harmonic excitations in the modal domain is conducted. Finite element modelling and analysis of the arc driver are also discussed. Analytical results of free vibration characteristics are compared favourably with the finite element results. Harmonic analyses of the three finite element models reveal changes of dynamic behaviours of three models and also imply operating frequencies with a significant travelling wave component. Parametric study of mathematical and finite element simulation results suggests that stable travelling waves can be generated to drive a rotor on the proposed curvilinear arc motor system.     

Enriched finite element method for three-dimensional viscoelastic interface crack problems

The enriched finite element method is developed for three-dimensional problems of an interface crack between elastic and viscoelastic (including dissimilar viscoelastic) materials. According to the displacement fields of elastic interface crack, the displacement fields of viscoelastic interface crack are derived through the correspondence principle. By incorporating the displacement expressions into the displacement model of regular element, the incremental formulations of enriched element are derived. The stress intensity factors and strain energy release rates can be solved based on the enriched degree of freedoms. A 3-D through interface crack at the center of jointed dissimilar viscoelastic plate subjected to remote tension and a quarter-circular viscoelastic interface corner crack subjected to uniform thermal loading was investigated using the enriched finite element method. It is shown that the present solutions are consistent with the analytical solutions, which indicates the present method is correct and efficient.

     

An efficient modeling methodology of structural systems containing viscoelastic dampers based on frequency response function substructuring

In this paper it is suggested a modeling methodology of structural systems supported by translational and rotational viscoelastic mounts or joints based on a frequency response function coupling technique. Such strategy enables to predict the dynamic behaviour of the composite systems given a set of frequency response functions of the main structure and a driving point frequency response function of the viscoelastic support. These frequency response functions can be obtained either experimentally or by finite element modeling. Both cases are considered in the study. After presenting the underlying theoretical aspects, the results of numerical simulations of two-dimensional structures are presented, emphasizing the procedure conceived to compute the frequency response functions of the viscoelastic mounts or joints from a detailed finite element model using commercial packages and material properties provided by manufacturers. The dependency of the viscoelastic behaviour on frequency and temperature is accounted for by using the complex modulus approach and the concepts of reduced frequency and shift factor. An investigation using experimentally acquired frequency response functions of a frame structure with a translational viscoelastic damper is presented. Based on the obtained results, the main features of the modeling methodology are highlighted.     

Stability loss analyses of the elastic and viscoelastic composite rotating thick circular plate in the framework of the three-dimensional linearized theory of stability

In the present paper, in the framework of the three-dimensional linearized theory of stability the rotationally symmetric stability loss problems of the elastic and viscoelastic composite rotating thick circular and annular discs are investigated. The method for solution to these problems is developed by employing Laplace transform and finite element method. It is supposed that the disc and annular disc have an insignificant rotationally symmetric initial imperfection and as a stability loss criterion, the case where this imperfection starts to increase and grows indefinitely, is taken. Numerical results related to the critical angular velocity for elastic problems and to the critical time for viscoelastic problems are presented.     

Use of simple finite elements for mechanical systems impact analysis based on stereomechanics, stress wave propagation, and energy method approaches

This paper examines the effectiveness of analyzing impact events in mechanical systems for design purposes using simple or low ordered finite elements. Traditional impact dynamics analyses of mechanical systems namely stereomechanics, energy method, stress-wave propagation and contact mechanics approaches are limited to very simplified geometries and provide basic analyses in making predictions and understanding the dominant features of the impact in a mechanical system. In engineering practice, impacted systems present a complexity of geometry, stiffness, mass distributions, contact areas and impact angles that are impossible to analyze and design with the traditional impact dynamics methods. In real cases, the effective tool is the finite element (FE) method. The high-end FEA codes though may be not available for typical engineer/designer. This paper provides information on whether impact events of mechanical systems can be successfully modeled using simple or low-order finite elements. FEA models using simple elements are benchmarked against theoretical impact problems and published experimental impact results. As a case study, an FE model using simple plastic beam elements is further tested to predict stresses and deflections in an experimental structural impact.     

弹性机构振动被动控制中模态损耗因子的确定

针对组成弹性机构的特点,给出了一种描述组成弹性机构的２节点８自由度约束阻尼平面刚架单元的形函数,建立了含大阻尼材料时弹性机构的动力学方程,基于此研究了弹性连杆机构模态损耗因子的预测问题。文中方法概念清晰、计算简单、预测可靠。可用于解决阻尼处理中的机构结构参数的优化设计问题。     

Enriched finite element method for 2-D and 3-D blunt crack problems in a viscoelastic medium

The analysis of two-dimensional and three-dimensional blunt crack problems in a linear viscoelastic medium is numerically investigated using the enriched finite element method. The enriched crack-tip elements are established by enriching the asymptotic displacement fields at the blunt crack front to the regular elements. The corresponding transition elements are formulated to eliminate displacement field incompatibility. The viscoelastic incremental formulations for the enriched finite element method in time domain are derived according to the Boltzmann superposition principle. The time-dependent deformations of crack are presented and the stress intensity factors are directly obtained from the enriched degree of freedoms. The numerical examples indicate that the enriched finite element method is extremely suitable for dealing with complicated blunt crack problems.     

基于粘弹本构模型的注射成型充填过程模拟研究

为反映聚合物粘弹属性对注塑产品质量的影响,基于粘弹本构模型,对三维薄壁制件的注射成型充填过程进行了数值模拟研究。针对三维薄壁件,经合理简化假设,建立了其充填成型过程的数学模型,采用不可压缩Leonov粘弹本构模型。采用有限元/有限差分法来求解压力场和温度场,采用控制体积法来实现前沿界面跟踪,采用4阶龙格-库塔方法求解弹性应变张量。以一薄壁圆盘为例,对其注射充填过程中的充填时间及压力、剪切应力和第一法向应力差分布进行了数值模拟。模拟结果与前人的实验结果吻合较好,说明了本文建立的模型和数值方法的有效性及可靠性。     

高阻尼无加强U形减振波纹管研究

利用粘弹阻尼技术,研制了一种减振降噪性能更优的高阻尼无加强U形减振波纹管。本文应用I-deas工程分析软件对高阻尼无加强U形减振波纹管的振动特性进行了分析,通过波纹管粘弹阻尼结构设计、计算机有限元模型的建立及波纹管固有频率、减振效果的计算机仿真计算,得到了高阻尼无加强U形减振波纹管振动特性的计算机仿真计算方法,同时,其计算结果得到了试验验证。     

Modélisation,identification et simulations éléments finis des phénomènes de délaminage dans les structures composites stratifiées

Modelling, identification and finite element predictions of delamination in laminated composite structures. In order to forecast the delamination initiation and propagation in a finite element context, a previously defined damage meso-modelling of composite laminates is used. At the meso-level, the laminate is described as an assembly of damageable layers and interlaminar interfaces. The present work concerns the modelling, the identification and the finite element predictions of delamination phenomena in composite structures. Finite element predictions are conducted with non-linear geometric and material hypothesis. The interface modelling is implemented in the finite element code Castem 2000 developped by CEA. Classic edge delamination tension and propagation tests are conducted in order to improve the interface damage model approach in the finite elements context.     

On the use of damped updated FE model for dynamic design

Model updating techniques are used to update the finite element model of a structure, so that updated model predicts the dynamics of a structure more accurately. The application of such an updated model in dynamic design demands that it also predicts the effects of structural modifications with a reasonable accuracy. Most of the model updating techniques neglect damping and so these updated models cannot be used for predicting amplitudes of vibration at resonance and antiresonance frequencies. This paper deals with updating of the finite element model using the FRF data with damping identification using complex modal data and its subsequent use for predicting the effects of structure modifications. The updated model is obtained in two steps. In the first step, mass and stiffness matrices are updated using FRF-based model updating method. In the second step, damping is identified using updated mass and stiffness matrices, which are obtained in first step. Structural modifications in terms of mass and beam modifications are then introduced to evaluate the updated model for its usefulness in dynamic design.     

复合材料低模量蒙皮结构的损伤特性探讨

低模量蒙皮设计概念是改进复合材料结构损伤容限特性的一种有效的设计方法。它不仅可用于改善结构在拉伸、剪切载荷下的损伤容限特性 ,同时也可提高蒙皮的抗冲击损伤特性。本文主要对用低模量蒙皮设计概念设计的复合材料壁板在拉伸和剪切载荷作用下的损伤扩展特性、剩余强度及其设计方法进行探讨。     

Stochastic model updating—Covariance matrix adjustment from uncertain experimental modal data

With deterministic methods finite element model parameters are updated by using a single set of experimental data. As a consequence the corrected analytical model only reflects this single test case. However, test data are inherently exposed to uncertainty due to measurement errors, different modal extraction techniques, etc. Even a more relevant factor for variability originates from production tolerances and consequently the question arises, how to describe model parameters from the stochastic point of view? Therefore it would be desirable to use statistical properties of multiple sets of experimental and to consider the update parameters as random variables. This paper presents an inverse approach how to identify a stochastic finite element model from uncertain test data. In detail, this work demonstrates a method to adjust design parameter means and their related covariance matrix from multiple sets of experimental modal data. Results are shown from a numerical example.     

Interval model updating with irreducible uncertainty using the Kriging predictor

Interval model updating in the presence of irreducible uncertain measured data is defined and solutions are made available for two cases. In the first case, the parameter vertex solution is used but is found to be valid only for particular parameterisation of the finite element model and particular output data. In the second case, a general solution is considered, based on the use of a meta-model which acts as a surrogate for the full finite element mathematical model. Thus, a region of input data is mapped to a region of output data with parameters obtained by regression analysis. The Kriging predictor is chosen as the meta-model in this paper and is found to be capable of predicting the regions of input and output parameter variations with very good accuracy. The interval model updating approach is formulated based on the Kriging predictor and an iterative procedure is developed. The method is validated numerically using a three degree of freedom mass-spring system with both well-separated and close modes. A significant advantage of Kriging interpolation is that it enables the use of updating parameters that are difficult to use by conventional correction of the finite element model. An example of this is demonstrated in an experimental exercise where the positions of two beams in a frame structure are selected as updating parameters.     

关键几何参数对药柱贮存刚度的影响分析

基于粘弹性理论,利用ANSYS有限元软件,建立药柱结构的有限元模型,确定影响药柱贮存刚度的关键几何参数,对不同药柱结构贮存期内的药柱刚度进行分析,研究不同几何参数对药柱贮存刚度的影响敏感度,为药柱结构完整性设计提供理论分析与研究基础。