圆管状立体机织复合材料的多尺度分析

采用多尺度耦合的数值模型研究了圆管状立体机织复合材料的力学性能。建立了反映纤维束中纤维/基体二相材料的微观尺度单胞和反映周期性编织结构的细观尺度扇形单胞,并重点讨论了扇形单胞的周期性边界条件。通过逐级计算微观单胞、细观单胞的平均弹性常数,得到了圆管状立体机织复合材料的刚度参数,实现了由组分材料性能及编织参数预测圆管的宏观弹性性能,模型预测刚度与试验结果吻合。另一方面,研究了从大到小各尺度耦合的应力分析,对于圆管环向应力非周期分布的情况,建立了嵌入细观单胞的环状模型,进行了复杂荷载下从宏观圆管结构、到细观纤维束尺度、再到微观纤维尺度之间的逐级应力分析。     

三维机织复合材料多尺度黏弹性分析

建立了一种三维机织复合材料多尺度的黏弹性分析模型。首先构造了微观尺度纱线束胞元和细观尺度复合材料周期结构胞元两级有限元模型, 由微观尺度胞元分析得到纱线束的弹性常数, 再代入细观尺度胞元计算出复合材料的平均弹性常数。两级胞元模型均施加周期边界条件, 保证了胞元边界上位移和应力满足周期性和连续性。随后分别建立了树脂基体和浸润树脂纱线束的蠕变模型, 用实验标定树脂的蠕变参数, 代入微观尺度胞元进行蠕变计算来修正纱线束蠕变模型的参数。最后将树脂和纱线束的蠕变本构关系应用于细观尺度胞元, 得到材料宏观平均的应力-应变响应, 模拟了三维机织复合材料的蠕变实验曲线。本文模型对于该种复合材料弹性常数和蠕变性能的预测, 均与实验吻合。      

二维二轴1×1编织复合材料细观结构模型及力学性能有限元分析

考虑纤维束相互挤压及横截面形状变化, 采用纤维束截面六边形假设, 建立了二维二轴1×1编织复合材料的参数化单胞结构模型。通过引入周期性位移边界条件, 基于细观有限元方法, 对编织材料的弹性性能进行预测, 讨论了编织角及纤维体积含量对面内弹性常数的影响, 并分析了典型载荷下单胞细观应力场分布。研究表明: 单胞结构模型有效反映了纤维束的空间构型和交织特征, 实现了不同编织工艺参数下模型的快速建立; 基于单胞有限元模型的弹性性能预测结果与试验结果较为吻合; 模型给出了单胞合理的应力场分布, 为二维编织复合材料的结构优化和损伤预测奠定基础。      

三维机织复合材料的一种梁单元细观力学模型

根据三维机织复合材料中纤维束排列和变形的周期性特点,推导了一种细观梁单元模型。该模型考虑了纤维束的拉 (压) 弯耦合效应和纤维束之间的相互作用,可以描述纤维束和基体中的细观应力分布,并得到宏观的力学性能。针对一种典型的三维机织复合材料,首先根据编织参数,确定其细观几何结构,取最小周期的一段纤维束作为分析胞元,用上述细观梁单元分析了该段纤维束在面内拉伸荷载下的细观应力分布,计算出平均模量, 并用材料试验和细观实体有限元对本模型进行了检验,结果与本文的预测吻合良好。研究表明,拉、弯耦合效应引起的纤维束中的细观弯曲应力同平均轴向应力相比,不可忽略。      

三维五向编织复合材料的力学性能分析Ⅱ: 细观应力数值模拟

在实验观察的基础上, 考虑轴纱的挤压变形及纱线填充因子变化, 修正了现有的细观结构模型, 建立了更加真实反映三维五向编织复合材料内部编织结构的单胞模型。利用该模型采用3D 有限元法计算了材料的轴向弹性模量, 数值预测与实验数据吻合较好。分析了单胞在拉伸载荷作用下的细观应力分布, 为材料进一步的强度预测奠定了基础。      

基于均匀化理论的三维编织复合材料弯曲细观应力数值模拟

从基于小参数渐近展开的多尺度均匀化理论出发,对三维编织复合材料的弯曲细观应力进行数值模拟。首先给出了等效弹性模量和细观应力的均匀化列式及有限元求解方程,然后讨论了三维编织复合材料细观单胞周期性边界条件的施加方法,最后对三点弯曲作用下三种单胞内应力分布进行了数值模拟。通过模拟比较了不同类型单胞及不同编织角材料弯曲应力的差异,总结出一些有益的结论,这些结论与实验结论都比较吻合。     

三维四向编织复合材料界面损伤机理数值分析

考虑界面脱粘表面压应力下摩擦力对材料界面力学性能的影响,建立损伤-摩擦相结合的界面本构模型,编写用户材料子程序VUMAT,实现其在有限元软件ABAQUS中的嵌入。基于周期性胞元分析思想,在单胞模型中纤维束/基体、纤维束/纤维束分界面引入界面单元,结合损伤-摩擦相结合的界面本构模型,建立含界面相三维四向编织复合材料的细观有限元模型。模拟典型载荷下界面损伤的起始和扩展过程,分析界面应力传递和界面破坏机理,研究界面性能对复合材料宏细观力学性能的影响规律,为实现三维四向编织复合材料界面性能优化设计和控制提供参考。      

三维六向编织复合材料渐进损伤模拟及强度预测

基于三维六向编织复合材料的细观结构,假设第六向纱线的截面形状为菱形,建立了三维六向编织复合材料的渐进损伤有限元模型。采用Linde等提出的失效准则,引入周期性位移边界条件,对三维六向编织复合材料的纵向拉伸应力-应变行为进行了渐进损伤数值模拟,讨论了单胞模型在纵向拉伸载荷作用下的细观损伤起始、扩展和最终失效的演化过程,并预测了材料的拉伸强度。在此基础上,进一步研究了编织角、纤维体积分数和编织纱水平取向角等参数对材料纵向拉伸力学性能的影响规律。研究结果表明,三维六向编织复合材料的轴向纱线拉伸断裂是导致其破坏的最主要因素。所得数值结果与现有试验值吻合较好,验证了该模型的有效性,为更深入研究此类材料的力学性能奠定了基础。     

高抗冲聚苯乙烯银纹化渐进损伤三维模拟

针对高抗冲聚苯乙烯,本文建立了细观单胞结构三维模型,引入周期性边界条件,采用非线性有限元法,研究了在单向拉伸载荷下银纹化损伤过程。采用最大主应力准则作为银纹化损伤判据,通过受损单元积分点刚度矩阵的折减实现材料力学性能的退化,运用材料的应力-应变曲线预测了其力学性能。数值结果与相关文献模拟结果吻合,表明本文损伤预测三维模型的合理有效性。     

缝合复合材料的细观力学分析

采用三维细观有限元模型,研究了缝合复合材料的力学性能.模型中引入了保证单胞边界面的应力和位移周期连续的边界条件,分析了缝合对层合板面内力学性能的影响,着重考察了缝合区域内细观应力和应变的分布,以及缝合对材料弹性常数的影响,并分析了缝线附近和富树脂区应力集中的规律.算例结果表明本文方法可以有效地预测缝合复合材料的弹性性能.研究还发现,受面内剪切作用时原来单胞的平面边界不再保持平面,各层间铺设角度相差越大,单向拉伸时应力集中现象越显著.     

2.5维C/SiC复合材料经向拉伸性能

将微观尺度的强度预测模型与单胞尺度有限元模型相结合, 建立了2.5维C/SiC复合材料的双尺度强度预测模型。该模型首先计算微观尺度的应力-应变曲线以及最终失效时的力学性能, 然后将其带入单胞模型, 对不同边界条件下单胞模型的弹性模量进行折减, 统计单胞模型的平均应力与应变, 最后得到单胞尺度的应力-应变关系和最终失效时的力学性能。通过2.5维C/SiC复合材料常温和高温条件下的经向单轴拉伸试验, 得到了2.5维C/SiC复合材料经向拉伸过程的应力-应变曲线以及最终失效时的力学性能。结果表明, 理论分析结果与实验值基本一致, 验证了该方法的有效性。     

Finite Element Analysis of Mechanical Properties of 3D Four-directional Rectangular Braided Composites—Part 2: Validation of the 3D Finite Element Model

In the first part of the work, we have established a new parameterized three-dimensional (3D) finite element model (FEM) which precisely simulated the spatial configuration of the braiding yarns and considered the cross-section deformation as well as the surface contact relationship between the yarns. This paper presents a prediction of the effective elastic properties and the meso-scale mechanical response of 3D braided composites to verify the validation of the FEM. The effects of the braiding parameters on the mechanical properties are investigated in detail. By analyzing the deformation and stress nephogram of the model, a reasonable overall stress field is provided and the results well support the strength prediction. The results indicate it is convenient to predict all the elastic constants of 3D braided composites with different parameters simultaneously using the FEM. Moreover, the FEM can successfully predict the meso-scale mechanical response of 3D braided composites containing periodical structures.     

上模压下速度对带阻尼台叶片精锻影响的研究

利用DEFORM-3D,采用刚粘塑性有限元法,建立了带阻尼台叶片精锻过程的三维有限元模型,模拟分析了上模压下速度对带阻尼台叶片精锻过程的影响规律.获得了不同上模压下速度时的等效应力、最大主应力等场变量分布及带阻尼台叶片精锻过程载荷-行程曲线,并根据最大主应力分布提出了对终锻坯料形状设计的建议.研究结果对带阻尼台叶片精锻工艺的制订具有重要的指导意义.     

A Numerical-analytic Method for Quickly Predicting Springback of Numerical Control Bending of Thin-walled Tube

Springback is one of important factors influencing the forming quality of numerical control （NC） bending of thin-walled tube. In this paper, a numerical-analytic method for springback angle prediction of the process was put forward. The method is based on springback angle model derived using analytic method and simulation results from three-dimensional （3D） rigid-plastic finite element method （FEM）. The method is validated through comparison with experimental results. The features of the method are as follows： （1） The method is high in efficiency because it combines advantages of rigid-plastic FEM and analytic method. （2） The method is satisfactory in accuracy, since the field variables used in the model is resulting from 3D rigid-plastic FEM solution, and the effects both of axial force and strain neutral axis shift have been included. （3） Research on multi-factor effects can be carried out using the method due to its advantage inheriting from rigid-plastic FEM. The method described here is also of general significance to other bending processes.     

Local Buckling Delamination of a Rectangular Sandwich Plate Containing Interface Embedded Rectangular Cracks and Made From Elastic and Viscoelastic Materials

A three-dimensional buckling delamination problem for a rectangular sandwich plate made from elastic and viscoelastic materials is studied. It is supposed that the plate contains interface embedded rectangular cracks and that the edge-surfaces of these cracks have initial infinitesimal imperfections. The evolution of these initial imperfections with an external bi-axial compressed force (for the case where the materials of the layers of the plate are elastic) or with duration of time (for the case where the materials of the layers of the plate are viscoelastic) is investigated. The corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model with the use of three-dimensional geometrically nonlinear field equations of the theory of viscoelastic bodies. This problem is solved by employing boundary form perturbation techniques, Laplace transform and FEM. According to the initial imperfection criterion, the values of the critical parameters are determined. Numerical results on the critical force and critical time are presented and discussed. In particular, it is established that the values of the critical forces obtained for the buckling delamination around the rectangular embedded interface cracks are significantly greater than those obtained for the corresponding edge and band cracks.     

基于三维有限元法的层合圆柱壳应力分析

针对空间结构中常见的蜂窝夹芯壳体提出了一种32节点相对自由度三层壳元,以及一种精确计算层间应力的后处理方案。这种32节点壳元可以更好地反映结构固有的特性,易与三维实体单元相连接,使变厚度、带有补强的蜂窝夹芯复合材料壳体等复杂结构问题得以正确建模。本文作者的后处理方案克服了位移有限元层间应力不连续的缺点,保证了应力精确满足边界条件。综合运用以上方法的典型算例表明:计算精度是令人满意的。     

爆破荷载作用下岩石边坡动态响应的FLAC3D模拟研究

已有的岩石边坡爆破动力响应分析多用有限单元法.作者尝试运用FLAC3D的动力分析模块进行岩石边坡爆破动力响应分析.建立了能够反映主要地质构造的三维岩石边坡数值模型.介绍了三维有限差分程序FLAC3D动力分析的理论基础,包括边界条件的设定、动力荷载的输入、阻尼的选取以及岩体本构模型的选择.采用FLAC3D模拟了该岩石边坡在爆破荷载作用下的动态响应.分析了爆破结束后边坡体内位移场、应力场、速度场以及塑性区的分布情况,并与爆破前进行对比.将计算结果与实测数据进行了比较,结果表明FLAC3D用于爆破荷载作用下岩石边坡动态响应的数值模拟是可行的.     

Hygrothermo-mechanical buckling of FGM plates resting on elastic foundations using a quasi-3D model

Hygrothermal and mechanical buckling responses of functionally graded (FG) plates resting on Winkler–Pasternak’s foundations are presented in this paper using a refined quasi-3D model. The effects due to transverse normal strain and shear deformation are both included. The present model exactly satisfies stress boundary conditions on the upper and lower surfaces of the FG plate without using shear correction factors. It is assumed that the material properties vary according to a power law of the thickness coordinate variable. The hygrothermal buckling equilibrium equations are derived from the principle of virtual work for FG plates resting on Winkler–Pasternak’s foundations with simply-supported boundary conditions. Two types of thermal and hygrothermal loading, uniform thermal and hygrothermal rise, linear thermal and hygrothermal distribution through the thickness are considered. Numerical results are presented to verify the accuracy of the present study. The effects played by Winkler–Pasternak’s parameters, plate aspect ratio, side-to-thickness ratio, gradient index, and loading type on the critical buckling of the FG plates are all investigated.     

Distributions of electric and elastic fields at domain boundaries

In this paper we describe the application of the finite element method (FEM) in modelling spatial distributions of electric and elastic fields in a ferroelectric crystals with two domains separated by a 90° domain wall. The domain boundary is idealized as a two-dimensional defect in an electro-elastic continuum. It represents the source of inhomogenity and internal distortion in both elastic and electric fields. The main results are distributions of electric field, strain and mechanical force along the domain boundary.     

Implicit boundary method for analysis using uniform B‐spline basis and structured grid

Several analysis techniques such as extended finite element method (X‐FEM) have been developed recently, which use structured grid for the analysis. Implicit boundary method uses implicit equations of the boundary to apply boundary conditions in X‐FEM framework using structured grids. Solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary. In this paper, this method is applied for analysis using uniform B‐spline basis defined over a structured grid. Solution structures that are C¹ or C² continuous throughout the analysis domain can be constructed using B‐spline basis functions. As a structured grid does not conform to the geometry of the analysis domain, the boundaries of the analysis domain are defined independently using equations of the boundary curves/surfaces. Compared with conforming mesh, it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted. Numerical examples are presented to demonstrate the performance of these B‐spline elements. The results are compared with analytical solutions as well as with traditional finite element solutions. Convergence studies for several examples show that B‐spline elements provide accurate solutions with fewer elements and nodes compared with traditional FEM. They also provide continuous stress and strain in the analysis domain, thus eliminating the need for smoothing stress/strain results. Copyright © 2008 John Wiley & Sons, Ltd.