基于Layerwise理论的共固化粘弹阻尼复合材料动特性分析

共固化粘弹性复合材料兼具结构承载和阻尼减振功能。针对传统的混合单元法在应用于粘弹性夹层复合材料结构阻尼性能分析时存在着前处理困难、计算规模大、精度低以及难以考虑正交各向异性铺层自身损耗能力的缺点,推导了一种基于Layerwise离散层理论的四节点四边形复合材料层合板单元,并利用直接复特征值解法建立了共固化粘弹性复合材料结构的阻尼性能分析方法。将该方法应用于不同的阻尼结构,分析结果与文献中已公开结果和混合单元法的计算结果进行了对比验证。结果表明,基于离散层理论的层合板单元具有计算精度高、前处理建模简单和计算规模小的优点,可有效应用于复杂共固化粘弹性复合材料结构的阻尼性能分析和设计。     

A GENERALIZED NEWTON METHOD FOR HIGHER-ORDER FINITE ELEMENT APPROXIMATIONS IN NON-LINEAR ELASTICITY

A generalized Newton method is proposed in conjunction with a higher-order Lagrangian finite element discretization of bodies undergoing finite elastic deformations. The method is based on a gradient-like modification of the Newton method, designed to suppress the sensitivity of higher-order elements during the early iterations, thus allowing for solutions to be obtained using moderately large step-sizes.     

A THREE-DIMENSIONAL FINITE ELEMENT FORMULATION FOR THERMOVISCOELASTIC ORTHOTROPIC MEDIA

This paper is concerned with the development of a numerical algorithm for the solution of the uncoupled, quasistatic initial/boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral form involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the finite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the finite element solution. Use is made of a Dirichlet–Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method. © 1997 John Wiley & Sons, Ltd.     

周期复合材料压电问题的双尺度数值模拟

利用渐近展开的方法对具有一般周期结构的复合材料中描述压电现象的电势与位移建立了二阶双尺度渐近展开式及边界层解, 得到了局部单胞内电场与位移场的相互耦合关系, 并给出了复合材料中电势与位移的双尺度结合边界层的有限元计算方法。数值算例表明了该方法的可行性与高效性。      

正交各向异性平面问题边界元——边境元素法研究

在文献[1]中,本文作者研究了正交各向异性平面问题边界元素法的有关基本理论和计算公式,在上述工作的基础上,本文进一步研究各向异性平面问题边界邻域的应力分析。当采用边界元素法分析应力时,由于边界积分的奇异性,边界邻域应力的计算结果往往存在一定误差。为解决此问题,本文提出一个基于修正余能原理的所谓边境元素,包括四节点边境元素、八节点边境元素和三节点边境元素等。在边界元素法求解的基础上,进一步利用本文所述边境元素法,得到了非常满意的计算结果。      

Experimental/Numerical Analyses of a Viscoelastic Body under Rolling Contact

In this paper, the authors discuss the first step in theapproach to the fundamental mechanism of small-scale local wear/fracturenear the contact surface between a viscoelastic body and a rigidtraveling roller. A rectangular viscoelastic strip made of epoxy resinwas loaded by a cylindrical hard roller moving along the upper straightedge. A convenient photoviscoelastic method using computer immageprocessing was applied to investigate the time-dependent stress andstrain around a contact region under a typical type of non-proportionalloading conditions. On the other hand, the finite element method (FEM)was used to analyze the viscoelastic stress and strain under the severalconditions. The results obtained from the two methods qualitativelycompared the time variation for the photoviscoelastic fringe patternsand the contour bands of stress/strain distribution patterns. Moreover,the time variation for principal stress differences, principal straindifferences and the directions of principal stress/strain undernon-proportional conditions, were evaluated, at which time the materialshowed remarkable viscoelastic and rubber-like properties.     

纤维增强塑料齿轮轮齿弯曲强度分析

本文由纤维增强塑料齿轮轮齿的细观结构建立了各向异性粘弹性力学的计算模型,采用Laplace变换和有限单元法相结合求解轮齿的粘弹性应力场。通过引入时间折算因子,改进了Schapery的数值反演过程,给出了一个可行的复合材料齿轮弯曲强度实用分析方法。     

纤维增强塑料齿轮轮齿弯曲强度分析

本文由纤维增强塑料齿轮轮齿的细观结构建立了各向异性粘弹性力学的计算模型,采用Laplace变换和有限单元法相结合求解轮齿的粘弹性应力场。通过引入时间折算因子,改进了Schapery的数值反演过程,给出了一个可行的复合材料齿轮弯曲强度实用分析方法。      

有限元法在粉末成形中的应用

对粉末成形的本构方程和有限元列式进行了系统全面的推导,并详细分析和讨论了有限元法分析粉体成形时的关键技术及目前粉末成形数值模拟存在的问题。     

Time-Dependent Compressive Strength of Unidirectional Viscoelastic Composite Materials

The strength of unidirectional composites is often lower in compressionthan in tension, making compressive strength an especially importantdesign criterion. Compressive strength in the fiber direction depends onthe stiffness of the matrix material, which softens over time due toviscoelastic effects, and thus lowers the strength of the composite.This reduction must be accounted for in assessing the long-termdurability of composite structures.The dependence of compressive strength on time and temperature hasbeen investigated for a unidirectional carbon/epoxy composite material.Experimental results for strength versus time are compared withanalytical predictions based on a one-dimensional fiber microbucklingmodel and numerical results from finite element analysis.     

摩擦力和样品厚度对压痕法测量生物试样弹性的影响

生物试样的弹性测量可为生物体疾病的早期诊断和治疗提供依据。利用压痕法对生物试样的弹性进行了测量,并用有限元软件对压痕过程进行了模拟。研究发现,试样厚度对弹性测量存在影响,试样厚度越大,测量结果越接近试样真实的杨氏模量。当试样厚度为压痕深度的75倍时,测量误差仅为0.74%。又研究了压头速度对弹性测量结果的影响。研究发现,当压头速度较大时,由于摩擦力的作用,测量结果与试样弹性的真实值之间存在一定的差异。在模拟过程中添加摩擦力可准确反演试样的弹性,误差在5%以下。     

A finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh

A Finite Volume (FV) procedure is described for solving the elastic solid mechanics equations in three dimensions on an unstructured mesh, for bodies undergoing thermal or mechanical loads. The FV procedure is developed in parallel with the conventional FE Galerkin procedure so that the differences in each approach may be clearly distinguished. The matrix form of the FV procedure is described, and is implemented in parallel with the FE procedure, both for two-dimensional quadrilateral and three-dimensional brick meshes. The FV and FE procedures are then compared against a range of benchmark problems that test the basic capability of the FV technique. It is shown to be approximately as accurate as the FE procedure on similar meshes, though its system matrix set-up time is twice as long for a node by node set-up procedure.     

VPF粘性介质粘弹性本构关系研究

为研究粘性介质的力学性能对板材变形的影响,通过剪切蠕变-回复和松弛试验分析了甲基乙烯基粘性介质的流变性能.实验结果表明粘性介质可以简化为线性粘弹性材料.建立了粘性介质的积分型粘弹性本构方程,并结合剪切蠕变-回复过程的有限元分析确定了方程中的材料参数.利用该本构方程对粘性介质压力胀形过程进行了有限元分析,模拟结果与试验结果对比表明,所建立的本构方程可以较好的预测板材的变形过程.     

非线性拟双曲方程的有限元配置法数值分析

基于有限元配置法,采用分片双三次Hermite插值多项式空间作为逼近函数空间,本文对粘性振动及神经传播过程中涉及的一类非线性拟双曲方程的初边值问题建立了二维半离散和全离散格式.并对两种格式证明了数值解的存在唯一性,应用微分方程先验估计的理论和技巧得到了L2模最佳阶误差估计.数值实验结果表明:所提方法在保证整体误差估计要求且不增加计算量的前提下,比传统有限元方法有更高的逼近精度,并扩展了配置法的应用范围.     

Twenty-four–DOF four-node quadrilateral elements for gradient elasticity

Computational analysis of gradient elasticity often requires the trial solution to be C¹, yet constructing simple C¹ finite elements is not trivial. In this paper, three four-node 24-DOF quadrilateral elements for gradient elasticity analysis are devised by generalizing some of the advanced element formulations for thin-plate analysis. These include the discrete Kirchhoff method, a relaxed hybrid-stress method, and the hybrid-stress method with equilibrating internal force modes. The first two methods start with the derivation of a C⁰ displacement, which is quadratic complete in the Cartesian coordinates. In the first method, at the midside points are derived and interpolated together with those at the nodes. Strain is derived from the displacement interpolation yet the second-order displacement derivatives are derived from the displacement-gradient interpolation. In the second method, only the assumed constant double-stress modes are employed to enforce the continuity of the normal derivative of the displacement. In the third method, the equilibrating internal force modes require the C¹ displacement to be defined only along the element boundary and the domain interpolation can be avoided. Patch test involving linear stress and constant double stress as well as other tests are presented to validate the proposed elements.     

大尺寸超声振动体的研究

文章中介绍了大尺寸超声振动体的研究进展。包括分析耦合振动的表观弹性法;用表观弹性法对短圆柱体、空心圆柱体和矩形六面体的振动进行分析;用开槽、开狭缝、附加弹性体和二次设计等方法对超声振动体的振动进行控制。对有关结果与用有限元方法进行计算的结果进行了比较,并作出了评价。