深海采矿柔性立管系统非线性有限元模拟

在海洋环境载荷及集矿机牵引作用下,深海采矿柔性立管系统的动力学响应涉及几何非线性和非保守载荷的双重非线性源.基于三维固体有限变形理论建立数学模型,在完全拉格朗日格式下推导了系统运动平衡方程,针对非保守载荷的等效计算、非线性切线刚度矩阵及非线性方程的数值求解等关键问题提出了有效处理方案.根据处理方案开发了数值计算程序,并...     

多孔硅橡胶材料有限元计算的切线本构矩阵

为进行多孔硅橡胶材料非线性有限元计算，针对用伸长比表示的应变能函数，推导了多孔硅橡胶材料非线性有限元计算中切线本构关系的具体形式。并采用便于编程的矩阵记法，给出了非线性有限元计算中克希荷夫应力和格林应变之间的切线关系式。     

基于牛顿-拉夫逊的拉压不同模量问题的数值求解

针对拉压模量不同引起的材料本构非线性,首先,通过引入改进的Heaviside函数将本构方程连续光滑化;然后,基于特征值与特征向量的求导策略,推导有限元求解模型中切线刚度矩阵的列式;最终,提出基于牛顿-拉夫逊迭代格式的拉压不同模量问题的数值求解算法。数值算例验证了本文算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于工程分析中大规模计算问题的求解。     

基于牛顿-拉夫逊的拉压不同模量问题的数值求解

针对拉压模量不同引起的材料本构非线性,首先,通过引入改进的Heaviside函数将本构方程连续光滑化;然后,基于特征值与特征向量的求导策略,推导有限元求解模型中切线刚度矩阵的列式;最终,提出基于牛顿-拉夫逊迭代格式的拉压不同模量问题的数值求解算法。数值算例验证了本文算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于工程分析中大规模计算问题的求解。     

基于欧拉描述的两节点索单元非线性有限元法

本文针对柔性悬索结构几何非线性分析的特点,提出了一种用欧拉描述来表示的两节点索单元非线性有限元模型,在索元变形后的位置上由虚功能建立了非线有限元基本方程及切线刚度矩阵。这样建立的非线性有限元分析方法可充分考虑拉索的几何非线性特性的影响并给悬索结构的初始平衡分析带来方便,算例结果表明,本文方法是精确有效的。     

四节点二十四自由度平板壳单元几何刚度矩阵显式解析式的推演算法研究

几何刚度矩阵的推演是结构几何非线性有限元分析的重点和难点之一。推导几何刚度矩阵显式解析表达式成为简化非线性有限元列式,提高分析效率的关键。本文在协同转动法框架下,基于刚体运动法则对四节点二十四自由度的平板壳单元几何刚度矩阵显式解析式进行了推导和讨论;分析了悬臂梁大转动、不同壁厚条件下简支圆柱形屋顶空间大变位两个经典算例。研究结果表明：（1）几何刚度矩阵的显式计算公式不仅为板壳结构几何非线性列式提供了方便而且具有良好的精度;（2）推导的几何刚度矩阵适用于各类型四边形二十四自由度平板壳单元模型;（3）与数值积分相比,采用解析形式的几何刚度矩阵可以显著提高非线性响应计算效率。     

UH模型切线刚度矩阵对称化及其应用

分析了目前常用的几种土的本构模型三维化方法以及变换应力方法的优势. 详细分析了用变换应力三维化本构模型非关联流动的本质, 针对因采用非关联流动法则而带来的本构模型切线刚度矩阵的非对称性, 建立了本构模型切线刚度矩阵的对称化方法. 将此方法应用于UH模型并进行了有限元分析, 进行了三轴伸长试验有限元分析. 通过以上分析比较发现, 切线刚度矩阵对称化方法能够明显改善有限元分析的收敛性, 缩短分析时间, 有着非常好的应用前景.      

等直杆单元切线刚度矩阵的精确分析方法

为了有效完成大型铰接单层网壳结构的后屈曲分析,本文采用对杆单元杆端力函数求导的方法推导出了等直杆单元切线刚度矩阵的精确形式。该切线刚度矩阵不受结构小变形限制,适用于结构产生任意大结点位移情况。以六角星桁架、平面圆拱桁架和大跨K8单层网壳结构为算例,采用广义位移控制法进行非线性后屈曲分析,其中预测子采用本文杆单元切线刚度矩阵。算例分析结果表明,本文杆单元切线刚度矩阵在大型铰接单层网壳结构的非线性后屈曲分析中有很强的预测能力。     

等直杆单元切线刚度矩阵的精确分析方法

为了有效完成大型铰接单层网壳结构的后屈曲分析,本文采用对杆单元杆端力函数求导的方法推导出了等直杆单元切线刚度矩阵的精确形式。该切线刚度矩阵不受结构小变形限制,适用于结构产生任意大结点位移情况。以六角星桁架、平面圆拱桁架和大跨K8单层网壳结构为算例,采用广义位移控制法进行非线性后屈曲分析,其中预测子采用本文杆单元切线刚度矩阵。算例分析结果表明,本文杆单元切线刚度矩阵在大型铰接单层网壳结构的非线性后屈曲分析中有很强的预测能力。     

一种适合橡胶类材料的非线性粘弹性本构模型

借助非线性流变模型建立大变形情况非线性粘弹材料的本构关系,考虑到大多数橡胶类材料具有的几乎不可压缩性,以及体积响应和剪切响应的流变性能不同,将变形梯度乘法分解为等容部分和体积变形部分,给出了一种适合橡胶类材料的非线性粘弹性本构模型,并模拟了粘滞效应。对于极快或极慢的过程,该模型退化为橡胶弹性理论;在小变形情况下退化为经典的广义Maxwell粘弹性材料。模型与热力学第二定律相容,适合于大规模数值分析。     

Nonlinear Vibration of Plane Structures by Finite Element and Incremental Harmonic Balance Method

A nonlinear steady state vibration analysis of a wide class of planestructures is analyzed. Both the finite element method and incrementalharmonic balance method are used. The usual beam element is adopted inwhich the nonlinear effect arising from longitudinal stretching has beentaken into account. Based on the geometric nonlinear finite elementanalysis, the nonlinear dynamic equations including quadratic and cubicnonlinearities are derived. These equations are solved by theincremental harmonic balance (IHB) method. To show the effectiveness andversatility of this method, some typical examples for a wide variety ofvibration problems including fundamental resonance, super- andsub-harmonic resonance, and combination resonance of plane structuressuch as beams, shallow arches and frames are computed. Most of theseexamples have not been studied by other researchers before. Comparisonwith previous results are also made.     

Geometrically nonlinear,steady state vibration of viscoelastic beams

The problem of geometrically non-linear steady state vibrations of beams excited by harmonic forces is considered in this paper. The beams are made of a viscoelastic material defined by the classic Zener rheological model - the simplest model that takes into account all the basic properties of real viscoelastic materials. The constitutive stress-strain relationship for this type of material is given as a differential equation containing derivatives of both stress and strain. This significantly complicates the solution to the problem. The von Karman theory is applied to describe the effects of geometric nonlinearities of beam deformations. The equations of motions are derived using the finite element methodology. A polynomial approximation of bending moments is used. The order of basis functions is set so as to obtain a coherent approximation of moments and displacements. In the steady-state solution of equations of motion, only one harmonic is taken into account. The matrix equations of amplitudes are derived using the harmonic balance method and the continuation method is applied for solving them. The tangent matrix of equations of amplitudes is determined in an explicit form. The stability of steady-state solution is also examined. The resonance curves for beams supported in a different way are shown and the results of calculation are briefly discussed.     

碳纳米管增强复合材料圆锥薄壳非线性自由振动

考虑碳纳米管复合材料作为功能梯度材料的不均匀性,基于连续介质理论以及哈密尔顿变分原理,建立了功能梯度碳纳米管增强复合材料开口圆锥薄壳结构的非线性运动偏微分控制方程,然后利用Galerkin法,将非线性偏微分控制方程转化为常微分控制方程,进而采用谐波平衡法求解了开口圆锥壳的非线性自由振动问题,并探讨了圆锥薄壳几何参数、碳纳米管参数对结构非线性自由振动的影响．数值研究表明结构的无量纲非线性自由振动频率与线性自由振动频率的比值随圆锥薄壳长厚比的增大而变小、并随圆锥角的增大而变大．     

线性等参单元逆变换的几何二分法及其修正

在证明线性等参单元的一个几何特性的基础上,提出了线性等参单元逆变换的几何二分法。几何二分法简单易行,避免求解高维高次非线性方程组。在几何二分法基础上,提出一种修正措施以消除畸形单元对所求结果的影响,几何二分法及其修正措施克服了以往方法存在的缺点,两个实例验证了由几何二分法及其修正措施进行等参逆变换的正确性。     

A FINITE ELEMENT METHOD FOR DIELECTRIC ELASTOMER TRANSDUCERS

We present a finite element method for dielectric elastomer(DE) transducers based on the nonlinear field theory of DE.The method is implemented in the commercial finite element software ABAQUS,which provides a large library functions to describe finite elasticity.This method can be used to solve electromechanical coupling problems of DE transducers with complex configurations and under inhomogeneous deformation.     

Steady nonlinear harmonic oscillations of discrete elastic structures

An algorithm is derived which can be used for the calculation of coefficients in the amplitude frequency equations for nonlinear harmonic oscillations of elastic structures using, e.g. the finite element method.     

Incremental harmonic balance method for periodic forced oscillation of a dielectric elastomer balloon

Dielectric elastomer(DE) is suitable in soft transducers for broad applications,among which many are subjected to dynamic loadings, either mechanical or electrical or both. The tuning behaviors of these DE devices call for an efficient and reliable method to analyze the dynamic response of DE. This remains to be a challenge since the resultant vibration equation of DE, for example, the vibration of a DE balloon considered here is highly nonlinear with higher-order power terms and time-dependent coefficients. Previous efforts toward this goal use largely the numerical integration method with the simple harmonic balance method as a supplement. The numerical integration and the simple harmonic balance method are inefficient for large parametric analysis or with difficulty in improving the solution accuracy. To overcome the weakness of these two methods,we describe formulations of the incremental harmonic balance(IHB) method for periodic forced solutions of such a unique system. Combined with an arc-length continuation technique, the proposed strategy can capture the whole solution branches, both stable and unstable, automatically with any desired accuracy.     

定向井有杆抽油系统动态性能分析方法

由于杆管间库仑摩擦的影响,定向井有杆泵抽油系统动态参数预测模型是一个非线性的偏微分方程,求解复杂。鉴于此,提出了一种新的分析方法。该方法以定向井有杆抽油系统中的抽油杆柱作为研究对象,根据三次样条插值模拟得到的定向井的井眼轨迹,利用静力有限元法计算出了油管对抽油杆柱的支反力,进而得出了杆柱与油管之间的库仑摩擦力;给出了杆柱单元的受力分析;建立了有限元形式的杆柱系统动力学方程并利用状态空间法对其进行了数值求解,获得了悬点示功图。文末给出了两口油井的预测实例,并将预测结果与实测结果进行了对比。对比结果表明本文所提的分析方法是正确和有效的。     

Accurate Higher-Order Analytical Approximate Solutions to Large-Amplitude Oscillating Systems with a General Non-Rational Restoring Force

A new approximate analytical approach for accurate higher-order nonlinear solutions of oscillations with large amplitude is presented in this paper. The oscillatory system is subjected to a non-rational restoring force. This approach is built upon linearization of the governing dynamic equation associated with the method of harmonic balance. Unlike the classical harmonic balance method, simple linear algebraic equations instead of nonlinear algebraic equations are obtained upon linearization prior to harmonic balancing. This approach also explores large parameter regions beyond the classical perturbation methods which in principle are confined to problems with small parameters. It has significant contribution as there exist many nonlinear problems without small parameters. Through some examples in this paper, we establish the general approximate analytical formulas for the exact period and periodic solution which are valid for small as well as large amplitudes of oscillation.