非线性有限元的若干基本问题

本文介绍了非线性有限元中的若干基本问题。其中包括有关应变、应力和非线性平衡方程的一些基本概念,基于不同非线性广义变分原理的位移模式、杂交模式和拟协调模式几何非线性有限元及其在壳体屈曲问题中的应用等。      

非线性多类变量有限元的进展

本文介绍了非线性多类变量有限元,即非线性的杂交元和拟协调元近几年来的发展及其变分基础.      

几何非线性混合应变元的构造及应用

本文基于由文献〔１〕导出的几何非线性混合应变元一般公式，构造了三个八节点六面体几何非线性混合应变元和Ｓｉｍｏ－Ｒｉｆａｉ的二维四边形线性应变元的几何非线性混合应变元。数值结果表明，所构造的二维及三维几何非线性混合应变元具有理想的性能。它们通过分片试验，且没有虚假剪切现象和不可压缩材料的自锁。同时，它们对歪扭网格不敏感，在利用粗疏网格离散时对线性和非线性（几何和材料）问题具有很高的精度。     

非线性广义杂交元

选择新的三类变量建立了放松单元间连续性条件的用于非线性有限元分析的泛函，并由此建立了基于不协调模式的非线性广义杂交元方法。     

应用分区非线性变分原理的杂交薄壳单元

本文讨论了高交杂交壳体元在材料非线性分析中的应用，为了更精确估计单元内各部分应力的不同影响，本文应用了分区非线性变分原理推导出杂交壳元在应力增量下应用初始应力法的失衡节点力，这使得高次杂交元在非线性分析中的优点得以充分发挥，从而大大提高了计算精度。     

应用分区非线性变分原理的杂交薄壳单元

本文讨论了高次杂交壳体元在材料非线性分析中的应用，为了更精确估计单元内各部分应力的不同影响，本文应用了分区非线性变分原理推导出杂交壳元在应力增量下应用初始应力法的失衡节点力，这使得高次杂交元在非线性分析中的优点得以充分的发挥，从而大大提高了计算精度。     

用于几何非线性分析的内参型非协调元法

本文把内参型非协调元的理论和方法推广应用于几何非线性分析。对方法的合理性、可行性、单元收敛条件及实用简化方案等诸方面作了初步探讨。文章以大位移平面问题为例进行了详细讨论,给出了有限元非线性列式的全过程和数值结果。     

基于加性四元数的SINS/CNS非线性紧组合方法

针对SINS/CNS组合导航系统中的非线性特性,提出了基于加性四元数的SINS/CNS非线性紧组合方法.从捷联惯性导航系统误差非线性建模和天文角度非线性量测两个方面出发,推导了基于加性四元数的捷联惯导误差传播特性,构建了天文导航的非线性量测模型,采用二阶插值滤波算法实现了SINS和CNS的非线性信息融合.计算机仿真显示,SINS/CNS非线性紧组合方法充分考虑系统的非线性特性,机动情况下的峰值误差较小,相对线性紧组合方法导航精度提高约15％.     

扁球壳的边界元几何非线性分析

本文从壳体位移的三个微分方程出发，采用付立叶积分变换的基本解，利用加权残值法推导了几何非线性边界积分方程。这种基本解的壳体边界元法类似于板的非线性边界元法，各种变量物理意义明确，能方便地处理各种复杂边界条件及有开口情况。文末算例说明本文方法的可行性、收敛性和精确性，并与二变量边界单元法或有限元结果相比较，吻合较好。     

非线性复合材料杂交应力有限元的有效迭代方法

推导了面内剪应力应变关系非线性的复合材料的杂交应力有限元列式,给出了位移迭代和应力迭代的策略和步骤．提出一种非线性应力场迭代格式的改进方案,不仅提高了收敛速度,而且克服了大载荷下简单迭代法循环迭代而无法收敛的关键问题,使得所提出的非线性杂交应力元方法几乎对任意大载荷都能够收敛．数值算例表明该方法是确实可行的．     

Nonlinear dynamics of three-dimensional belt drives using the finite-element method

In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models that have different numbers of degrees of freedom and different modes of deformation. Both three-dimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other three-dimensional element used in this investigation is a cable element obtained from a more general three-dimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element formulations are compared and the convergence of the two finite-element solutions is examined.     

考虑变形耦合的几何非线性空间梁单元

以"精确几何模型梁单元"为代表的很多几何非线性梁单元,在构造过程中分别对描述截面转动的转角和描述截面形心位置的位移进行了独立插值,由此引起了诸如运动学描述冗余和剪切闭锁等困难。其根本原因在于单元形函数没能体现细长梁中的变形耦合关系。本文对这类传统单元进行了改造,通过深入研究单元变形之间的内在联系,提出了一种变形场完全满足Bernoulli梁变形耦合关系的新单元,避免了构造过程中对转动矢量的插值,并通过数值算例检验了单元的有效性。     

Deteriorated Geometrical Stiffness for Higher Order Finite Elements with Application to Panel Flutter

Higher order elements were first design for linear problems where, in certain situations, they present advantages over the lower order elements. A method to efficiently extend their use to geometrical nonlinear problems as panel flutter and postbuckling behavior is presented. The chaotic and limit-cycle oscillations of an isotropic plate are obtained based on direct integration of the discretized equation of motion. The plate is modeled using the von Karman theory and the geometrical nonlinearities are separated in a nonlinear term of the first kind which manifests especially in the prebuckling and buckling regimes, and a nonlinear term of the second kind which is responsible for the postbuckling behavior. A fifth order, fully compatible element has been used to model thin plates while the inplane loads where introduced through a membrane element. The aerodynamics was modeled using the first order 'piston theory. The method introduces the concept of a deteriorated form of the second geometric matrix which is equivalent to neglecting higher order terms in the strain energy of the plate. This allows for a drastic reduction in the computational effort with no observable loss of accuracy. Well established results in the literature are used to validate the method.     

钢筋混凝土板动力非线性有限元研究

从目前的文献看 ,关于钢筋混凝土板动力非线性分析方面的研究较少。本文在建立钢筋混凝土材料动力模型的基础上 ,采用广义协调矩形分层单元、显式 Newmark法编制了钢筋混凝土板的动力有限元程序。数值算例表明 ,所编程序原理正确 ,结果可靠。     

Optimal Slewing of a Flexible Spacecraft

An optimal slewing program is designed within the class of Euler rotations for a spacecraft with elastic elements. The mathematical model constructed accounts for an arbitrary number of partial modes of elastic vibrations. An optimal reorientation problem is formulated using a nontraditional performance criterion, which minimizes the dynamic overloads of the elastic elements in relative motion. An algorithm for solving the corresponding nonlinear boundary-value problem is developed and implemented in a software package of FORTRAN-programs. A neural network is generated in the space of slew parameters; it may be trained during a preflight period. Known radial basis functions are used to model the process of fast in-flight computation of the optimal reorientation program     

关于广义等参有限单元的讨论

研究了新近提出的广义等参单元,讨论了这一新方法与现有方法的关系,提出了一个建立广义有限单元的一般性方法。     

FRP strengthened walls with delaminated regions – Geometrically nonlinear response

The paper studies the geometrically nonlinear behavior of walls that are strengthened with fiber reinforced polymer (FRP) composite materials but include pre-existing delaminated regions. The paper uses an analytical–numerical methodology. Three specially tailored finite elements that correspond to perfectly bonded regions, to delaminated regions where the debonded layers are in contact, and to delaminated regions where the debonded layers are not in contact are presented. All finite elements are based on a high order multi layered plate theory. The geometrical nonlinearity is introduced by means of the Von Karman nonlinear strains whereas the contact nonlinearity is handled iteratively. The validity and convergence of the finite element models is demonstrated for each type of element through comparison with closed form analytical solutions available for specific cases. The unified model that combines the three types of finite element is then used for studying the nonlinear behavior of a locally delaminated FRP strengthened wall under in-plane normal and in-plane shear loads. Finally, conclusions regarding the effect of the delamination on the response of the strengthening system, on the conditions that evolve in the bonded region that surrounds the delamination, and on the global response of the multi-layered structure are drawn. Additional conclusions regarding the application of the modeling approach to other delamination sensitive layered structural systems close the paper.     

弹性接触过程分析的有限元数值模拟

本文针对机械行业中的弹性接触问题，在有限元分析中，引主接触面单元和预留单元。以滚针轴承为例，对接触问题进行了深入的探讨，为准确地描述两接触体之间相互作用及变形协调的接触过程，提供了一种新方法。