多体无摩擦弹性接触问题的罚有限元法

一、引言弹性接触问题属于局部非线性问题,这是由于系统的接触状态不能事先确定而引起的。一般用有限元法进行求解时,首先要假定接触区域,然后根据接触定解条件来建立系统的刚度方程,由此可解出各节点的位移分量并计算出各接触节点的法向力     

NONLINEAR DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEM

The nonlinear dynamic equations of a multibody system composed of ?exible beams are derived by using the Lagrange multiplier method. The nonlinear Euler beam theory with inclusion of axial deformation e?ect is employed and its deformation ?eld is …     

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。     

高精度九节点非协调曲边三角形平面应力单元

本文利用[1]的方法,构造了一个九节点非协调三角形平面单元.与一般有限元相比可以提高一阶收敛精度,应力可直接在单元节点上得到.形成单刚矩阵时,不需要在单元域内进行数值积分,容易构造曲边单元.文末的算例表明,仅用很少的单元,位移和应力即可获得较高的精度.     

柔性系统力学中的主要课题

本文对多刚体系统力学的研究结果进行简要的小结,介绍了柔性系统的力学模型以及该领域中的主要研究课题.     

三维连续与非连续变形分析

将石根华博士所提出的二维非连续变形分析——Discontinuous Deformation Analysis（DDA）方法扩展到三维情况,并对三维不连续块体进行有限元网格剖分,即块体之间的接触采用DDA描述,块体内部的位移场和应力场则采用有限单元法描述,从而将三维DDA与有限元方法结合起来,增强了DDA方法与有限元方法解决实际工程问题的能力,实现了三维连续与非连续变形分析.给出了基本公式的推导过程和各子矩阵的形式.典型接触、碰撞算例证明了所提出方法的有效性和正确性.     

受r^n分布载荷的楔：佯谬的解决

对表面受与ｒｎ（ｎ≥０）成正比的分布载荷的楔，当楔顶角２α与ｎ之间满足一定关系时，经典解为无穷大，这是一个佯谬．本文采用复变函数方法，研究了这个佯谬的所有情形，并发现存在二次佯谬，即对某些特定的（ｎ，α），佯谬解仍为无穷大，对此本文也予以解决     

从受拉杆变形浅析弹性力学中的最小势能原理

最小势能原理是弹性力学中较难理解的知识点。本文通过对弹性杆轴向受拉时的弹性势能、外力势能和总势能的变分分析,得出总势能变分是位移变分或应变变分的二阶无穷小量,并在位移变分或应变变分为零时,总势能取得极小值。弹性杆轴向受力变形的分析应验了最小势能原理,有助于对一般情况下最小势能原理的深刻理解。     

时变固体力学的黏弹性解

基于时变力学的对应性原理,建立一种黏弹性时变力学的一般性解法,适用于一类时变力学问题的求解。     

Dynamic analysis of a rigid-flexible inflatable space structure coupled with control moment gyroscopes

The vibration generated by the inflatable structure after deployment has a great impact on the performance of the payloads. In this paper, the influence of the control moment gyroscopes (CMGs) on the dynamic responses and characteristics of an inflatable space structure is studied, based on the flexible multibody dynamics in a combination of the absolute nodal coordinate formulation (ANCF) and the natural coordinate formulation (NCF). Firstly, the ANCF and NCF are used to accurately describe the large deformations and large overall motions of flexible inflatable tubes and rigid satellites, respectively. Then, instead of modeling gyroscopic flexible bodies, this paper pioneers a rigid body dynamic model of the CMG in detail by using the NCF modeling scheme, which can be attached to and coupled with any flexible bodies without any assumptions. Then, the orbital dynamic equations of the inflatable space structure coupled with distributed CMGs are obtained by considering the effects of Coriolis force, centrifugal force, and gravity gradient through coordinate transformation. The dynamic characteristics of the inflatable space structure are also analyzed by deriving the eigenvalue problem of a flexible multibody system. Finally, the accuracy of the CMG dynamic model is verified via a classic heavy top example. Several numerical examples are presented to study the influence of the magnitudes and directions of the rotor angular momentum of the CMGs on the dynamic responses and characteristics of the inflatable space structure.

     

A coupled theory of fluid permeation and large deformations for elastomeric materials

An elastomeric gel is a cross-linked polymer network swollen with a solvent (fluid). A continuum-mechanical theory to describe the various coupled aspects of fluid permeation and large deformations (e.g., swelling and squeezing) of elastomeric gels is formulated. The basic mechanical force balance laws and the balance law for the fluid content are reviewed, and the constitutive theory that we develop is consistent with modern treatments of continuum thermodynamics, and material frame-indifference. In discussing special constitutive equations we limit our attention to isotropic materials, and consider a model for the free energy based on a Flory-Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical-mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains. As representative examples of application of the theory, we study (a) three-dimensional swelling-equilibrium of an elastomeric gel in an unconstrained, stress-free state; and (b) the following one-dimensional transient problems: (i) free-swelling of a gel; (ii) consolidation of an already swollen gel; and (iii) pressure-difference-driven diffusion of organic solvents across elastomeric membranes.     

做大范围运动复合材料板的动力学建模研究

基于经典层合板理论建立了大范围运动复合材料板的动力学方程,考虑了传统建模方法忽略的二次耦合变形量。采用有限元法对复合材料板进行离散,利用Lagrange方法推导了大范围运动复合材料板的动力学方程。通过编制matlab程序计算了带中心刚体的旋转复合材料板的变形,将得到的结果分别与不计耦合变形量的传统方法的计算结果进行比较,随着转速的提高,本文方法收敛,而传统方法趋于发散。研究了铺层角度对作大范围运动复合材料板变形影响以及复合材料板和各向同性板在经历相同运动时角点最大变形的差异。     

Modeling and analysis of a coupled rigid-flexible system

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A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: Formulation

In this Part I, of a two-part paper, we present a detailed continuum-mechanical development of a thermo-mechanically coupled elasto-viscoplasticity theory to model the strain rate and temperature dependent large-deformation response of amorphous polymeric materials. Such a theory, when further specialized (Part II) should be useful for modeling and simulation of the thermo-mechanical response of components and structures made from such materials, as well as for modeling a variety of polymer processing operations.     

FEM-FDM coupled liquefaction analysis of a porous soil using an elasto-plastic model

The phenomenon of liquefaction is one of the most important subjects in Earthquake Engineering and Coastal Engineering. In the present study, the governing equations of such coupling problems as soil skeleton and pore water are obtained through application of the two-phase mixture theory. Using au-p (displacement of the solid phase-pore water pressure) formulation, a simple and practical numerical method for the liquefaction analysis is formulated. The finite difference method (FDM) is used for the spatial discretization of the continuity equation to define the pore water pressure at the center of the element, while the finite element method (FEM) is used for the spatial discretization of the equilibrium equation. FEM-FDM coupled analysis succeeds in reducing the degrees of freedom in the descretized equations. The accuracy of the proposed numerical method is addressed through a comparison of the numerical results and the analytical solutions for the transient response of saturated porous solids. An elasto-plastic constitutive model based on the non-linear kinematic hardening rule is formulated to describe the stress-strain behavior of granular materials under cyclic loading. Finally, the applicability of the proposed numerical method is examined. The following two numerical examples are analyzed in this study: (1) the behavior of seabed deposits under wave action, and (2) a numerical simulation of shaking table test of coal fly ash deposit.     

Multibody Formulation with Large Bending Finite Elements (LBFE)

The goal of this paper is to present a flexible multibody formulation for Euler-Bernoulli beams involving large displacements. This method is based on a discretisation of internal and kinetic energies. The beam is represented by its line of centroids and each section is oriented by a frame defined by three Euler angles. We apply a finite element formulation to describe the evolution of these angles along the neutral fibre and describe the internal energy. The kinetic energy is approximated as the one of two rigid bars tangent to the neutral fibre at the ends of the beam. We derive the equations of motion from a Lagrange formulation. These equations are solved using the Newmark method or/and the Newton-Raphson technique. We solve some very classic problems taken from the literature as the curved beam presented by Simo [Simo, J. C., ‘A three-dimensional finite-strain rod model. the three-dimensional dynamic problem. Part I’, Comput. Meths. Appl. Mech. Engrg. 49, 1985, 55–70; Simo, J. C. and Vu-Quoc, L., ‘A three-dimensional finite-strain rod model, Part II: Computationals aspects’, Comput. Meths. Appl. Mech. Engrg. 58, 1988, 79–116] and Lee [Lee, Kisu, ‘Analysis of large displacements and large rotations of three-dimensional beams by using small strains and unit vectors’, Commun. Numer. Meth. Engrg. 13, 1997, 987–997] or the rotational rod presented by Avello [Avello, A., Garcia de Jalon, J., and Bayo, E., ‘Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory’, Int. J. Num. Methods in Engineering 32, 1991, 1543–1563] and Simo [Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part I’ Jour. of Appl. Mech. 53, 1986, 849–854; Simo, J. C. and Vu-Quoc, L., ‘On the dynamics of flexible beams under large overall motions – the planar case. Part II’, Jour. of Appl. Mech. 53, 1986, 855–863].