桥梁地震碰撞分析中不同接触单元模型的对比分析

地震时邻梁间的碰撞是引起桥梁局部损坏甚至落梁的主要原因。为合理分析桥梁的地震碰撞响应, 基于所开发的结构精细化模拟分析平台FENAP, 对比分析了桥梁地震碰撞分析中不同接触单元模型的计算精度和适用条件。在FENAP平台上引入线性弹簧、Kelvin-Voigt、Hertz和Jan-Hertz-damp等四种接触单元模型, 建立了结构地震碰撞分析平台, 并通过数值验证以及对正弦波和地震动激励下的模型试验的数值分析, 对比分析了不同接触单元模型对结构碰撞响应的影响。研究表明：所建立的结构地震碰撞分析平台具有较高的计算精度和效率;在四种接触单元模型中, Kelvin-Voigt和Jan-Hertz-damp模型的计算精度和适用性更高, 而线性弹簧和Hertz模型, 由于未考虑碰撞过程中的能量损失, 仅适用于恢复系数较高的近似弹性碰撞情况。     

结构地震碰撞分析的线性粘弹性碰撞模型

针对结构地震碰撞模拟问题,该文中结合Kelvin模型和Hertz-damp模型构造了新的碰撞阻尼函数,提出了线性粘弹性碰撞模型,并基于现有的碰撞试验数据检验了其正确性和碰撞模拟精度。研究结果表明：线性粘弹性碰撞模型可以消除Kelvin模型中出现的撞击力跳跃和拉力的缺陷;相比其他常用的结构地震碰撞分析模型而言,线性粘弹性碰撞模型和Hertz-damp模型都具有较高的碰撞模拟精确度,且线性粘弹性碰撞模型的表达形式比Hertz-damp模型的更为简单易用。分析对比中还发现,如在碰撞模型中忽略碰撞过程中的耗能,数值模拟结果将会高估碰撞对结构的破坏效应。     

基于精细积分法的相邻结构弹塑性地震碰撞分析

罕遇地震作用下,结构会不可避免进入塑性状态,并且相邻结构会产生碰撞现象。将相邻的复杂结构简化为多个单自由度结构,并在相邻结构间增加接触单元,以模拟多点碰撞。地震反应过程区分为分离状态和碰撞状态,分别建立了增量动力平衡方程和全量动力平衡方程,推导了分离状态增量动力平衡方程和碰撞状态全量动力平衡方程的精细积分法,并解决了滞回曲线界点的精确分析和分离-碰撞状态转换问题。设计了增量精细积分法和全量精细积分法相结合求解弹塑性地震碰撞反应的算法。通过算例分析,验证该算法能精确地模拟结构的材料非线性行为和碰撞行为。在此基础上,对接触单元模型进行参数化分析,结论有助于进一步理解相邻结构碰撞现象。     

多孔介质矩形薄板的精细积分模型

基于三维Biot理论和弹性薄板理论,考虑多孔介质薄板骨架与流体的耦合作用,导出了多孔介质矩形薄板在谐激励作用下的一阶常微分矩阵方程。利用齐次扩容精细积分方法,对两对边简支矩形薄板在均布荷载和集中荷载两种情况下的弯曲振动问题进行了求解,对比经典算例,验证了所建模型的可行性和有效性。相对于数值方法,本文提出的方法适用于中高频段的分析计算。     

基于Hertz接触模型的柔性梁碰撞振动分析

首先研究两弹性体碰撞振动中的接触力，用多项式逼近具有分数指数的Ｈｅｒｔｚ模型来实现近似解析分析，然后讨论与碰撞有关的各因素对两柔性梁受迫碰撞振动的影响。当耦合模态解增加时，碰撞强度增大，系统呈现典型的非线性     

地震时桥梁碰撞分析的等效Kelvin撞击模型

建立地震时桥梁碰撞分析的Kelvin撞击模型的参数确定方法。基于Hertz接触理论,考虑波动效应,按照最大撞击力与最大撞击变形的比值,确定Kelvin撞击模型的碰撞刚度;数值分析了影响Kelvin撞击模型阻尼系数取值的邻梁碰撞恢复系数。结果表明:Kelvin撞击模型的碰撞刚度随Hertz接触刚度、撞击速度以及短梁与长梁的长度比的增大而增大;波动效应对碰撞刚度的影响明显,不能忽略;邻梁碰撞恢复系数随撞击速度增大而减小,随短梁与长梁的长度比减小而减小;确定Kelvin撞击模型的碰撞刚度和邻梁碰撞恢复系数对城市桥梁的合理取值范围应分别为3×105kN/m―6×105kN/m和0.7―0.95。     

多维非平稳随机地震响应分析的混合型精细时程积分

在一维虚拟激励法的基础上,通过激励功率谱的分解,建立多维非平稳地震激励作用下结构随机响应的虚拟激励法。根据演变随机激励的调制函数取不同形式,推导不同的特解精细积分格式,并混合应用这些格式于结构响应时变功率谱分析,可获得高效精确的数值结果。最后,通过算例讨论地震动各分量相关性对非对称结构地震响应的影响,得到一些有意义的结论。     

地震作用下结构碰撞的模型参数及其影响分析

地震作用下,结构的碰撞问题被认为是影响结构地震反应和结构抗震性能的一个重要因素,碰撞是一种十分复杂的非线性问题,在计算分析中涉及到较多参数,需要分析其模型参数对碰撞现象以及结构的影响。通过单墩模型分析研究,在尽量少的参数变化下,初步得到了桥梁结构发生碰撞时模型参数对碰撞及结构的影响。     

一种基于变恢复系数的接触碰撞力模型

为了有效描述机械系统中的接触-碰撞现象,在考虑材料屈服强度和初始碰撞速度的基础上,提出一种变恢复系数模型,进而建立了一种改进的、变恢复系数的接触-碰撞模型;随后,分别以轴-轴承、球-球以及平面曲柄滑块机构为例,通过大量数值模拟和实验测试,以及二者间的对比分析,对改进模型的有效性、准确性进行了验证。研究结果表明,改进的模型能够更加准确的描述间隙铰链处的接触碰撞效应,以及间隙铰链对机械系统动态特性的影响规律。     

桥梁结构地震反应邻梁碰撞分析等效刚体模型

在基于直杆共轴碰撞理论建立的桥梁地震反应邻梁碰撞分析模型基础上,结合动量守恒定律和能量守恒定律,给出了与之等效的刚体碰撞模型,所定义的等效恢复系数r由邻梁长度比12/ll和碰撞弹簧刚度比a唯一决定。一座实际桥梁地震反应邻梁碰撞效应分析表明,等效刚体碰撞模型可以得到与弹性杆碰撞模型几乎一致的结果。     

基于精确齿面建模的ZA蜗杆蜗轮有限元接触分析

为了研究不同情况下蜗杆蜗轮间的接触应力和蜗杆扭转角与驱动力矩之间的关系,根据齿面方程建立具有精确齿面的ZA蜗杆蜗轮实体模型,利用ANSYS对此模型在同一载荷不同啮合位置和同一啮合位置不同载荷条件下进行有限元接触分析,研究在一个轮齿啮合周期内,各啮合齿对的接触应力分布和载荷在不同齿对上的分配情况.分析结果表明:理论接触应...     

A finite element solution method for contact problems with friction

A new finite element solution method for the analysis of frictional contact problems is presented. The contact problem is solved by imposing geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated. The algorithm does not require any a priori knowledge of the pairs of contactor nodes or segments. The contact condition of sticking, slipping, rolling or tension release is determined from the relative magnitudes of the normal and tangential global nodal forces. Contact iterations are in general found to converge within one or two iterations. The analysis method is applied to selected problems to illustrate the applicability of the solution procedure.     

Numerical solution of the point contact problem using the finite element method

The elastohydrodynamic lubrication problem, in which the lubricant pressure and film thickness are sensitive to surface deformation, is solved by using a finite element procedure and the Newton method. The numerical procedure is applied to the point contact problem, in which a thin lubricant film is maintained between two balls loaded together by a high load under conditions of pure rolling. The present analysis shows that pressure spikes are formed near the outlet region, a result which has been found in the line contact problem and which has been conjectured in the present problem.     

Krylov precise time‐step integration method

An efficient precise time‐step integration (PTI) algorithm to solve large‐scale transient problems is presented in this paper. The Krylov subspace method and the Padé approximations are applied to modify the original PTI algorithm in order to improve the computational efficiency. Both the stability and accuracy characteristics of the resultant algorithms are investigated. The efficiency can be further improved by expanding the dimension to avoid the computation of the particular solutions. The present algorithm can also be extended to tackle nonlinear problems without difficulty. Two numerical examples are given to illustrate the highly accurate and efficient algorithm. Copyright © 2006 John Wiley & Sons, Ltd.     

Shape sensitivity analysis of composites in contact using the boundary element method

This paper presents the application of the boundary element method to the shape sensitivity analysis of two-dimensional composite structures in contact. A directly differentiated form of boundary integral equation with respect to geometric design variables is used to calculate shape design sensitivities for anisotropic materials with frictionless contact. The selected design variables are the coordinates of the boundary points either in the contact or non-contact area. Three example problems with anisotropic material properties are presented to validate the applications of this formulation.     

A finite element model for contact analysis of multiple Cosserat bodies

The objective of this paper is to develop a finite element model for multi-body contact analysis of Cosserat materials. Based on the parametric virtual work principle, a quadratic programming method is developed for finite element analysis of contact problems. The contact problem with friction between two Cosserat bodies is treated in the same way as in plastic analysis. The penalty factors, that are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of contact problems of Cosserat materials, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. Compared with the conventional work on Cosserat elasticity, the newly developed model is on the contact analysis of the Cosserat materials and is seldom found in the existing literatures. Four examples are computed to illustrate the validity and importance of the model developed.     

A general boundary element method approach to the solution of three-dimensional frictionless contact problems

A direct boundary element method is presented for three-dimensional stress analysis of frictionless contact problems. The isoparametric formulation of the boundary element method is implemented for the general case of contact in the absence of friction, which is limited to linear elastic homogeneous and isotropic materials. An iterative procedure is employed to determine the correct size of the contact zone by finding a boundary solution compatible with the contact condition. The applicability of the procedure is tested by application to three problems of advancing and conforming contact. The computed results are compared with numerical and analytical solutions where possible.     

Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model

An adhesive elasto-plastic contact model for the discrete element method with three dimensional non-spherical particles is proposed and investigated to achieve quantitative prediction of cohesive powder flowability. Simulations have been performed for uniaxial consolidation followed by unconfined compression to failure using this model. The model has been shown to be capable of predicting the experimental flow function (unconfined compressive strength vs. the prior consolidation stress) for a limestone powder which has been selected as a reference solid in the Europe wide PARDEM research network. Contact plasticity in the model is shown to affect the flowability significantly and is thus essential for producing satisfactory computations of the behaviour of a cohesive granular material. The model predicts a linear relationship between a normalized unconfined compressive strength and the product of coordination number and solid fraction. This linear relationship is in line with the Rumpf model for the tensile strength of particulate agglomerate. Even when the contact adhesion is forced to remain constant, the increasing unconfined strength arising from stress consolidation is still predicted, which has its origin in the contact plasticity leading to microstructural evolution of the coordination number. The filled porosity is predicted to increase as the contact adhesion increases. Under confined compression, the porosity reduces more gradually for the load-dependent adhesion compared to constant adhesion. It was found that the contribution of adhesive force to the limiting friction has a significant effect on the bulk unconfined strength. The results provide new insights and propose a micromechanical based measure for characterising the strength and flowability of cohesive granular materials.     

Three-dimensional contact mechanics analysis of crack problems using the boundary element method

In this paper, a formulation based on the iterative-load incremental approach for the three-dimensional frictional contact mechanics analysis of fracture problems using the boundary element method (BEM), is presented. Special crack front elements are employed to provide a quick and direct means of obtaining the stress intensity factor. The veracity of the formulation is demonstrated with four crack problems. Three of these problems involve crack closure under bending loads, and the fourth is that of a pin-loaded rectangular plate with corner cracks at the pin-hole. The computed BEM solutions are compared, where possible, with those available in the literature, and there is generally good agreement between them. The numerical examples serve also to illustrate the need for a proper contact mechanics treatment to obtain accurate stress intensity factors for such problems.