弹塑性强化结构在考虑二阶几何效应下的动力安定理论

本文是在采用分段线性屈服面和对结构进行离散化的基础上,在考虑惯性力、阻尼力以及二阶几何效应的情况下,对结构进行了安定分析,提出了两个推广的动力安定定理.     

Dynamic shakedown theory allowing for second order geometric effects

Summary Two necessary and sufficient conditions for shakedown in a structure subjected to given histories of external loads and imposed strains, in the presence of significant inertia and damping effects, are established. Structural discretization and piecewise linearization of constitutive laws are adopted. This permits to consider several hardening materials and geometric effects, in the spirit of second order theory. The statements can be regarded as a generalization to a broader context of the classical Bleich-Melan and Koiter shakedown theorems. With respect to previous work, the main novelty is the simultaneous coverage of dynamic and second order effects.

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Sommario Si dimostrano due condizioni necessarie e sufficienti per l'adattamento in campo elastico di strutture soggette ad assegnate storie di carichi e distorsioni, in presenza di non trascurabili forze d'inerzia e di smorzamento. La discretizzazione della struttura e la linearizzazione a tratti del legame costitutivo consentono di considerare una larga classe di materiali incrudenti e gli effetti geometrici, nello spirito della teoria del second'ordine. Gli enunciati costituiscono una generalizzazione dei classici teoremi di Bleich-Melan e Koiter. A differenza di risultati precedenti, gli enunciati sono validi in presenza di concomitanti effetti dinamici e geometrici del second'ordine.

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Research sponsored by the (Italian) National Research Committee (CNR).     

Bilateral bounds for structures under dynamic shakedown conditions

Bounds to functions of the plastic strains produced during the elastic-plastic stage of a dynamic loading process leading to shakedown can be constructed on the basis of the solution of a single, static, holonomic elastic-plastic problem. This bounding procedure is described in detail with respect to the case of periodic external loading, and the generalization to an arbitrary dynamic loading condition is provided. Simple examples illustrate the bounding effectiveness of the proposed technique.

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sommario Si mostra come sia possibile produrre delimitazioni di funzioni delle deformazioni plastiche che avvengono durante la fase iniziale di un processo dinamico che si concluda con l'adattamento in regime elastico (shakedown). Si illustra in dettaglio la procedure di delimitazione con riferimento al caso di carichi esterni periodici, e si fornisce l'estensione concettuale al caso di una condizione di carico generica. Due esempi numerici mostrano l'accuratezza e l'efficienza numerica della tecnica proposta.

     

On shakedown theory for elastic-plastic materials and extensions

The idea that an elastic-plastic structure under given loading history may shake down to some purely elastic state (and hence to a safe state) after a finite amount of initial plastic deformation, can apply to many sophisticated material models with possible allowable changes of additional material characteristics, as has been done in the literature. Despite some claims to the contrary, it is shown; however, that the shakedown theorems in a Melan-Koiter path-independent sense have been extended successfully only for certain elastic-plastic hardening materials of practical significance. Shakedown of kinematic hardening material is determined by the ultimate and initial yield stresses, not the generally plastic deformation history-dependent hardening curve between. The initial yield stress is no longer the convenient one (corresponding to the plastic deformation at the level of 0.2%) as in usual elastic-plastic analysis but to be related to the shakedown safety requirement of the structure and should be as small as the fatigue limit for arbitrary high-cycle loading. Though the ultimate yield strength is well defined in the standard monotonic loading experiment, it also should be reduced to the so-called “high-cycle ratchetting” stress for the path-independent shakedown analysis. A reduced simple form of the shakedown kinematic theorem without time integrals is conjectured for general practical uses. Application of the theorem is illustrated by examples for a hollow cylinder, sphere, and a clamped disk, under variable (including quasiperiodic dynamic) pressure.     

弹塑性结构安定下限分析的无网格局部

将基于Voronoi结构的无网格局部Petrov-Galerkin法与减缩基技术相结合,建立了一种安定下限分析的新方法．为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻近插值构造试函数.通过引入基准载荷域上载荷角点的概念,消除了安定下限分析中由时间参数所引起的求解困难．利用减缩基技术,将安定分析问题化为一系列未知变量较少的非线性规划子问题．在每个非线性规划子问题中,自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟,而这些自平衡应力场基矢量可应用弹塑性增量分析中的平衡迭代结果得到．算例结果证明了提出的分析方法的有效性．      

变曲率连续滚滑接触安定性的数值方法研究

针对接触表面变曲率的特点,引入局部坐标系,构造出局部坐标下残余应力应变场的分布状态,建立了变曲率连续啮合过程中安定状态残余应力的计算方法。该数值方法将弹塑性问题分解为弹性问题和特征应变决定的残余问题,并采用增量映射方法求解特征应变决定的残余问题,可直接得到接触安定状态下的接触残余应力,并随之进行安定极限的判定。采用该数值方法计算了不同曲率处接触点的安定极限,给出了安定极限与摩擦因数之间的关系,并与有关数值结果相比较,验证了该算法的有效性。     

桁架结构几何非线性问题的力密度法

桁架结构大都具有较强的几何非线;浊,受荷载后易出现较大的脯变形。提出一种基于力密度的针对桁架结构几何大变形问题的解法;引入杆件单元的力密度矩阵,推导出相应非线性方程的Jacobi矩阵;与有限单元法集成求解的思想相同,采用力密度矩阵建立结构变形后整体的精确非线性平衡方程。研究结果表明：应用Newton-Raphson迭代法求解,采用适当的迭代收敛精度可得到较精确的桁架结构位移解。     

平面梁杆结构几何非线性分析的一种简便方法

本文提出了一种新的几何非线性分析方法，适用于结点位移任意大，单元刚体转角任意大、单元局部弯曲比较小的平面梁杆结构。文中的刚度矩阵和附加荷载列阵都是以显式形式给出的，可直接应用。     

An efficient algorithm for elasto-viscoplastic vibrations of multi-layered composite beams using second-order theory

An efficient time-domain algorithm for plane non-linear flexural vibrations of multi-layered composite beams, which are driven into the inelastic range by severe transverse loadings, is presented. The influence of an axial static preload is considered in the sense of the quasi-linear second-order theory of structures. The inelastic parts of strain are treated as additional sources of selfstress in the linear elastic background-structure, driving the elastic response into the inelastic one. The efficiency of this exact formulation lies in the fact that linear solution techniques can be used in their most powerful form: Rubin's useful formulation for the quasi-static second-order transfer-matrix of linear elastic structures is applied in combination with modal analysis. Having in mind multi-metal beams, the classical lamination theory is assumed to be valid. Beams with overhang composed of ideal elastic-plastic and viscoplastic layers are studied as example structures. The fictitious sources of selfstress are calculated from the different material laws of the layers in a numerical time-stepping procedure, where a generalized midpoint-rule in combination with Crisfield's secant-Newton procedure is used.     

细长结构几何非线性分析的子结构方法

将细长结构沿长度方向划分为多个子结构,并在每个子结构上建立一个随结构一起运动的连体基,则结构内任意点的位移可分解为连体基的转动和相对于连体基的小位移。利用细长结构这样的变形特征,本文详细讨论了连体基的转动,给出了与连体基选择方式相协调的节点位移及其虚变分表达式,并将子结构内部位移凝聚到了边界节点上。在此基础上,提出了一种细长结构几何非线性分析的子结构方法,可在不损失计算精度的前提下大幅度降低求解规模,从而提高了计算效率。数值算例验证了所提方法的有效性。     

Modification in the theory on flexural-torsional buckling of structures

I.IntroductionltwasuntiIl899thattheflrsttreatmentwaspub1ishedofflexural-torsionalbucklingbyMichelII1]whoconsideredthelateralbucklingofbeamsofnarrowrectangularcross-sectionandwhoseworkwasextendedin19O5byTimoshenkol2ltoincludetheeffectsofwarpingtorsioninI-s…     

A multiscale approach of fatigue and shakedown for notched structures

The aim of this paper is to analyse the fatigue phenomena in the presence of stress gradients. It is well-known that most fatigue criteria fail to predict the lifetime of components in the presence of high stress concentrations or stress gradients, as it is the case in the neighbourhood of cracks, holes notches and encountered for example in riveted or threaded structures. Proposed is a numerical approach in the framework of the high cycle fatigue domain in order to give a qualitative answer. The work starts from the numerical computation of macroscopic loading corresponding to some fatigue experiments on specimens with an inclusion of metallic grains embedded in a macroscopic matrix. The computed fields are then analysed in terms of the HCF (high cycle fatigue) criterion [1], which is based on the estimation of the shakedown limit at the grain scale. The infinite lifetime prediction is based on the assumption that fatigue occurs if at least one grain fails, i.e. reaches plastic shakedown. The predictions at mesoscopic and macroscopic scales are close if the macroscopic stress distribution is homogeneous. However in the case of the stress gradient, lifetime predicted at the macroscopic scale is underestimated when compared to the predictions made at the mesoscopic scale. Another result is that the gap between microscopic and macroscopic predictions obtained from these numerical computations can roughly be estimated by a diminution of stress of the same order of magnitude as found in the experiments and phenomenological observations.     

计及二阶效应的门座起重机变幅工况动力学分析

对门座起重机的变幅工况进行了计及二阶效应的大范围运动弹性动力分析。使用柔性多体系统动力学方法描述柔性体的变形和运动,结合非线性有限元理论推导了一般运动柔性单元在局部坐标系下的计及二阶效应的动力学方程,进而使用三结点Euler-Bernoulli梁单元的形函数,推导了柔性梁单元的动力学方程。对该方程进行静力凝聚并使用随动坐标法,得到便于系统动力学方程组集的整体坐标系下的两结点梁单元动力学方程。对某型门座起重机臂架系统的变幅工况进行了计及二阶效应的弹性动力分析,结果表明:二阶弹性位移和内力均为相应线性解上的波动,且波动幅值较大,因此对大柔度重载机械应进行考虑二阶效应的弹性动力分析。     

含初缺陷裂纹损伤梁的冲击动力屈曲

由Hamilton原理导出考虑初始缺陷及横向剪切变形时裂纹梁的动力屈曲控制方程;应用断裂力学中常用的线弹簧模型将裂纹引入到屈曲控制方程中;基于B-R动力屈曲判断准则,采用数值方法求解了受轴向冲击载荷作用时裂纹梁的动力屈曲;对比讨论了不同冲击速度、初始几何缺陷大小以及分布形式等因素对梁冲击动力屈曲的影响。     

变截面高层筒体结构的有限元线法整体稳定和二阶分析

本文用有限元线法对变截面的高层简体结构进行空间整体稳定和二阶分析。先把实际框筒结构分段连续化为正交各向异性折板结构；用有限元线法，通过有限条元半离散化，取结线上位移为基本未知函数，由势能驻值原理建立稳定和二阶分析的常微分方程组；由常微分方程求解器直接求解。     

高层筒体结构整体稳定及二阶位移分析的改进条元法

根据柱壳理论,构造了一种柱壳曲条,本文结合柱壳曲条和平壳条元求解高层筒体结构的整体稳定及二阶位移。采用三次H erm ite插值函数模拟条元横截面的翘曲位移变化,能较好地反映筒体受力“剪切滞后”效应;采用一族能较好地逼近弯剪型变形曲线的正交多项式作基函数来描述位移沿竖向变化。用最小势能原理建立稳定及二阶位移分析方程。该方法适用于任意平面形状的高层建筑筒体结构及剪力墙结构的稳定及二阶位移分析。与其它方法相比,该方法具有精度高、通用性强、计算量小等优点。     

二阶滑移边界对微型气浮轴承稳态性能的影响

考虑微型气浮轴承的尺寸特征,内部气流不再满足连续流的假设,根据Knudsen数可确定内 部气流为滑移流. 分别利用一阶速度滑移模型和二阶速度滑移模型对连续流的状态方程进行 修改,得到一阶滑移流和二阶滑移流机制下修正的雷诺方程. 利用有限差分法对连续流、一 阶滑移流和二阶滑移流的雷诺方程分别求解,得出相应的承载力和偏位角. 经过对比分析, 发现采用滑移流模型得到的轴承的稳态力学性能与连续流机制的结果存在较大差异,一阶滑 移流与二阶滑移流间的差异随偏心率增加而增加. 说明在MEMS环境下必须考虑滑移流效应 对微型气浮轴承稳态力学性能的影响. 在大偏心率工作状态下,二阶滑移流模型能够得到最 好的结果.     

Neural networks for computing in the elastoplastic analysis of structures

A neural network model is proposed and studied for the treatment of elastoplastic analysis problems. These problems are formulated as Q.P.P.s with inequality subsidiary conditions. In order to treat these conditions the Hopfield model is appropriately generalized and a neural model is proposed covering the case of inequalities. Finally, the parameter identification problem is formulated as a supervised learning problem. Numerical applications close the presentation of the theory and the advantages of the neural network approach are illustrated.

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Sommario Si propone un modello di rete neurale con l'obiettivo di usarlo per la trattazione di problemi di analisi elastoplastica, formulati come problemi di programmazione quadratica con disequazioni sussidiarie. Allo scopo di trattare queste condizioni si generalizza il modello di Hopfield e si propone un modello neurale che copre il caso di disequazioni. Inoltre il problema di identificazione parametrica viene formulato come un problema di apprendimento guidato. La presentazione della teoria è seguita da esempi di applicazioni numeriche e dalla illustrazione dei vantaggi dell'uso delle reti neurali.

     

Linearization criteria for a system of second-order quadratically semi-linear ordinary differential equations

Conditions are derived for the linearizability via invertible maps of a system of n second-order quadratically semi-linear differential equations that have no lower degree lower order terms in them, i.e., for the symmetry Lie algebra of the system to be sl(n + 2, ℝ). These conditions are stated in terms of the coefficients of the equations and hence provide simple invariant criteria for such systems to admit the maximal symmetry algebra. We provide the explicit procedure for the construction of the linearizing transformation. In the simplest case of a system of two second-order quadratically semi-linear equations without the linear terms in the derivatives, we also provide the construction of the linearizing point transformation using complex variables. Examples are given to illustrate our approach for two- and three-dimensional systems.