Coupled analysis of elastic plate-infinite nonhomogeneous layered medium

The static interaction problem between an elastic plate and infinite medium is studied by the semi-numerical (in one direction) and semi-analytical (in two directions) method-semianalytical element method, a simple practical and effective method for coupled analysis between above-ground structure and infinite soil medium with complex material character in engineering.     

弹性薄板与层状无限非均匀介质的耦联分析

本文采用一维离散、二维解析的半解析单元法研究弹性薄板与无限介质静力相互作用问题,为工程上解决具有复杂材料特性的无限土体介质与明置结构的耦联分析提供一种简便、实用、有效的方法。文中还对耦联问题中介质特性效应、相对刚度效应、板件形状效应、土层深度效应以及非均质性影响等作了较为全面的分析。     

一种三维饱和土-基础-结构动力相互作用分析方法

地震波入射时土与结构动力相互作用分析是地震工程领域的重要问题.由于问题的复杂性,以往的研究大多考虑地基土为干土情形.而实际工程中,土体中经常充满孔隙水,土层往往是含水层或部分含水层.孔隙水对土层的地震反应影响较大,进而影响支撑于其上的基础和上部结构的响应.因此,有必要考虑饱和土-基础-结构动力相互作用问题.基于此,土体采用Biot模型,利用集中质量显式有限元方法并结合多次透射人工边界进行模拟;结构经有限元离散后,采用Newmark隐式时步积分方法进行分析,可通过ANSYS等有限元软件实现;基础假定为刚性,采用显式时步积分进行求解;土体和结构(及基础)可分别采用不同的时间步距;通过FORTRAN程序实现了三维饱和土-基础-结构系统在地震作用下的整体分析.从饱和多孔介质动力微分方程出发可知,干土是饱和土的特殊情形,通过将流体体积模量及孔隙率置为零,可将饱和土退化到干土,从而将干土统一到饱和土的计算框架中,通过土-结构相互作用算例对此进行了验证,进一步实现了干土与饱和土混合情形时的土-结构动力相互作用分析,使得问题的模拟更贴近实际工程(如考虑地下水位情形).通过算例对比了饱和土地基、干土地基、干土覆盖饱和土地基(考虑地下水位)情形时,土-结构相互作用对基础和结构响应的影响,结果表明地下水位对基础和结构响应的影响较大.     

非饱和弹性半空间地基的稳态响应半解析法研究

应用半解析法研究简谐荷载下非饱和弹性半空间地基的稳态响应。基于非饱和土的动力控制方程以及非饱和弹性半空间的边界条件,建立地基层单元的半解析函数,应用加权残数法得到在简谐荷载下非饱和弹性半空间地基的稳态响应半解析方程。对半解析方程求解,得到了竖向简谐荷载作用下非饱和弹性地基水平位移和竖向位移幅值,数值分析了饱和度和地基深度等参数对孔压和位移幅值的影响。研究结果表明,应用本文方法研究非饱和弹性半空间地基的稳态响应是切实有效的。     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。     

Dispersion error reduction for acoustic problems using the smoothed finite element method (SFEM)

The smoothed finite element method (SFEM), which was recently introduced for solving the mechanics and acoustic problems, uses the gradient smoothing technique to operate over the cell‐based smoothing domains. On the basis of the previous work, this paper reports a detailed analysis on the numerical dispersion error in solving two‐dimensional acoustic problems governed by the Helmholtz equation using the SFEM, in comparison with the standard finite element method. Owing to the proper softening effects provided naturally by the cell‐based gradient smoothing operations, the SFEM model behaves much softer than the standard finite element method model. Therefore, the SFEM can significantly reduce the dispersion error in the numerical solution. Results of both theoretical and numerical experiments will support these important findings. It is shown clearly that the SFEM suits ideally well for solving acoustic problems, because of the crucial effectiveness in reducing the dispersion error. Copyright © 2015 John Wiley & Sons, Ltd.     

SEMI-ANALYTICAL AND SEMI-NUMERICAL METHOD FOR DYNAMIC ANALYSIS OF FOUNDATION

A semi-analytical and semi-numerical method is proposed for the dynamic analysis of foundations. The Lamb's solution and the approximate formulae were used to establish the relation of the contact force and deflection between the foundation and soil. Therefore, the foundation can be separated from soil and analyzed by FEM as for the static cases. The plate can be treated as that the known forces are acting on the upper surface, and the contact pressure from soil can be represented as the deflection. So that only the plate needs to be divided into elements in the analysis. By this method, a series of vibration problems, including various shapes and rigidities of foundations, different excitation frequencies, were analyzed. Furthermore, it can be used for the embedded foundation. The numerical examples show that this method has simplicity, highly accurate and versatile. It is an effective method for the dynamic analysis of foundations.     

由Gurtin变分原理求解一维动力响应的半解析法

基于Gurtin变分原理本文提出了求解动力响应问题的半解析法.该方法在空间域内进行有限元离散,在时间域上取级数。实例表明,该方法是求解动力响应问题的一种非常有效的方法。本文引入了一种节点位移函数,使所导出的位移模式可以求解各种初始条件和载荷的一维动力响应问题。     

振动台模型试验中地基土域的数值模拟

针对土－结构动力相互作用振动台模型试验中有限地基土域的模拟问题，本文分别采用有限元法和边界元法对地基土模型的侧向人工边界和底部人工边界的合理位置问题进行了计算分析。文中首先采用三维有限元方法，探讨了地基土侧向垂直人工边界不同位置对群桩基础和箱形基础地震反应的影响，提出了侧向人工边界合理位置的具体建议；然后利用层土动力Green函数建立边界元模型，通过对埋入式条形基础的动力反应分析，探讨了底部水平人工边界的合理位置，提出了相应的建议。     

智能板结构振动特性的半解析法

为智能板结构振动特性的分析提出了一种半解析法.根据压电材料修正后的Hellinger-Re issner变分原理,推导了压电材料的Ham ilton ian等参元.智能板结构的基体板和压电块(压电传感器或驱动器)被看作独立的三维体,并用Ham ilton ian等参元分别离散板和压电块.考虑到板和压电块在连接界面上广义应力和广义位移的连续性,联立板和压电块的方程得到整个结构的方程组.数值实例的分析结果证明了方法的可靠性.     

A work softening joint element used in dynamic analysis of soil-structure

This paper introduces an elasto-plastic joint element characterised by strain hardening and softening in the analysis of dynamic soil-structure interaction. The phenomena of separation and sliding on the contact surface between soil and structure can be better simulated and the process can also be described. The interaction problems in a typical soil-structure system are analyzed in terms of elasto-plastic joint element as well as elastic ones. The results show that the elasto-plastic joint element is much better than the elastic one in modelling, especially in that the relative displacements accross the joint element can be much greater than that of the elastic case. Separation and sliding are not only related to the coefficient of friction and cohesion but also to their changes with plastic volumetric strain. The project is supported by the Sciences Foundation of the Chinese Academy of Sciences and the Disaster Provention Institute of Kyoto University (Japan).     

二维弹性接触问题中随机边界元法与可靠性分析

发展了二维弹性接触问题中的随机边界元法，推导并建立了相应的随机边界元基本方程，并将所发展的方法用于静强度的可靠性分析，讨论了其数值解技术。通过算例分析表明，本文发展的方法是可行的。     

爆炸波作用下地下防护结构与围岩的非线性动力相互作用分析

针对实际地下工程中普遍存在的材料非线性以及半无限介质域的处理问题,给出了基于时间有关基本解的时域边界元法与非线性动力有限元法的耦合方法,应用该耦合方法计算了一马蹄形截面地下防护结构与围岩受爆炸冲击波作用下非线性相互作用的时间历程,并与线弹性情况进行了比较分析。结果表明:本文的方法具有较高精度,真实地再现了波在弹性层中传播以及反射的全过程。     

断裂力学的相似边界元法及其应用

首先对弹性力学的相似边界元法进行了研究,推导了相应的计算公式。与传统的边界元法相比,相似边界元法由于只需在少数单元上进行数值积分,当边界单元数目较多时大大减少了计算量。在此基础上,将相似边界元法应用于断裂力学,对路面断裂力学问题进行了计算,与有限元法的结果比较,说明了本文方法在减少计算量的情况下仍能较好地保证精度。     

弹性体的正则方程和加筋板的固有频率分析

应用弹性力学的Hamilton正则方程理论和其半解析法，为整体加筋板的固有频率分析提出了一种新颖的数学模型. 采用同一种平面元素离散板和加强筋，并分别建立板和加强筋的线性方程组. 考虑到板和加强筋连接界面上应力和位移的连续性，联立板和加强筋的方程得到全结构的方程组和求解固有频率的特征方程. 主要优越性表现为：结构的旋转惯性、剪切变形等都得到了考虑，且不限制结构的板厚度和加强筋的高度. 多个数值实例的收敛分析和结果证明了方法是可靠的. 该方法很容易被修改用来分析加筋壳、加筋压电材料层合板或带有压电材料传感器和驱动器块的板壳问题.     

以DIASS程序为基础的饱和土与防护结构相互作用动力分析研究

介绍了新开发的防护结构动力有限元分析程序DIASS系统。该系统装有空爆冲击波荷载数值自动生成器,并可将基础土壤模拟为饱和多孔介质模型,采取多重子结构技术进行结构与土体相互作用的动力分析。文中利用该程序系统进行数值试验,给出若干初步结论。     

Elastic responses of underground circular arches considering dynamic soil-structure interaction: A theoretical analysis

Due to the wide applications of arches in underground protective structures, dynamic analysis of circu- lar arches including soil-structure interactions is important. In this paper, an exact solution of the forced vibration of circular arches subjected to subsurface denotation forces is obtained. The dynamic soil-structure interaction is considered with the introduction of an interfacial damping between the structure element and the surrounding soil into the equation of motion. By neglecting the influences of shear, rotary inertia and tangential forces and assuming the arch incompressible, the equations of motion of the buried arches were set up. Analytical solutions of the dynamic responses of theprotective arches were deduced by means of modal superposition. Arches with different opening angles, acoustic impedances and rise-span ratios were analyzed to discuss their influences on an arch. The theoretical analysis suggests blast loads for elastic designs and predicts the potential failure modes for buried protective arches.     

ELASTO-PLASTIC COUPLED ANALYSIS OF BURIED STRUCTURE AND SOIL MEDIUM BY PERTURBATIONAL SEMI-ANALYTIC METHOD

I.IntroductionMoreandmoreelasto-plasticanalysesareusedinCivilEngineering.TheMohr-Coulombyieldconditionisoftenappliedtorockandsoilmediumtostudythesituationofdestruction.Theperturbationalmethodwasfirstusedinthestudyofcelestialmechanics,thenithasbeenusedinsolidmechanicstocarryoutthegeometricallyandphysicallynonlinearanalysis[']'12].Forlarge?scalcproblems,thegeneralnumericalmethodsmaynotbeapttothiscomplexcalculation,butsemi-analyticalmethodscandoitwell.Touseanalyticalfunctionsinoneortwodirectio…     

土与结构界面接触问题研究进展评述

针对土与结构相互作用研究中的土-结构界面接触问题,本文从界面接触力学特性及界面接触模拟两个方面的研究展开评述.分析了接触面(带)的力学特性和变形分布规律方面的试验方法和取得的成果,讨论了现有试验方法的不足;随后,对土-结构界面接触行为的两类模拟方法--接触面单元方法和接触力学方法进行了讨论;最后提出了今后工作的重点.      

Hamiltonian parametric element and semi-analytical solution for smart laminated plates

Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.