砂井地基的一个简化计算模型

基于三维有限元方法，提出了一个预测和评价砂井地基的简化计算模型。该计算模型采用块体单元模拟砂井周围的土体，用砂井单元模拟砂井的竖向排水和水平排水过程，并且推导了反映土体单元和砂井单元之间排水过程的连续性方程。克服了以往有限元法计算砂井地基时，需要将砂井和周围土体作均质化等价的缺点，并可用弹塑性模型反映砂井周围土体的非线性变形和强度特性。计算了单个砂井地基固结排水过程。通过和理论解的比较表明，用本文简化计算模型得到的结果和理论解比较接近。同时，还计算了日本某高速公路路基用砂井 堆载预压法处理的过程，通过分析表明，该简化模型能反映砂井地基的固结排水过程，可以应用于实际工程。     

复合地基群井固结模型理论研究

针对复合地基固结问题,考虑井阻和土体径竖向渗流的影响,建立以"桩–土–桩"为单元的复合地基群井计算模型,采用解析解法,推导出瞬时载荷作用下复合地基群井固结解析解,讨论了复合地基固结特点和孔压等的变化规律。研究表明,复合地基群井固结模型为复合地基固结理论的研究提供了一种新思路,在井径比大于5时,基于中心桩、边桩流量相等假设,复合地基群井固结理论所求固结度和传统固结理论所求固结度相差很小,可忽略不计;桩体渗透系数、内外扰动区土体径向渗透系数、土体竖向渗透系数越大,复合地基固结速率越快;堆载越大,最终达到稳定时的沉降量和竖向应变越大;地基表层土体的孔压消散速率和竖向应变速率大于地基深部土体。     

平面三角形单元有限元差分法

本文基于有限元差分法的构造方法,建立了平面三角形单元的有限元差分法。该方法的计算过程简单、规范,能够形成通用的计算程序。它直接给出连续的应力场,能够通过常应变收敛试验,具有较常规有限元法高得多的计算精度。更重要的是,该方法的构造思路能够推广于人们熟知的任何单元中。     

A CONSOLIDATION MODEL OF GROUP WELLS ON COMPOSITE FOUNDATION1)

针对复合地基固结问题,考虑井阻和土体径竖向渗流的影响,建立 以"桩-土-桩"为单元的复合地基群井计算模型,采用解析解法,推导出瞬时载荷作用下复合地基群井固结解析解,讨论了复合地基固结特点和孔压等的变化规律。研究表明,复合地基群井固结模型为复合地基固结理论的研究提供了一种新思路,在井径比大于5 时,基于中心桩、边桩流量相等假设,复合地基群井固结理论所求固结度和传统固结理论所求固结度相差很小,可忽略不计;桩体渗透系数、内外扰动区土体径向渗透系数、土体竖向渗透系数越大,复合地基固结速率越快;堆载越大,最终达到稳定时的沉降量和竖向应变越大;地基表层土体的孔压消散速率和竖向应变速率大于地基深部土体。     

基于边光滑有限元法的加筋板静力和自由振动分析

运用边光滑有限元法,研究分析了加筋板结构的静力和自由振动问题。在边光滑有限元法中,将基于边的应变光滑技术用于对原来的应变场进行光滑操作;由于应变光滑技术能够适当地软化原来过刚的有限元模型,从而能够得到更加接近于系统准确刚度的光滑有限元模型;鉴于三角形单元良好的适用性,选用三角形单元对模型进行网格划分;同时,为了解决低阶Reissner-Mindlin板单元弯曲过程中的横向剪切自锁问题,采用了一种新型的离散剪切间隙技术。算例的数值计算结果表明,与传统的有限元法相比,边光滑有限元法能够得到精度更高的计算结果,且收敛更快,计算效率更佳。     

排水固结法加固软基变形简化计算分析

插板和砂井堆载预压是处理软基有效方法之一,现有的沉降变形计算方法大部分采用轴对称理论的解析解和以太 沙基或比奥固结理论为基础的数值解,仍较为复杂。根据软基排水固结机理,采用固结度等效原理,对渗透系数进行调整,把 砂井(插板)地基简化为均质成层地基。运用有限元对某软土路基处理工程进行简化计算,并和监测结果进行对比分析,对简 化计算方法进行验证。发现具有较好的准确性,为实际软基处理工程的沉降变形分析提供了一种简单实用的方法。     

混合Trefftz有限元法反平面断裂问题的探讨

基于修正变分原理,采用满足控制微分方程的应力和位移混合Trefftz函数,满足裂纹单元断裂性质的特殊Trefftz函数以及满足裂纹尖端条件的附加试函数,推导出混合Trefftz有限元法反平面断裂问题公式,给出应力集中因子解析表达式.同时,给出单个边裂纹、单个曲折裂纹和三个边裂纹反平面裂纹问题三个算例,探讨特殊Trefftz函数个数、破裂单元个数、高斯点数以及不同附加试函数对结果的影响.最后,将计算结果与一般有限元算法或其它方法结果进行对比,分析了混合Trefftz有限元法的精确性和高效性.     

SiC/Al梯度功能材料紧凑拉伸试件裂纹扩展分析

SiC/Al梯度功能材料各梯度层由不同体积浓度的陶瓷和金属组成,由于材料组分梯度变化,克服了双材料界面的应力突变问题,获得了优异的使用性能.本文首先采用激光云纹干涉法,对具有四个梯度层的SiC/Al梯度功能材料紧凑拉伸试件在机械荷载作用下的拉伸实验位移场进行记录,进而获得紧凑拉伸试件裂纹口位移P-V曲线以及材料断裂韧度实验值;然后根据层合梯度功能材料理论分析模型,建立FGM紧凑拉伸试件的渐近分网有限元平面应变模型,采用通用有限元软件的单元删除模块对试件模型进行裂纹扩展单元的应变模拟分析,从计算所得的裂纹尖端应变图像分析得出梯度材料试件的裂纹扩展规律.     

弹性地基上Timoshenko梁的精确数值解

研究了弹性地基上Timoshenko梁的高精度有限元分析方法,利用控制微分方程的基本解建立了单元形函数,提出了弹性地基上Timoshenko梁分析的Trefftz单元。通过对引入的非节点自由度进行静力凝聚,得到的精确单元与常规单元具有相同的节点自由度。文中还讨论了有效降低计算过程中舍入误差的方法。算例结果表明,采用提出...     

用拟协调元直接构造平面任意四边形单元——进入有限元的禁区

利用拟协调元方法,在直角坐标系下直接构造了一族平面任意四边形单元,对其收敛性进行了分析,并与平面等参元进行了对比研究.结果证明平面任意四边形单元可采用多项式基函数直接列式,并可以保障单元的收敛性;拟协调元列式可以使平面问题的有限元方法得到统一.与平面等参元相比,单元列式简单,性能稳定,具有显式的刚度阵,计算量小,这说明对于有限元平面问题拟协调元是一个更正确、有效的做法.      

Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites

A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories.     

一个改进的平面梁单元

根据有限单元法基本原理 ,提出了一个变截面平面梁单元 ,推导了其单元钢度矩阵。这一改进的梁单元用于分析梁高呈线性变化及二次抛物线变化的矩形截面梁 ,将得到准确解。文中给出了一个变截面悬臂梁算例 ,计算表明 ,这一改进的梁单元使变截面梁的分析大大简化     

A new finite element method for strain gradient theories and applications to fracture analyses

A new compatible finite element method for strain gradient theories is presented. In the new finite element method, pure displacement derivatives are taken as the fundamental variables. The new numerical method is successfully used to analyze the simple strain gradient problems – the fundamental fracture problems. Through comparing the numerical solutions with the existed exact solutions, the effectiveness of the new finite element method is tested and confirmed. Additionally, an application of the Zienkiewicz–Taylor C1 finite element method to the strain gradient problem is discussed. By using the new finite element method, plane-strain mode I and mode II crack tip fields are calculated based on a constitutive law which is a simple generalization of the conventional J₂ deformation plasticity theory to include strain gradient effects. Three new constitutive parameters enter to characterize the scale over which strain gradient effects become important. During the analysis the general compressible version of Fleck–Hutchinson strain gradient plasticity is adopted. Crack tip solutions, the traction distributions along the plane ahead of the crack tip are calculated. The solutions display the considerable elevation of traction within the zone near the crack tip.     

An improvement of the Prandtl-Reuss theory and the hybrid / mixed vari-stiffness method of finite element analysis

The common Prandtl-Reuss theory has been improved in this paper. A quasi-flow law of the isotropic hardening Mises materials has been proposed as well, on the basis of which, an efficient iterative algorithm of finite element analysis, hybrid / mixed vari-stiffness method, has been obtained. The numerical examples calculated by the plane stress / strain element model are given. Compared with the common initial stress method, the hybrid / mixed vari-stiffness method shows its advantages in the convergent speed, calculating accuracy and treatment scheme of the incompressibility of materials.     

分区界面元-有限元-无限元混合模型

利用界面元良好的相容性,引入过渡界面元的概念．实现了界面元与有限元二种数值计算方法的结合,并提出了一种界面元-有限元-无限元混合模型。这种混合模型既可以发挥界面元计算精度高、适用于不连续变形等优点．又能够充分利用有限元的计算效率和无限元方便处理无限域介质的特点,较为和谐地解决了计算精度和计算效率的矛盾。数值算例表明,本文所建立的混合模型的有效性,揭示此类混合模型具有广阔的工程应用前景。     

基于有限单元柔度法的材料与几何双重非线性空间梁柱单元

从有限单元柔度法的基本思想出发,基于完全拉格朗日格式(TL格式),建立了能考虑材料与几何双重非线性的一般化空间梁柱单元,适用于满足Euler-Bernoulli梁柱二阶分析理论假定的空间杆系结构非线性分析。另外,在梁柱单元截面分析中引入纤维模型,使其适用于解决钢筋混凝土这类复合材料结构的非线性分析问题。对钢筋混凝土双向偏心受压柱试验结果的模拟分析表明,本文所提方法是正确、可靠的,能有效地分析钢筋混凝土框架柱的材料与几何双重非线性问题。     

钢－混凝土组合梁非线性有限元分析

提出了部分剪力连接钢-混凝土组合梁非线性有限元分析的简化模型，该模型同时考虑了钢、混凝土材料的非线性本构关系和剪力连接件的滑移非线性对组合梁刚度和强度的影响，推导了考虑滑移的剪力连接件单元刚度矩阵。利用该模型计算了连续组合梁的极限荷载、挠度、应力以及滑移，与已有的理论计算结果和实验结果吻合，证明本方法分析钢-混凝土组合梁非线性的可靠性和实用性。     

矩形空腔内Stokes流的状态空间有限元法

基于Hellinger-Reissner二类变分原理,从平面Stokes流问题的平衡方程、连续性要求和边界条件出发,得到相应的Hamilton函数,建立Hamilton正则方程后,采用分离变量法对场变量进行离散求解:在x方向采用有限元插值,在y方向采用状态空间法给出控制坐标方向的解析解。计算过程中的指数矩阵均采用精细积分法求解,使得本文算法具有高效率、高精度、对步长不敏感的优点。通过对侧边自由液面边界条件的单板驱动矩形空腔Stokes流问题的求解,得到与文献相同的结果,从而验证了本文方法的有效性。本文旨在将弹性力学状态空间有限元法的思想引入到低雷诺数流体力学中,为Hamilton体系下研究复杂边界Stokes流问题提供新的途径。     

On constitutive modelling of porous neo-Hookean composites

In this paper a hyperelastic constitutive model is developed for neo-Hookean composites with aligned continuous cylindrical pores in the finite elasticity regime. Although the matrix is incompressible, the composite itself is compressible because of the existence of voids. For this compressible transversely isotropic material, the deformation gradient can be decomposed multiplicatively into three parts: an isochoric uniaxial deformation along the preferred direction of the material (which is identical to the direction of the cylindrical pores here); an equi-biaxial deformation on the transverse plane (the plane perpendicular to the preferred direction); and subsequent shear deformation (which includes “along-fibre” shear and transverse shear). Compared to the multiplicative decomposition used in our previous model for incompressible fibre reinforced composites [Guo, Z., Peng, X.Q., Moran, B., 2006, A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54(9), 1952–1971], the equi-biaxial deformation is introduced to achieve the desired volume change. To estimate the strain energy function for this composite, a cylindrical composite element model is developed. Analytically exact strain distributions in the composite element model are derived for the isochoric uniaxial deformation along the preferred direction, the equi-biaxial deformation on the transverse plane, as well as the “along-fibre” shear deformation. The effective shear modulus from conventional composites theory based on the infinitesimal strain linear elasticity is extended to the present finite deformation regime to estimate the strain energy related to the transverse shear deformation, which leads to an explicit formula for the strain energy function of the composite under a general finite deformation state.