加筋土地基模型试验边界效应与承载性能分析

为进一步探讨边界效应对加筋土地基的影响,基于室内方形基础下加筋土地基大模型试验,采用ABAQUS有限元软件建立加筋土地基数值模型,主要分析了模型宽度L和加载板宽度B对加筋土地基承载性能、地基内部土体应力应变及筋材变形的影响.结果表明:无筋地基与加筋土地基极限承载力均随L/B的减小而增大,当L/B＞5时,可忽略边界效应对...     

梯度弹性基础上正交异性薄板的弯曲

基于能量法和变分原理,采用双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板在分布载荷作用下的弯曲问题。首先,根据能量法与变分原理,给出了梯度弹性基础上正交异性薄板的弯曲微分平衡方程,并得到了梯度弹性基础刚度系数 与 的计算表达式;进而,假设 向正应力在厚度方向上均匀分布,推导了弹性基础 向位移衰减函数 的计算式。在算例中,通过将梯度弹性基础退化为均质基础,并与Vlazov模型对比,证明了本文理论的正确性;最后,求解了弹性模量呈幂律分布的梯度基础上薄板的挠度分布,分析了基础上下表层材料弹性模量比 与体积分数指数 对薄板挠度分布的影响。     

饱和地基上弹性圆板的动力响应

研究弹性圆板在饱和地基上的垂直振动特性,即首先应用Hankel变换方法求解饱和土波动方程,然后按混合边值条件建立饱和地基上圆板垂直振动的对偶积分方程,用一种简便的方法,对偶积分方程可化为易于数值计算的第二类Fredholm积分方程。文末的数值分析得出了板振动的一些规律性,由此表明当板的挠曲刚度D趋于无穷大且不计板的质量时,其结果和无质量刚性圆盘在饱和地基上的振动特性完全一致。     

饱和地基上基础动力阻抗函数的一种分析方法

提出了一种基础阻抗函数的时域求解方法, 并用于饱和地基情形. 通过给基础输入脉冲位移, 应用集中质量显式有限元方法结合局部透射人工边界, 得到地基施加于基础的反力时程, 然后根据阻抗函数的定义, 应用傅立叶变换求得基础阻抗函数. 通过算例, 与 Halpern 的结果进行了对比, 验证了该方法的有效性. 并以一方形基础为例, 分别讨论了泊松比、孔隙率、渗透系数和埋深对无量纲动力柔度的影响. 与以往方法相比, 该方法可以考虑复杂地基情形和不规则基础形式.      

简支方板在弹性基础上的塑性动力响应

用加权残值法中的矩量法解简支方板塑性动力响应，分析弹性基础对方板塑性动力响应的影响，解出了弹性基础上方板残余挠度和终止运动时间。     

An efficient solution methodology to study the response of a beam on viscoelastic and nonlinear unilateral foundation: Static response

Many engineering materials and foundations such as soils demonstrate nonlinear and viscoelastic behaviour. Yet, it is challenging to develop static and dynamic models of systems that include these materials and are able to predict the behaviour over a wide range of loading conditions. This research is focused on a specific example: a pinned–pinned beam interacting with polyurethane foam foundation. Two cases, when the foundation can react in tension and compression as well as only in compression, are considered. The model developed here is capable of predicting the response to static as well as dynamic forces, whether concentrated or distributed. Galerkin’s method is used to derive modal amplitude equations. In the tensionless foundation case, the contact region changes with beam motion and the estimation of the co-ordinates of the lift-off points is embedded into the solution procedure. An efficient solution technique is proposed that is capable of handling cases where there are multiple contact and non-contact regions. Depending on the loading profiles a high number of modes may need to be included in the solution and to speed up computation time, a convolution method is used to evaluate the integral terms in the model. The adaptability of the solution scheme to complicated loading patterns is demonstrated via examples. The solution approach proposed is applicable to dynamic loadings as well and in these cases the automated treatment of complicated response patterns makes the convolution approach particularly attractive. The influence of various parameters on the static response is discussed.     

地基梁动-静态响应的比较分析

采用分离变量法求得了冲击荷载作用下的开尔文地基上两端自由有限长梁动态挠曲线方程的级数解;分析了地基梁结构参数和冲击荷载作用时间对梁挠曲线特征值（最大挠度和挠曲线面积）的影响规律;比较地基梁动态挠曲线与静荷载引起的地基梁静态挠曲线之间差异,发现：(1)等效地基梁动态最大挠度或挠曲线面积的当量静荷载值与冲量之间不存在良好对应关系;(2)依据地基梁动态挠曲线用静态方法反演得到的地基梁结构参数有可能含有较大的偏差．     

基于遗传算法的弹性地基加肋板肋梁无网格优化分析

基于遗传算法及一阶剪切理论, 提出一种弹性地基上加肋板肋条位置优化的无网格方法. 首先, 通过一系列点来离散平板及肋条, 并用弹簧模拟弹性地基, 从而得到加肋板的无网格模型; 其次, 基于一阶剪切理论及移动最小二乘近似原理导出位移场, 求出弹性地基加肋板总势能; 再次, 根据哈密顿原理导出结构的弯曲控制方程, 并通过完全转换法处理边界条件; 最后, 引入遗传算法和改进遗传算法, 以肋条的位置为设计变量、弹性地基板的中心点挠度最小值为目标函数, 对肋条位置进行优化达到地基板控制点挠度最小的目的. 以不同参数、载荷布置形式的弹性地基加肋板为例, 与ABAQUS有限元结果及文献解进行比较. 研究表明, 采用所提出的无网格模型可有效求解弹性地基上加肋板弯曲问题, 结果易收敛, 同时基于遗传算法与改进混合遗传算法所提出的无网格优化方法均可有效优化弹性地基加肋板肋条位置, 后者计算效率相对较高, 只进行了三次迭代便可获得稳定的最优解, 此外在优化过程中肋条位置改变时只需要重新计算位移转换矩阵, 又避免了网格重构.      

Bending problems of rectangular Reissner plate with free edges laid on tensionless Winkler foundations

In this paper,an analytical method for solving the bending problems of rectangularReissner plate with free edges under arbitrary loads laid on tensionless Winkler foundationsis proposed.By assuming proper form of Fourier series with supplementary terms,whichmeet derivable conditions,for deflection and shear force functions,the basic differentialequations with given boundary conditions can be transformed into a set of simple infinitealgebraic equations.For common Winkler foundations,this set of equations can be solveddirectly and for tensionless Winkler foundations,it is a set of weak nonlinear algebraicequations,the solution of which can be obtained easily by using iterative procedures.     

计算复杂地基动力柔度系数的分段递推方法

介绍复杂地基动力柔度系数的一个快速有效计算方法——分段递推法。这一方法的基本思想是：将频率域分为若干子域，利用子域中点频率处的动力柔度系数向前或向后递推子域内其它频率点处的动力柔度系数，以简化计算过程。文中讨论了实施这一方法的基本过程，并提出了迭代计算方法，进一步改善计算精度。在算例中，近似解与解析解相比，具有很好的近似精度。     

弹性地基板的无奇异边界元解法

本文用无奇异边界单元法,分析弹性地基上薄板的弯曲问题,考虑Winkler和双参数地基模型,选择第三类复变量的Bessel函数作为该问题的基本解,由此导出了一组权函数,在数值解法中,对面荷载积分项均统一化为边界积分,避免了在域内划分网格,文中还给出了一种考虑桩支承的边界元分析方法及域内点弯矩和接触应力的计算公式。     

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。     

高次数值流形方法及其在弹性地基板中的应用

根据数值流形方法的思想,用Hermite插值函数表示三角形板单元位移模式中的权函数,并在此基础上,在不增加额外覆盖数的条件下,构建了一种新的更高次痊移模式,各种条件的计算结果表明这种位移模式具有精度高的,优点,很有实用意义。     

Boundary Element Analysis of Raft Foundations on Piles

The boundary element method is used in the formulation of models for the analysis of raft foundations on piles. Two models are considered: a Kirchhoff plate on a layered elastic half-space and a Kirchhoff plate on a Winkler soil. The plates are modelled using conforming boundary elements and the piles by using linear finite elements. Mindlin's solution is used as influence function within the half-space while Boussinesq's solution, a precursor although a particular case of Mindlin's solution, is used to derive the deflections of the soil surface. The models are used in the analysis of some raft foundations on piles and the results and relative merits are discussed.     

弹性地基上含孔隙功能梯度材料板的自由振动和动力响应

为研究弹性地基上含孔隙的材料特性沿厚度呈Sigmoid函数变化的功能梯度材料(S-FGM)板的振动特性,本文基于改进的Voigt模型,分别建立了孔隙为均匀分布和非均匀分布两种类型的功能梯度材料的物性参数模型.根据复合材料薄板理论导出了弹性地基上含孔隙的功能梯度材料板的运动方程,用伽辽金法寻求四边简支边界条件下板自由振动...     

自然单元法在Winkler地基薄板计算中的应用

自然单元法是一种基于Voronoi图及Delaunay三角形剖分图,以自然邻接点插值为试函数的一种无网格数值方法.本文以目前该方法中自然邻接点的Laplace插值形函数为基础,求出了其一阶及二阶导函数,建立了Winkler地基上薄板弯曲挠度的自然单元法求解控制方程,并编制了相应的计算程序,通过算例分析表明了本文方法的可行性和有效性.     

Nonlinear bending behavior of orthotropic Mindlin plate resting on orthotropic Pasternak foundation using GDQM

Rectangular plates resting on elastic foundations are operational activities of large transportation aircraft on runways, footings, foundation of spillway dam, civil building in cold regions, and bridge structures. Hence, in the present work, nonlinear bending analysis of embedded rectangular plates is investigated based on orthotropic Mindlin plate theory. The elastic medium is simulated by orthotropic Pasternak foundation. Adopting the nonlinear strain–displacement relation, the governing equations are derived based on energy method and Hamilton’s principle. The generalized differential quadrature method is performed for the case when all four ends are clamped supported. The influences of the plate thickness, shear-locking, elastic medium constants, and applied force on the nonlinear bending of the rectangular plate are studied. Results indicate that increasing the plate thickness decreases the deflection of the plate. It is also observed that increasing the applied force increases the deflection of the plate. Furthermore, considering elastic medium decreases deflection of the plate, and the effect of the Pasternak-type is higher than the Winkler-type on the maximum deflection of the plate. Also, it is found that the present results have good agreement with previous researches.     

A parametric study for thick plates resting on elastic foundation with variable soil depth

The soil depth is generally considered to be constant for the analysis of plates resting on elastic foundation in the literature. However, it is most reasonable to have a variable subsoil depth as the plate dimensions get larger. In present study, linearly varying subsoil depth is considered as well as constant, linear and quadratic variation of modulus of elasticity with subsoil depth. Also, a parametric study is performed to demonstrate the behavior of thick plates on elastic foundations with variable soil depth. Modified Vlasov Model is used for the analysis of the plate foundation system, and 8-noded Mindlin plate element incorporating shear strain throughout plate thickness is used for the finite element model. Numerical examples are obtained from the literature to compare results and to show the influence of variable soil stratum depth on the behavior of plates. Displacements, bending moments, and shear forces are presented in tabular and graphical formats. As far as results are compared, it can be concluded that variable soil depth significantly affects the variation of the displacements and therefore the internal forces of the plate while keeping it constant ends up with unrealistic results.     

基于梁挠度函数的板解法

基于相应边界支撑和载荷下的梁挠度形函数, 构建板的挠度形函数,求解板的变形, 并用典型算例进行了验证; 对于狭长矩形板,依据其变形特点进行了修正; 结果与三维有限元结果基本一致,说明了该方法的适用性和准确性. 由于板结构内部的相互作用没有得到充分反映,为了更贴近板变形的物理实际, 引入弹性基础梁的挠度函数代替普通梁的挠度函数,进一步完善本文方法. 本文研究成果为工程板件变形的理论分析提供了准确且简便易行的计算方法.     

薄板小波有限元理论及其应用

利用样条小波尺度函数构造了常用的三角形和矩形薄板单元的位移函数,得到了利用小波函数表示的形函数。采用合理的局部坐标,对单元进行压缩,使单元在局部坐标区间上有其值,成功地推导出了分域的三角形和矩形薄板小波有限元列式。在此基础上,提出了弹性地基薄板的小波有限元求解方法。通过两个算例对薄板的挠度和弯矩进行了计算,数值结果表明,求解结果具有收敛快、精度高的特点。