Linear and nonlinear vibration of non-uniform beams on two-parameter foundations using p-elements

A hierarchical finite element is presented for the geometrically nonlinear free and forced vibration of a non-uniform Timoshenko beam resting on a two-parameter foundation. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem. With the enriching degrees of freedom, the accuracy of the computed results and the computational efficiency are greatly improved. The arc-length iterative method is used to solve the nonlinear eigenvalue equation. The computed results of linear and nonlinear vibration analyses show that the convergence of the proposed element is very fast with respect to the number of Legendre orthogonal polynomials used. Since the elastic foundation and the axial load applied at both ends of the beam affect the ratios of linear frequencies associated with the internal resonance, they influence the nonlinear vibration characteristics of the beam. The axial tensile stress of the beam in nonlinear vibration is investigated in this paper, and attention should be paid to the geometrically nonlinear vibration resulting in considerably large axial tensile stress in the beam.     

预应力锚索格构梁作用下边坡土中应力分布的室内模型试验研究

预应力锚索格构梁由于其多方面的优点而在工程中得到了广泛的应用。但到目前为止，对预应力锚索格构梁的设计计算还没有提出一个合理的计算模型。本文针对现有计算模型对格梁底部地基反力的分布假设的不足，进行了预应力锚索格构梁的室内模型试验，并对格梁底部土体应力的实际分布情况进行了分析。分析结果显示，土中应力随锚索预应力的增大而增大，且格梁底部的基底反力并非成直线或线性变化，而是与所加锚索的位置有关，因此不能简单地将格构梁看成刚性梁。最后，就本模型试验所存在的不足对今后的研究方向提出了几点建议。     

钻井船插桩对邻近桩影响的耦合欧拉-拉格朗日有限元方法研究

依据模拟钻井船在黏土层中插桩对邻近桩影响的离心模型试验结果,研究了通过耦合欧拉-拉格朗日（CEL）有限元计算并结合非线性地基梁有限元计算,分析钻井船插桩对邻近桩影响问题的可行性。CEL有限元方法将产生大变形的土体设为欧拉体,采用欧拉有限元方法计算该区域的变形响应,计算过程中,欧拉体的空间网格形状、大小位置保持不变,物质可在网格之间运动;其他土体设为拉格朗日体,采用拉格朗日有限元方法计算变形响应,计算过程中,物质的运动和网格的变形保持一致。运用罚函数方法实现欧拉体与拉格朗日体的耦合。通过CEL有限元计算,可以确定钻井船插桩导致的邻近桩桩身水平位移。进一步通过非线性地基梁有限元模型计算确定桩身弯矩。计算结果表明,利用CEL有限元方法并结合非线性地基梁有限元方法计算出的桩身位移和弯矩沿桩长的变化与离心模型试验结果基本一致。说明采用CEL有限元方法并结合非线性地基梁有限元方法分析黏土层中插桩对邻近桩的影响问题是可行的。CEL有限元模型中欧拉土体范围的设置对计算结果有明显影响。研究表明,若插桩深度小于0.75倍桩靴直径,可将欧拉土体范围设置成1.00～1.25倍桩靴直径;若插桩深度大于0.75倍桩靴直径,将欧拉土体范围取为插桩深度以下0.5倍桩靴直径是恰当的。     

刚性桩复合地基沉降计算的简化方法

既简便又具有较好精度的刚性桩复合地基沉降计算方法仍是工程实践中迫切需要而又有待于解决的问题,文中提出了一个解决的简化方法。在刚性桩复合地基中,由于桩间土荷载水平不高,将桩间土荷载-沉降曲线近似为线性。当桩的荷载水平不高时,对桩的沉降可按线性考虑,线性关系可按线弹性方程计算得到。若桩可能进入非线性甚至塑性,则假设桩的荷载-沉降曲线满足双曲线规律,可较好地考虑桩的非线性沉降过程。通过计算单桩承载力特征值下的沉降,然后通过双曲线方程特点得到桩的非线性沉降方程。对于有单桩静载试验的情况,提出直接利用单桩试验曲线建立单桩的双曲线方程。最后依据共同作用时桩和桩间土的变形协调条件和静力平衡方程,即可计算其实际基础下复合地基的沉降,从而得到一个刚性桩复合地基沉降计算的简化方法。工程实例表明,简化是方法既简便又具有较好的精度,可为工程实践提供一个有效实用的计算方法。     

非线性破坏准则与岩土材料地基承载力研究

根据线性Mohr-Coulomb破坏准则,前人运用极限平衡法、滑移线理论或极限分析等方法求解地基承载力问题,但实际上岩土在剪切破坏过程中破坏准则具有非线性。因此,为了研究非线性破坏准则对地基承载力的影响,基于上限定理,通过“切线法”引进变量,根据能量耗散情况,将承载力问题转变为非线性规划问题,运用“序列二次规划算法”求出地基承载力的最优解。数值计算结果表明,当非线性破坏准则转变为线性破坏准则时,非线性参数对地基承载力有重要影响。     

考虑位移的柔性挡墙上土压力计算

针对地下连续墙等柔性挡土结构, 根据土体的渐进破坏机制,建立了非极限状态下改进的库仑土压力公式,并推导了填土内摩擦角及墙土接触面上外摩擦角的发挥与土体位移的非线性关系。将这一公式运用到改进的弹性抗力法中,得到了一种新的考虑位移的柔性挡墙上土压力计算方法。算例分析表明,模型板上土压力计算值和试验实测值吻合得较好。该计算方法可用于柔性挡墙的设计及验算。     

Free vibration of functionally graded beams resting on Winkler-Pasternak foundation

In the present study, the free vibration of functionally graded beams resting on two parameter elastic foundation was examined. The properties of the functionally graded materials were presumed to vary continuously along the thickness direction. The foundation medium was assumed to be linear, homogeneous, and isotropic, and it was modeled by the Winkler-Pasternak model with two parameters for describing the reaction of the elastic foundation on the beam. The functionally graded beam was modeled with classical beam theory. The governing equation including the effects of functionally graded material properties, Winkler-Pasternak elastic foundation was solved using separation of variables. The eigenvalues of yielding fundamental equation versus clamped-clamped, clamped-free, clamped-simply supported, and simply supported-simply supported boundary conditions were found. To corroborate the results, comparisons were carried out with available results for homogeneous and functionally graded beams. The effects of Winkler-Pasternak type elastic foundation and functionally graded material properties on the values of dimensionless frequency parameter of beams were discussed. Briefly, it was found that the dimensionless frequency parameters of beam change according to material properties, presence of elastic foundation, and boundary conditions; moreover, the separate effects of these quantities on each other are interesting.     

基于原位试验成果的地基非线性沉降分析

提出了利用小尺寸载荷试验（PLT）及标准贯入试验（SPT）成果准确求解地基非线性沉降的新方法。首先利用压板载荷试验成果经过双曲线拟合,确定出某一土层地基土的修正切线模量;然后根据不同深度的SPT标贯击数按照线性相关关系,确定该土层不同深度各分层土的修正切线模量;最后依据分层总和法求解地基或基础的非线性沉降。该方法的特点是能进行加载至极限状态的全过程非线性沉降分析,而计算原理简单,计算参数全部来自现场原位测试,附加应力依据压板试验成果进行自动修正。分析广东某大型油罐地基及某高层建筑筏板基础的沉降结果表明,该方法计算结果准确可靠,能满足以沉降控制为目标的地基基础工程设计要求。     

边坡加固中预应力锚索框架地梁的杆系有限元分析

提出利用杆系有限元,考虑地梁与岩土体相互作用的方法,对边坡加固中的预应力锚索框架地梁进行计算。基于线弹性Winkler地基模型,分别考虑结构的弯曲变形和扭转变形,对框架地梁有限元计算模型进行了详细地分析说明。应用该方法对某工程实例进行了计算,与实测值的对比分析结果表明了该方法的可行性。     

六面体有限覆盖的三维数值流形方法的非线性分析

对三维问题的分析是数值流形方法发展的必然,在数值流形方法覆盖位移函数的基础上构造了一种六面体有限覆盖的三维流形单元,推导了相应的应变矩阵、刚度矩阵及平衡方程等表达式。同时,由于目前数值流形方法的模拟分析主要是采用线弹性模型,而对于非线性模型分析研究很少;根据数值流形方法的特点和岩土体的本构模型,给出了适用于数值流形方法进行非线性分析的算法。该方法利用中点增量法进行求解,以改变 模型和 模型中弹性模量的方式来反映非线性,其实质是用分段线性来取代非线性。通过地基沉降计算算例表明,数值流形方法在三维岩土体中进行非线性分析中是有效的。     

考虑基础刚度影响的风机梁板式桩筏基础模型试验研究

梁板式桩筏基础作为新型风机基础,前景广阔,适当优化结构,可节约成本。采用大型室内模型试验,研究了梁板式桩筏基础在不同筏板刚度情况下的受力变形特性,同时讨论了桩土荷载分担比的关系。研究表明,在工作荷载范围内,适当增大筏板刚度,桩平均轴力增加,外圈桩承担的荷载增大,内圈桩的轴力减小,环梁及肋梁弯矩减小,但继续增加刚度,对桩身轴力、环梁弯矩、肋梁弯矩的影响并不大;随着荷载的增大,土体承担的荷载比逐步增大,趋于稳值。随着梁板式基础刚度增加,基础内外差异沉降减少,但是达到一定刚度后再增加刚度对变形影响较小。梁板式基础刚度的变化会影响基底反力分布的均匀性,且存在一个最优刚度,使基础底部反力分布最为均匀,本次试验中12梁的梁板式基础基底反力比6梁和实体基础更均匀。桩基的分布和梁的分布存在相互影响,改变梁的分布会影响桩顶力,而桩基在梁底下又会使梁的应力产生重新分布。研究成果可为设计桩筏基础提供参考依据。     

多级线性荷载下饱和软黏土一维大应变固结解析解

在软土地基工程中,荷载往往都是分级施加,随着固结地基强度增加到一定值后,再施加下一级荷载以确保地基稳定。基于谢康和饱和软黏土一维大应变固结解析解,采用数学归纳法推导了任意形式多级线性荷载作用下的解,并编制了相应的通用计算程序,可以方便进行计算分析。通过与线性小应变假定下解的计算对比表明,在实际工程中基于非线性大应变进行计算分析更为合理。     

变基床系数弹性地基梁解法及其应用

从实测的P-S曲线（基地压力与沉降的关系）出发,将P-S曲线拟合成分段线性函数,把分段线性函数的斜率作为基床系数,推导出变基床系数弹性地基梁的基本理论方程式,并将它变换成与常基床系数弹性地基梁相同的方程形式,从而,可以用初参数法解出它的一般解。此方法可以推广到变截面梁和非均质地基的情况。     

Analysis of geocell-reinforced mattress with consideration of horizontal–vertical coupling

Geocell reinforcement has been increasingly applied to road embankment engineering. Deformation calculation is one of the major concerns during the design process. In this paper, the power-series method was employed to investigate the performance of a geocell-reinforced mattress under symmetric loads. The geocell-reinforced mattress was idealized as a beam on a Winkler foundation. In the analysis, the soil–foundation beam interface resistance, related to the horizontal deformation coupling with the vertical deformation, was considered. Semi-analytic solutions were developed to assess the deformations and internal forces of the foundation beam and verified against an existing finite element method [9]. The results of the proposed method were close to the results from the finite element method. Moreover, the effects of various factors, such as height of embankment, horizontal and vertical foundation coefficients, composite elastic modulus and height of geocell-reinforced mattress, on the foundation beam settlement and the tension force within the beam are discussed. It was found that the interface resistance related to the horizontal deformation of the beam has a reduction effect on the embankment settlement, and it is beneficial to reduce the embankment settlement by increasing the beam rigidity and strengthening the subgrade soil body.     

预应力锚索地梁与地基共同作用分析

针对现阶段预应力锚索地梁与地基共同作用机理研究方面存在的问题,以预应力锚索地梁和地基岩土体之间荷载、变形协调关系为基础,通过对预应力锚索地梁体系的分解和离散化处理,建立了能考虑预应力锚索地梁体系共同作用的预应力锚索地梁计算理论和方法。通过与实测资料的比较,表明本文理论有较高的计算精度。     

非均质基础与结构共同作用的随机动力反应分析

假定基础的剪切模量随深度呈线性变化,并引入结构微分算子,利用连续线性系统的随机振动理论,研究了非均质基础地震的动力反应问题。将上部结构简化为多自由度体系,将基础简化为一剪切梁,分析了基础与结构共同作用的随机地震反应。通过进一步分析,得到了基础与结构的地震随机反应及平稳输入时土层最大位移的动力可靠性分析参数。采用模态叠加法进行反应分析,与普通的分离变量法相比较,此方法概念明确、步骤简单。     

线性分布基床系数弹性地基梁有限单元法改进

弹性地基梁法常用于研究土和结构的相互作用,对于均布荷载和边界条件简单的弹地基梁,采用理论解即可方便地进行计算。侧向荷载作用下桩体、嵌入式挡墙一般根据弹性地基梁理论进行分析,并假定基床系数随深度增加。对于基床系数呈线性分布或呈均匀分布但边界条件复杂的弹性地基梁理论求解困难,通常采用有限差分法或有限单元法近似求解。采用有限单元法计算线性分布基床系数弹性地基梁时,若单元划分数量不够,就存在计算精度不足的问题。采用加权余量法推导了更为精确的2节点5次位移函数和相应的单刚矩阵,得出了线性分布荷载作用下挠度的5次多项式近似解,从而实现只需划分很少的单元数,节点位移及单元内位移的分布即可达到较高的计算精度,极大地提高了计算效率,单元内力的分布可直接由位移函数导出,简化了后处理计算程序。     

A Timoshenko finite element straight beam with internal degrees of freedom

We present hereafter the formulation of a Timoshenko finite element straight beam with internal degrees of freedom, suitable for nonlinear material problems in geomechanics (e.g., beam type structures and deep pile foundations). Cubic shape functions are used for the transverse displacements and quadratic for the rotations. The element is free of shear locking, and we prove that one element is able to predict the exact tip displacements for any complex distributed loadings and any suitable boundary conditions. After the presentation of the virtual power and the weak form formulations, the construction of the elementary stiffness matrix is detailed. The analytical results of the static condensation method are provided. It is also proven that the element introduced by Friedman and Kosmatka in 1 , with shape functions depending on material properties, is derived from the new beam element. Validation is provided using linear and material nonlinear applications (reinforced concrete column under cyclic loading) in the context of a multifiber beam formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

Three dimensional Finite Element modeling of seismic soil–structure interaction in soft soil

Earthquakes in regions underlain by soft clay have amply demonstrated the detrimental effects of soil–structure interaction (SSI) in such settings. This paper describes a new three dimensional Finite Element model utilizing linear elastic single degree of freedom (SDOF) structure and a nonlinear elasto-plastic constitutive model for soil behavior in order to capture the nonlinear foundation–soil coupled response under seismic loadings. Results from an experimental SSI centrifuge test were used to verify the reliability of the numerical model followed by parametric studies to evaluate performance of linear elastic structures underlain by soft saturated clay. The results of parametric study demonstrate that rigid slender (tall) structures are highly susceptible to the SSI effects including alteration of natural frequency, foundation rocking and excessive base shear demand. Structure–foundation stiffness and aspect ratios were found to be crucial parameters controlling coupled foundation–structure performance in flexible-base structures. Furthermore, frequency content of input motion, site response and structure must be taken into account to avoid occurrence of resonance problem.     

Analytical solutions for Euler‐Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads

In this paper, the dynamic response of an infinite beam resting on a Pasternak foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The mechanical resistance of the Pasternak foundation is modeled using two parameters, that is, one accounts for soil resistance due to compressive strains in the soil and the other accounts for the resistance due to shear strains. Because the Winkler model only represents the compressive resistance of soil, comparatively, the Pasternak model is more realistic to consider shear interactions between the soil springs. The governing equation of the beam is simplified into an algebraic equation by employing integration transforms, so that the analytical solution for the dynamic response of the beam can be obtained conveniently in the frequency domain. Both inverse Laplace and inverse Fourier transforms combined with convolution theorem are applied to convert the solution into the time domain. The solutions for several special cases, such as harmonic line loads, moving line loads, and travelling loads are also discussed and numerical examples are conducted to investigate the influence of the shear modulus of foundation on the beam responses. The proposed solutions can be an effective tool for practitioners. Copyright © 2017 John Wiley & Sons, Ltd.