Efficient mixed Timoshenko–Mindlin shell elements

The precise representation of rigid body motions in the displacement patterns of curved Timoshenko–Mindlin (TM) shell elements is considered. This consideration requires the development of the strain–displacement relationships of the TM shell theory with regard to their consistency with the rigid body motions. For this purpose a refined TM theory of multilayered anisotropic shells is elaborated. The effects of transverse shear deformation and bending‐extension coupling are included. The fundamental unknowns consist of five displacements and eight strains of the face surfaces of the shell, and eight stress resultants. On the basis of this theory the simple and efficient mixed models are developed. The elemental arrays are derived using the Hu–Washizu mixed variational principle. Numerical results are presented to demonstrate the high accuracy and effectiveness of the developed 4‐node shell elements and to compare their performance with other finite elements reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd.     

An adaptive non‐conforming finite‐element method for Reissner–Mindlin plates

Adaptive algorithms are important tools for efficient finite‐element mesh design. In this paper, an error controlled adaptive mesh‐refining algorithm is proposed for a non‐conforming low‐order finite‐element method for the Reissner–Mindlin plate model. The algorithm is controlled by a reliable and efficient residual‐based a posteriori error estimate, which is robust with respect to the plate's thickness. Numerical evidence for this and the efficiency of the new algorithm is provided in the sense that non‐optimal convergence rates are optimally improved in our numerical experiments. Copyright © 2003 John Wiley & Sons, Ltd.     

Dynamic response of a Mindlin elastic rectangular plate under a distributed moving mass

The elastodynamic response of a rectangular Mindlin plate subjected to a distributed moving mass is investigated. The set of governing characteristic partial differential equations that include the effects of shear deformation and rotary inertia is expressed in its dimensionless form. A finite difference algorithm is employed to transform the differential equations into a set of linear algebraic equations. Simply supported edge conditions were used as an illustrative example. The analysis is also valid for other edge conditions. It is found that the maximum shearing forces, bending and twisting moments occur almost the same time. Also, the values of the maximum deflections are higher for Mindlin plates than for non-Mindlin plates.     

耦合效应下压力型锚索锚固机理的拟静力分析

为了更加精确地对地震作用下软弱岩土体中压力型锚索抗震性能进行理论研究,基于长期荷载作用下钢绞线的材料松弛现象,推导了锚索预应力与岩土体蠕变的耦合效应下锚索预应力表达式和预应力损失量表达式;结合地震作用效应的拟静力等效法、Mindlin问题解和积分简化方法,推导了砂浆体在圆形均布荷载作用下压力型锚索锚固段的等效压应力表达式和等效剪应力表达式。通过案例分析可知:锚索预应力初期损失较大,中期损失稳定,至后期基本保持不变,预应力损失速率是递减的;压力型锚索锚固段砂浆体的等效应力主要集中在承压板0.5 m的范围内,等效应力最大值不在承压板与砂浆体的接触面上,而在承压板0.1 m的范围内。该研究成果丰富了压力型锚索抗震设计理论研究内容,可为深化压力型锚索抗震机理研究提供一定的理论依据,也可为合理考虑压力型锚索加固边坡的抗震设计提供有益的参考。     

Recovery of strong equilibrium from displacement‐based finite element models of Reissner‐Mindlin plates

In this paper, we extend to Reissner‐Mindlin plate bending problems a technique, originally proposed in the context of two‐dimensional and three‐dimensional continua, for recovering fully equilibrated stresses from the solution of a compatible finite element model. The technique involves partition of unity functions and the analyses of overlapping star patches modelled with hybrid equilibrium plate elements. The patches are subjected to balanced systems of loads composed of partitioned and fictitious loads, where the latter are derived from the stresses of the compatible solution. The special case of assumed linear displacement fields of both deflection and rotation for the compatible model is included. This case requires additional fields of stress resultants to correct possible rotational imbalances of star patches, and these are derived elementwise. Other cases of nonconforming elements are briefly considered. Numerical examples are presented to illustrate the effectiveness of these techniques in terms of the deviation of the recovery, which compares the complementary strain energy of a recovered solution with that obtained by a global equilibrated analysis based on the same stress approximations.     

Strain gradient differential quadrature finite element for moderately thick micro-plates

In this study, we integrate the advantages of differential quadrature method (DQM) and finite element method (FEM) to construct a C¹-type four-node quadrilateral element with 48 degrees of freedom (DOF) for strain gradient Mindlin micro-plates. This element is free of shape functions and shear locking. The C¹-continuity requirements of deflection and rotation functions are accomplished by a fourth-order differential quadrature (DQ)-based geometric mapping scheme, which facilitates the conversion of the displacement parameters at Gauss-Lobatto quadrature (GLQ) points into those at element nodes. The appropriate application of DQ rule to non-rectangular domains is proceeded by the natural-to-Cartesian geometric mapping technique. Using GLQ and DQ rules, we discretize the total potential energy functional of a generic micro-plate element into a function of nodal displacement parameters. Then, we adopt the principle of minimum potential energy to determine element stiffness matrix, mass matrix, and load vector. The efficacy of the present element is validated through several examples associated with the static bending and free vibration problems of rectangular, annular sectorial, and elliptical micro-plates. Finally, the developed element is applied to study the behavior of freely vibrating moderately thick micro-plates with irregular shapes. It is shown that our element has better convergence and adaptability than that of Bogner-Fox-Schmit (BFS) one, and strain gradient effects can cause a significant increase in vibration frequencies and a certain change in vibration mode shapes.     

耦合效应下压力型锚索锚固机理的近似理论分析

为了更加精确地研究压力型锚索的锚固机理,基于锚索预应力与岩土体蠕变的耦合效应推导了锚索预应力方程。在此基础上根据Mindlin问题解,推导了耦合效应作用下锚索砂浆体的压应力和剪应力近似解,并考虑锚索预应力与岩土体蠕变之间的耦合效应进行了案例分析。研究结果表明:锚索预应力和砂浆体受到的应力峰值均按反幂函数随时间逐渐衰减并稳定;承压板的长宽比与压应力峰值之间存在正相关关系,与剪应力峰值之间存在负相关关系;岩土体的泊松比与应力峰值之间存在正相关关系。该成果丰富了压力型锚索锚固机理的理论研究,可为边坡锚固设计提供一定的理论依据。     

基于时空关系的盾构开挖地表沉降规律

基于武汉地铁四号线某区间隧道盾构开挖引起的地表沉降数据分析,考虑地表沉降的时空关系,将地表沉降划分为无影响阶段、前期沉降阶段、通过阶段、盾尾空隙沉降阶段、工后沉降阶段,并给出了各个阶段的大致范围及其地表沉降占总沉降的比值。通过对Mindlin解引入时间参数,针对不同阶段地表沉降影响因素进行分析,在前影响距离范围内,盾构机与土体的摩擦力和地层损失对地表沉降的影响占优,在后影响距离范围内,地层损失对地表沉降起到了绝对的控制作用,前期沉降阶段的土层隆起与正面附加推力、摩擦力有关,而正面附加推力、摩擦力和注浆压力导致了工后沉降阶段的土体回弹,由此获得了实时地表沉降预测的理论公式。研究结果表明:理论预测值与实测值能较好的吻合,该公式能够较为准确地实时预测地表沉降。     

基于Mindlin解的柔性桩临界桩长计算

依据Mindlin位移解和位移协调条件,本文推导了柔性桩桩周摩阻力分布公式和轴力变化公式,获得的公式与能反应实际摩阻力分布的特征。在此基础上,推导了柔性桩临界桩长的计算公式,并与有限元方法的计算结果做了比较。比较显示,本文提出的柔性桩临界桩长计算方法结果合理,操作简单,便于工程应用。     

复杂地基中桩基承载机理计算研究

对复杂地基中单桩承载性能进行进一步的分析探讨，分析比较了目前应用于桩基分析计算中的各种弹性理论法的适用性及局限性，建立了一套更接近实际的桩土体系模型，提出了一种新的计算分析复杂地基模型的桩基础计算分析方法——广义弹性理论法，与传递函数法、线性变形层模型、镜象法相结合，利用改进的Mindlin解，对复杂地基中桩基承载性能进行了计算研究。利用优化反分析方法所编制的正、反分析计算程序，不仅可计算复杂地基中桩身各点的荷载．沉降关系曲线，而且可以利用静载试验所得的荷载-沉降关系曲线，反演分析桩周和桩端土的力学参数值，用于指导同类型桩基工程的设计和施工。对大量的工程实例进行了分析计算，并与静载试验进行对比验证，得到了较为令人满意的结果。