基于新型大变形平板壳单元的剪力墙模型及其在OpenSees中的应用

数值模拟是研究超高层建筑地震灾变行为的重要手段。地震作用下,剪力墙作为超高层结构的重要抗侧力构件往往呈现出复杂的受力状态,甚至因结构倒塌而产生大变形破坏,因此有必要开发一个能准确考虑大变形的剪力墙单元。该文基于广义协调元理论和更新Lagrangian列式,提出了一种高性能四边形平板壳单元及其几何非线性列式,并将该模型集成于开源有限元程序OpenSees中,以经典算例验证了该单元的性能和应用于大变形计算的可靠性。通过将该单元与分层壳截面结合,该文对多种类型的剪力墙构件进行了模拟,并将模拟结果与试验结果进行对比,验证了该单元能较好的模拟剪力墙的复杂受力特性,且能有效模拟钢筋混凝土构件倒塌的关键特性,为进一步开展基于OpenSees的超高层结构地震灾变行为研究提供参考。     

几何非线性扩展有限元法及其断裂力学应用

该文将扩展有限元方法应用到几何非线性及断裂力学问题中,并研制开发了扩展有限元Fortran程序。扩展有限元法其计算网格与不连续面相互独立,因此模拟移动的不连续面时无需对网格进行重新剖分。该文推导了几何非线性扩展有限元法的公式,在常规有限元位移模式中,基于单位分解的思想加进一个阶跃函数和二维渐近裂尖位移场,反映裂纹处位移的不连续性,并用2个水平集函数表示裂纹;采用拉格朗日描述方程建立了有限变形几何非线性扩展有限元方程;采用多点位移外推法计算裂纹应力强度因子并通过最小二乘法拟合得到更精确的结果。最后给出的大变形算例表明该文提出的几何非线性的断裂力学扩展有限元方法和相应的计算机程序是合理可行的,而且对于含裂纹及裂纹扩展的问题,扩展有限元法优于传统的有限元法。     

基于隔离非线性的实体单元模型与计算效率分析

实体有限元模型计算中往往需要较多的计算单元与结点数量,且这些单元状态判定以及大规模的刚度矩阵分解将消耗大量的计算资源,计算效率低。该文基于隔离非线性法理论建立了线性四面体与六面体等参单元分析模型,采用直接积分格式的6积分点替代六面体等参单元的8高斯点作为非线性应变插值点,能够在保证计算精度的同时提高单元状态判定效率。控制方程采用Woodbury公式与组合近似法联合求解,使得整个求解过程只有矩阵回代以及矩阵与向量的乘积,进一步提高了求解效率。基于时间复杂度的计算效率分析表明:随着结点自由度数目的增加,该文方法的计算效率相对传统变刚度法显著提高,数值算例验证了实体单元模型的正确性以及算法的高效性。     

GSQ24壳体单元用于板壳结构的几何非线性分析

在考虑剪切变形的Von Karman大变形小应变假设下,基于全Lagrange描述方法,将平面内带有旋转自由度的GSQ24壳体单元用于板壳结构的几何非线性分析,给出了板壳结构大变形下的小位移刚度矩阵、初应力刚度矩阵、初位移刚度矩阵有限元列式。同时,文中也给出了既考虑材料非线性,又考虑几何非线性的强非线性问题的板壳结构分析时的有限元列式。数值算例与变分法和级数解结果比较,表明本文方法的可行性。     

爆炸冲击载荷作用下夹层开顶扁球壳的非线性动力稳定性分析

该文对爆炸冲击作用下夹层开顶扁球壳的非线性轴对称动力稳定性问题进行研究.基于Reissner假设和Hamilton原理,得到了夹层开顶扁球壳在冲击载荷作用下的非线性动力控制方程;采用Galerkin方法对非线性动力控制方程进行求解,得到以刚性中心位移表达的非线性动力响应方程,并应用Runge-Kutta方法进行数值求解...     

复合材料大变形任意加筋壳单元

构造了用于复合材料偏心加筋壳形结构大变形分析的任意加筋壳单元。在此模型中,肋骨连同壳的整体被视为一个单元偏心加筋壳单元。肋骨可放在壳单元内的任意位置和任意方向。所构造单元的特点是在网格划分时,可不必考虑肋骨的位置,这就给网格划分带来了很大的灵活性。在壳和肋骨的方程中,引用Von-Karman大变形理论计及几何非线性的影响,按照Mindlin-Reissner一阶剪切变形理论考虑横向剪切变形。     

载流悬臂柱壳的非线性数值分析

针对在电磁场和机械场耦合作用下的载流柱壳的非线性变形问题的数值解法进行了研究。给出了载流柱壳在耦合场作用下的几何方程、物理方程、二维电动力学方程、磁弹性非线性运动方程和洛仑兹力表达式,建立了差分格式和线性化迭代方程,给出了这些方程的数值解系统,并以悬臂柱壳为例,计算了该壳在电磁场和机械载荷耦合作用下的应力及变形;讨论了其应力及变形与外加电磁参量之间的关系;证明了变化电磁参量可以对壳的工作状态实施控制。     

压电曲壳单元及其形状控制

板壳结构作为航空、航天工程中的主要工作元件,要承受多种环境荷载,而对形状变化非常敏感的机翼、天线等结构,有必要进行形状控制。推导了空间压电曲壳单元的有限元方程,采用约束方程法连接压电曲壳和主体结构,建立了整体结构的有限元分析模型,并基于等效应变原则验证了模型的正确性。在此基础上,利用最小二乘法对结构进行了形状控制,得到压电驱动器上电压的最优分布。算例表明:该文模型能提高计算精度和速度,达到形状控制的要求。     

基于开源计算程序的特大跨斜拉桥地震灾变及倒塌分析

现阶段大跨桥梁弹塑性分析多基于商用有限元软件,一定程度上的限制了相关研究的深入开展。该文基于开源有限元程序OpenSees,以我国拟建的琼州海峡大桥斜拉桥设计方案为例,采用分层壳单元模拟桥墩(桥面板),桁架单元模拟预应力斜拉索,建立了主跨1500 m 的特大跨斜拉桥有限元模型,实现了其地震灾变及倒塌全过程的模拟,并通过与商用有限元软件MSC.Marc 计算结果的比较,验证了该文开发的计算单元和模型的可行性与正确性。其研究成果可为进一步开展基于开源有限元程序的特大跨斜拉桥抗震研究提供参考。     

基于有限元与块体元法的地下洞室变形及稳定分析

本文把有限元与块体无法结合起来,用来分析地下洞室围岩的变形及稳定性。此法在洞室附近使用块体元模型,以反映节理岩体变形的不连续性,而在远处使用连续的有限元模型,以减少计算工作量。文中推导了有限元与块体元法统一力学模型的支配方程,所编制的数值分析程序应用于某一实际工程问题,说明此法可行。     

Optimum Design of Laminated Composite Plates Undergoing Large Amplitude Oscillations

The optimum design of composite laminated plates under going large amplitude free vibration is discussed. Von Karman's nonlinear strain displacement relations are considered to account for large amplitude. A higher order shear deformation theory with parabolic variation of transverse shear stresses through thickness is used in the finite element formulation. A nine-noded isoparametric element with 7 dof per node is adopted. Ritz formulation for nonlinear finite element analysis is implemented and the direct iteration method is used to solve the governing nonlinear equation. Optimization is carried out using genetic algorithm (GA) with tournament selection scheme.     

Modelling cohesive crack growth using a two-step finite element-scaled boundary finite element coupled method

A two-step method, coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM), is developed in this paper for modelling cohesive crack growth in quasi-brittle normal-sized structures such as concrete beams. In the first step, the crack trajectory is fully automatically predicted by a recently-developed simple remeshing procedure using the SBFEM based on the linear elastic fracture mechanics theory. In the second step, interfacial finite elements with tension-softening constitutive laws are inserted into the crack path to model gradual energy dissipation in the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the proposed method. The numerical results demonstrate that this two-step SBFEM-FEM coupled method can predict both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for crack growth problems with strong snap-back phenomenon. The effects of the tensile strength, the mode-I and mode-II fracture energies on the predicted load-displacement relations are also discussed.     

固端法:二维有限元先验定量误差估计与控制

该文基于有限元超收敛计算的单元能量投影(Element Energy Projection,简称EEP)法,尝试将一维有限元中新近提出的先验定量误差估计的“固端法”拓展到二维有限元分析,以Poisson方程为例,用EEP公式预先估算出各单元的误差,可以不经有限元求解计算而直接给出满足精度要求的网格划分。该文给出的初步数值算例验证了该法的有效性。     

FEM prediction of buckling distortion induced by welding in thin plate panel structures

Welding distortion generated during assembly process has a strongly nonlinear feature, which includes material nonlinearity, geometric nonlinearity, and contact nonlinearity. In order to obtain a precise prediction of welding distortion, these nonlinear phenomena should be carefully considered. In this study, firstly, a prediction method of welding distortion, which combines thermo-elastic-plastic finite element method (FEM) and large deformation elastic FEM based on inherent strain theory and interface element method, was developed. Secondly, the inherent deformations of two typical weld joints involved in a large thin plate panel structure were calculated using the thermo-elastic-plastic FEM and their characteristics were also examined. Thirdly, using the developed elastic FEM and the inherent deformations, the usefulness of the proposed elastic FEM was demonstrated through the prediction of welding distortion in the large thin plate panel structures. Finally, the influences of heat input, welding procedure, welding sequence, thickness of plate, and spacing between the stiffeners on buckling propensity were investigated. The numerical simulation method developed in this study not only can be used to predict welding distortion in manufacturing stage but also can be employed in design or planning stage.     

A general higher-order shell theory for compressible isotropic hyperelastic materials using orthonormal moving frame

The primary objective of this study is threefold: (1) to present a general higher-order shell theory to analyze large deformations of thin or thick shell structures made of general compressible hyperelastic materials; (2) to formulate an efficient shell theory using the orthonormal moving frame, and (3) to develop and apply the nonlinear weak-form Galerkin finite element model for the proposed shell theory. The displacement field of the line normal to the shell reference surface is approximated by the Taylor series/Legendre polynomials in the thickness coordinate of the shell. The use of an orthonormal moving frame makes it possible to represent kinematic quantities (e.g., the determinant of the deformation gradient) in a far more efficient manner compared with the nonorthogonal covariant bases. Kinematic quantities for the shell deformation are obtained in a novel way in the surface coordinate described in the appendix of this study with the help of exterior calculus. Furthermore, the governing equation of the shell deformation has been derived in the general surface coordinates. To obtain the nonlinear solution in the quasi-static cases, we develop the weak-form finite element model in which the reference surface of the shell is modeled exactly. The general invariant based compressible hyperelastic material model is considered. The formulation presented herein can be specialized for various other nonlinear compressible hyperelastic constitutive models, for example, in biomechanics and other soft-material problems (e.g., compressible neo-Hookean material, compressible Mooney–Rivlin material, Saint Venant–Kirchhoff model, and others). A number of numerical examples are presented to verify and validate the formulation presented in this study. The scope of potential extensions are outlined in the final section of this study.     

Stabilized finite element methods for vertically averaged multiphase flow for carbon sequestration

A computationally efficient numerical model that describes carbon sequestration in deep saline aquifers is presented. The model is based on the multiphase flow and vertically averaged mass balance equations, requiring the solution of two partial differential equations – a pressure equation and a saturation equation. The saturation equation is a nonlinear advective equation for which the application of Galerkin finite element method (FEM) can lead to non‐physical oscillations in the solution. In this article, we extend three stabilized FEM formulations, which were developed for uncoupled systems, to the governing nonlinear coupled PDEs. The methods developed are based on the streamline upwind, the streamline upwind/Petrov–Galerkin and the least squares FEM. Two sequential solution schemes are developed: a single step and a predictor–corrector. The range of Courant numbers yielding smooth and oscillation‐free solutions is investigated for each method. The useful range of Courant numbers found depends upon both the sequential scheme (single step vs predictor–corrector) and also the time integration method used (forward Euler, backward Euler or Crank–Nicolson). For complex problems such as when two plumes meet, only the SU stabilization with an amplified stabilization parameter gives satisfactory results when large time steps are used. Copyright © 2016 John Wiley & Sons, Ltd.     

The boundary element method applied to the analysis of two-dimensional nonlinear sloshing problems

This paper deals with an application of the boundary element method to the analysis of nonlinear sloshing problems, namely nonlinear oscillations of a liquid in a container subjected to forced oscillations. First, the problem is formulated mathematically as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions, assuming the fluid to be inviscid and incompressible and the flow to be irrotational. Next, the governing equation (Laplace equation) and boundary conditions, except the dynamic boundary condition on the free surface, are transformed into an integral equation by employing the Galerkin method. Two dynamic boundary condition is reduced to a weighted residual equation by employing the Galerkin method. Two equations thus obtained are discretized by the use of the finite element method spacewise and the finite difference method timewise. Collocation method is employed for the discretization of the integral equation. Due to the nonlinearity of the problem, the incremental method is used for the numerical analysis. Numerical results obtained by the present boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory. Good agreements are obtained, and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems.