平面内压弯作用下圆柱形曲板的极限承载力:EN1993-1-5规范延伸

为研究纵向无约束、加载端简支(截面内置单元)的短圆柱形曲板的后屈曲性能,对平面内压弯作用下圆柱形曲板进行了数值分析,包括曲率和载荷类型(纯压缩和平面内弯曲)的影响。研究确定了其他相关参数以及它们对圆柱形曲板极限强度的影响。通过参数研究得到极限折减系数的数值分析结果,利用迭代程序将其转换成几何(宽度)折减系数。随后,基于有效宽度的概念,对EN1993-1-5中内置板构件极限承载力的计算准则进行改进。结果表明(短粗板除外):随着曲率参数的增大,圆柱形曲板的承载力提高,EN 1993-1-5给出的承载力上限是合理的。最后,统计研究结果表明,该方法能够准确估计圆柱形曲板的极限承载力。     

空间杆系结构的蒙板程序编制及其工程应用

屋面静、活载及风载的荷载施加问题是空间杆系结构分析中的重要环节.本文首先探讨了空间杆系结构的两种加载方法,建议采用面层板加载法来较好地模拟实际结构情况及方便地施加各种荷载,但此法对手工操作而言是一项繁复的工作.针对此问题,本文编制了相应的空间杆系结构的表面蒙板程序,实现了选择杆件后程序根据节点及杆件的拓扑关系为其蒙上表面板单元的功能.程序内容主要包括了获取空间节点坐标、空间网格平面投影、平面网格封闭区域识别、平面区域的空间还原等步骤.程序应用于多个实际大型体育场馆的有限元建模分析中,效果良好,具有工程实用价值.最后文章针对蒙板分析中的加载模式、多边形区隔划分等问题进行了探讨研究.     

全装配式RC楼盖平面内受力性能试验研究

为研究全预制装配式钢筋混凝土楼盖的平面内受力性能,对1/2缩尺的楼盖模型进行了楼盖平面内拟静力试验,对楼盖的裂缝分布、破坏形态、平面内变形特征、滞回曲线、位移延性、刚度退化和耗能能力等进行了研究,分析了楼盖模型各连接件在加载过程中的板缝剪力和轴力分布规律。结果表明：新型楼盖具有较大的平面内刚度和较好的整体性能,在加载过程中梁 板连接件和板缝连接件均表现出良好的传力性能;新型楼盖具有一定的延性,但耗能能力不理想,说明基于弹性楼盖的抗震设计方法是必要的;加载初期楼盖的变形呈弯曲型,加载中后期随着楼盖损伤的积累,板缝间相对位移增大,变形模式逐渐向剪切型发展;新型楼盖在平面内荷载作用下内力分布规律与简支梁相近,研究成果可为新型楼盖平面内受力性能的理论分析提供参考。     

侧向受荷板桩极限承载力的下限有限元分析

基于结构和平面应变单元,采用数值下限法分析结构–土体接触的稳定性问题。下限分析的求解借助锥形规划中原–对偶内点算法。提出了可以考虑轴力、剪力和力矩复合加载形式下的结构屈服形式;并以侧向受荷板桩为例,得出了水平力和力矩共同作用下的破坏包络线。结果显示:侧向受荷板桩的极限承载力H/(cL)是相对强度参数Mp/(cL2)的函数。该结果与Davis(1961)的刚性桩近似计算比较吻合。本文是下限有限元法首次采用结构和平面应变单元复合形式在深基础中的应用。     

单向加劲矩形板面内振动特性分析

采用能量法研究典型边界条件下加劲矩形板的面内自由振动特性。将矩形板、加强筋沿交界面切开,分别采用平面应力理论和欧拉梁理论建立其面内振动的总能量方程,利用第一类Chebyshev多项式构造矩形板的位移试函数,由Rayleigh-Ritz法得加劲矩形板的面内振动特征方程。数值结果表明,本文方法收敛性好,并用本文解验证了有限元软件ANSYS结果的精度。本方法具有计算简单的特点,可以得到任意阶次的固有频率。最后分析了加强筋宽度与板宽比值(b_0/b)对加劲板无量纲固有频率的影响。     

对加劲板在局部和整体弯曲作用下的后屈曲及强度的半解析分析

对经受平面内双轴及剪切荷载作用下的带缺陷加劲板的预先和后屈曲分析采用半解析方法分析。结合了Rayleigh-Ritz方法的大变形理论,可以分析板局部及整体的平衡。采用vonMises屈服标准预测的极限强度作为膜压力的破坏标准。采用Fortran程序计算的结果也被非线性有限元分析的结果证实。该法因此也适用于结构优化设计以及可靠性研究。     

利用四边形面积坐标法构建的4结点膜单元的几何非线性分析

最近,一种4结点膜单元AGQ6-I已经被成功地用来分析线性平板问题。由于这种模型是由四边形面积坐标法(QACM)构建的,QACM是一种用于研究四边形有限元模型的新自然坐标系统,因此模型比其他4结点等参单元对网格畸变的敏感度要小得多,它也避免了各种由于几何网格不规则性产生的相关问题。为了将QACM的这些优点应用到非线性应用软件上,本文建立了AGQ6-I的完全拉格朗日公式,这也是平面QACM理论第一次被应用于模糊几何非线性分析。几何非线性分析的数例表明,此公式能保证应用于严重畸变网格的有效性,因此QACM优于其他的4结点等参单元。分析结果表明:在几何非线性分析中,QACM对于开发简单有效及可信赖的板膜单元是非常有效的。     

局部和整体弯曲下加劲板半解析大挠度分析中的强度标准

为预测任意加劲板的极限强度,研究了可能应用于半解析方法的多种强度准则。以评估强度准则在预测平面内加载（局部和整体弯曲）下的板极限强度的适用性。利用大挠度理论和Rayleigh-Ritz方法来求解平衡方程,得到后屈曲作用下薄板的残余强度。将计算结果与具有不同板尺寸及各种规则和不规则布置的加劲肋的非线性有限元分析的结果进行对比。结果发现,在板和加劲肋的标准组合下,两者具有良好的一致性。当采用这种准则时,按所提出的求解方法可以进行非常有效而且准确的计算。     

玻璃纤维复材筋拉结预制混凝土夹芯墙板平面外抗弯性能研究

为研究采用玻璃纤维复材筋拉结制作的预制混凝土夹芯保温外墙板的平面外抗弯性能,采用7块夹芯保温墙板和4个现浇混凝土墙板作为对比进行平面外静力加载试验。试验研究表明:夹芯保温墙板具有一定的弱组合性,且随着保温板与混凝土板之间黏结力的破坏,组合程度逐渐降低;按照非组合板进行设计,仅考虑内叶板受力的夹芯保温墙板在设计荷载作用下有较大的安全储备,基本处于未开裂阶段;内叶板采用带肋板形式的夹芯保温墙板可以在满足承载力和变形要求的前提下,有效减轻构件质量,提高经济性。     

改进型无网格Galerkin法与有限元法的耦合及其应用研究

改进型无网格伽辽金法是基于一种改进的移动最小二乘(an improved moving least-squares,IMLS)近似。IMLS近似比现有的MLS近似有更高的计算效率和精度,且不会导致系统方程产生病态。这种耦合的方法不仅解决了无网格Galerkin法力学边界条件施加的难点,避免系统方程产生病态,而且还克服了无网格Galerkin法耗时较多的缺点。运用线弹性断裂力学理论,采用了加权正交基函数,对有限板单边裂纹的应力强度因子和受拉单边斜裂纹矩形板进行了分析。数值计算结果表明:该方法是一种具有收敛快、精度高、简便有效的通用方法,在工程中具有广阔的应用前景。     

Large deflection analysis of flexible plates by the meshless finite point method

The classical finite difference technique and methods based on series expansions can only be adopted for solving plates with simple geometry, loading and boundary conditions. In contrast, the finite element method has been widely used for general analysis of bending and flexible plates (coupled bending and in-plane effects). Lack of stress continuity and relatively expensive mesh generation and remeshing schemes have led to the emergence of meshless methods, such as the finite point method (FPM). FPM is a strong form solution which combines the moving least square interpolation technique on a domain of irregularly distributed points with a point collocation scheme to derive system governing equations. In this study, coupled nonlinear partial differential equations of fourth order are solved to analyse large deflection behaviour of plates subjected to lateral and in-plane loadings. Several plate problems are solved and compared with analytical solution and other available numerical results to assess the performance of the proposed approach.     

Analysis of chloride diffusion in concrete structures for prediction of initiation time of corrosion using a new meshless approach

In this paper, a finite point method (FPM) is developed and adopted for solving the chloride diffusion equation for prediction of service life of concrete structures and initiation time of corrosion of reinforcements. Diffusion of chloride ions is generally assumed to follow the Fick’s second law. FPM is a truly meshless method which uses a moving least square approximation within a collocation strong form for solving the governing differential equation. Several 1D and 2D problems are solved using FPM and the results are compared with the analytical solution, classical finite element and finite difference methods, and weak form meshless based element free Galerkin method.     

基于有限质点法的结构倒塌破坏研究I：基本方法

动力荷载作用下的结构倒塌破坏问题一直是一个复杂而重要的研究课题。基于有限质点法对结构的倒塌破坏过程进行模拟和分析。有限质点法是基于向量式结构力学的数值分析方法，它将分析域离散为质点，质点间通过单元相连，质点间作用力的关系依靠单元变形描述，质点运动遵循牛顿第二定律，该方法通过描述质点的运动行为来追踪结构行为。给出了有限质点法的基本概念，以空间杆系结构为例建立质点的运动方程及其求解步骤。通过单元虚拟运动分离单元的刚体运动和纯变形，推导了空间梁系结构的计算公式。有限质点法计算结构非线性行为无需迭代求解非线性方程或特殊修正，计算构件断裂行为不受网格划分限制，与传统方法相比在结构复杂行为分析中具有优势。     

Bending analysis of folded plates by the FSDT meshless method

In this paper, a meshfree Galerkin method that is based on the first-order shear deformation theory (FSDT) will be introduced to analyse the elastic bending problem of stiffened and un-stiffened folded plates under different loadings and boundary conditions. Folded plates are regarded as assemblies of plates that lie in different planes. The stiffness matrices of the plates are given by the meshfree method. Employing the element concept, which is borrowed from the finite element method, and treating every plate as a big element, the global stiffness matrix of the whole folded plate is obtained by superposing the stiffness matrices of the plates. This is about the same for the analysis of stiffened folded plates. They are considered as assemblies of stiffened plates. The stiffness matrices of the stiffened plates are also given by the meshfree method. Superior to the finite element methods, no mesh is required in determining the stiffness matrices for the plates and the stiffened plates in this paper, which means time-consuming and accuracy-suffering remeshing is entirely avoided for problems such as large deformation or crack propagation in folded plates or stiffener position changes of stiffened folded plates. To demonstrate the accuracy and convergence of the method, several numerical examples are calculated by it and the finite element commercial software ANSYS. Good agreement is observed between the two sets of results.     

Benchmark symplectic solutions for bending of corner-supported rectangular thin plates

This work presents the first ever analytical solutions for bending of a rectangular, thin plate supported only at its four corners. This breakthrough analysis employs a new symplectic elasticity approach that extends beyond the limitation of the classical plate bending methods such as Timoshenko's method, Navier method, Levy method and the polynomial approximation analysis of Lee and Ballesteros (Int J Mech Sci 1960;2:206). The classical methods are, in fact, special cases of this symplectic approach in the real eigenvalue regime for wavenumber with at least one pair of opposite sides of plates simply supported. For plate problems that do not fall into this category, the classical methods fail to yield any analytical solutions, but the symplectic approach does because in these cases the plate bending problems enter the complex eigenvalue regime for wavenumber. Another distinctive feature of this new approach is its necessity to pose an eigenvalue problem even for plate bending. In short, this innovative approach establishes the relationship between eigenvalue problem and bending. The novelty of this approach lies in the use of the Hamiltonian principle in a symplectic geometry space to derive a Hamiltonian system and a full state vector. The free boundaries with corner supports are dealt with using the variational principle. Analytical bending modes are then derived by expansion of eigenfunctions. The solutions are compared with other known (approximate) results and numerical finite element solutions but some of the results are not in agreement. Because the analytical bending moment and shear force solutions thus derived fulfill all natural and geometric boundary conditions, it leaves ample room for authentication of the benchmarks in the future. In addition, the twisting moment at the corners satisfies the condition for static bending equilibrium, in which the finite element solutions fail.     

Eigenvalue analysis of flexural-torsional buckling of angle-bar stiffened plates

Equilibrium method is employed to analyze interaction of flexural and torsional buckling of angle-bar stiffened plates. The cross sectional areas of the angle-bar stiffened plate for these two modes are different (hybrid beam). In flexural buckling mode, angle-bar and attached plate buckle together, however in torsional buckling mode only angle-bar would be buckled. Basic equations of equilibrium for flexural and torsional buckling modes of angle-bar stiffened plates are deduced based on hybrid beam concept and new strain distribution assumption for sideway bending of stiffeners. Elastic buckling stress of different angle-bar stiffened plates are calculated and compared with finite element method and those available in the literature. It is shown that present method has very good agreements with finite element method for isolated rigid angle-bar and isolated rigid angle-bar with rigid attached plate. For isolated rigid angle-bar with pin connected to rigid attached plates it has better agreement than previously proposed method.     

Linear elastic isoparametric spline finite strip analysis of perforated thin-walled structures

This paper describes the application of the isoparametric spline finite strip method to the linear elastic analysis of tri-dimensional perforated folded plate structures. The general theory of the isoparametric spline finite strip method is introduced. Kinematics assumptions and the procedure for combining in-plane (membrane) and bending effects are set out. Particular attention is paid to the procedure for rotating the stiffness matrix and load vector from local to global coordinates. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square stiffened perforated plates in compression and bending are analysed.     

Plate bending analysis by unequally spaced splines

A cubic B-spline finite strip method (BFSM) is developed to analyze thin plates in bending. The basic mathematical relationships are derived for a direct stiffness formulation using a series type strip displacement function. Longitudinal behavior is modeled by a spline series in which unequal spline spacing is permitted. This feature allows local refinement of the discretization near patch and concentrated loads. Accuracy and convergence vis-à-vis alternative methods are compared. These include various finite element models, the conventional finite strip method and the BFSM with equally spaced splines. Comparisons show comparable accuracy with improved convergence. Oscillatory convergence due to Gibb's phenomenon, evident in some of the models, is avoided in the BFSM.     

Buckling of thin flat-walled structures by a spline finite strip method

A method of buckling analysis of thin flat-walled structures of finite length subjected to longitudinal compression and bending, transverse compression as well as shear is described. The analysis uses the spline finite strip method and allows for boundary conditions other than simply supported ends as required in the semi-analytical finite strip method of buckling analysis.Convergence studies with increasing numbers of section knots are described for plates in compression, bending and shear, and for long columns with different support conditions subjected to compression. A buckling analysis of a stiffened plate subjected to compression and shear is compared with results from a finite element analysis.     

采用FSDT无网格法对折板进行弯曲分析

采用基于一阶剪切变形理论(FSDT)的无网格Galerkin方法分析不同荷载和边界条件下的带加劲肋和无加劲肋的折板弹性弯曲问题。折板由不同平面的板组合而成,这些板的刚度矩阵由无网格法给出。借用有限元概念,将每一块板都视为一个单元,整块板的整体刚度矩阵就可以通过这些单块板的刚度矩阵而得到。加劲板也同样如此,采用无网格法给出加劲板的刚度矩阵。比有限元方法优越的是,在确定板刚度矩阵的时候不需要网格,这意味着在折板或加劲肋位置变化处的大变形或者裂缝发展时,可以避免耗时过长,以及网格重组带来的对精度的影响。为验证此法的精确度和收敛性,本文采用此法及ANSYS对多个数学模型进行计算,结果表明两组结果非常一致。