An effective four node degenerated shell element for geometrically nonlinear analysis

The development of a new four node degenerated shell element is presented for the analysis of the shell structures undergoing large deformations. In the formulation of the new element, the assumed covariant transverse shear strains are used to avoid the shear locking problem, and the assumed covariant membrane strains which are separated from the covariant inplane strains by mid-surface interpolation, are applied to eliminate the membrane locking problem and also to improve the membrane bending performance. This element is free of serious shear and membrane locking problems and undesired spurious kinematic deformation modes. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements and rotations. The resulting nonlinear equilibrium equations are solved by the Newton-Raphson method combined with load or arc-length control. The versatility and accuracy of this new degenerated shell element is demonstrated by solving several numerical examples.     

TL法和UL法对几何非线性桁架问题的适用性

在对ＴＬ列式法和ＵＬ列式法进行理论推导的基础上,分别编制了这两种方法对弹性阶段小应变大位移桁架问题的计算程序,并对一些典型例题进行了计算。文中除对“中等程度转动”大致界定外,还探讨了诸如结构刚度、轴向力的大小和方向对这些适用性的影响。     

A parametric finite element study of cracked plates and shells

The overall behavior of plates and shells as affected by the presence of a through crack in the elastic range has been studied. Due attention has been paid to finite element modeling aspects of the problem. Forty different cracked plate and shell FE models have been generated and analyzed by a special computer program developed for the purpose of this study. The significance of various parameters such as the order of mesh refining at the crack tip, the effect of boundary conditions, Poisson's ratio, crack length and shell curvature are studied. FE model consisting of isoparametric 4-noded shell elements moderately refined at the crack tip predicted the overall stress and displacement field with acceptable precision.     

Quadrilateral shell element for rotational shells

A doubly curved shell element of quadrilateral shape which is suitable for the analyses of rotational shells is derived. Geometry is defined in a polar coordinate system while displacements are specified in cartesian coordinates. The element is a C° element which includes transverse shear deformations and is intended for modelling shells which follow a circular curve form in one direction.     

Stability analysis of cross-ply laminated shells of revolution using a curved axisymmetric shell finite element

A curved axisymmetric shell finite element based on a consistent first-order shear deformable shell theory is developed for the linear stability analysis of cross-ply laminated shells of revolution under compressive loads. Finite element analysis results are presented for isotropic, orthotropic and cross-ply laminated shells of revolution in comparison with the analytical and numerical results found in the literature. These comparisons demonstrate the applicability and the high performance of the element in stability analysis of thin and moderately thick cross-ply laminated composite shells of revolution under compressive loads.     

拱结构空间几何非线性分析的曲梁单元

利用势能原理和插值函数推导了一种供结构空间几何非线性分析的曲梁单元。采用固定Lagrange坐标系和Newton-Raphson求解法。使用本文的方法与其他方法相比，该方法将轴向应变的非线性部分取平均值，提高了结果的精确性，而且单元数量大大减少。     

Pseudo-linearization procedure of nonlinear ordinary differential equations for large deflection problem of circular plates

The large deflection problem of the circular plate is considered in this paper. Generally, there are some nonlinear terms in the ordinary differential equation resulted. For example, one term takes the form (dw/dr)², where w(r) is the deflection function and r is the radial coordinate. Different from the previously suggested procedures, an alternative procedure is suggested in this paper. In the procedure, one factor dw/dr in the nonlinear term (dw/dr)² is replaced by a temporarily given function g(r). This means that the term (dw/dr)² is replaced by g(r)(dw/dr) where the function g(r) is obtained from the previous round iteration. A linear ordinary differential equation is obtained by using this substitution and we can make the relevant iteration. Therefore, the method is called a pseudo-linearization procedure in this paper. It is proved that the convergence range for the nondimensional loading is significantly elevated by using this approach.     

A unified approach for the linear and nonlinear analysis of plates and shallow shells

The geometric nonlinear behaviour of thin plates and shells is studied in this paper by using a boundary integral equation approach. Two types of plates and shells are considered. One of them is rectangular with movable edges and the other is axisymmetric with various boundary conditions. A plate analog procedure is suggested to simplify the solution. With such simplification, only a knowledge of the boundary integral equation of plates is required in the present study. A number of numerical examples are given in the paper to show the effectiveness of the proposed method.     

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.     

Buckling and geometrically nonlinear analysis of frames using one element/member

The commonly used Hermite cubic element represents the solution for the linear differential equilibrium equation of a straight beam under the Bernoulli hypothesis. However, this element grossly over-estimates the buckling load of a strut when only a single element is used to model a member. This paper presents a simple higher-order element capable of predicting the buckling load of a strut with various boundary conditions by using only a single element for each member. It is found that a direct introduction of a displacement degree of freedom to the mid-length of the cubic element will improve significantly its performance in a nonlinear analysis. The computational efficiency and formulation of this new element are very similar to those for the cubic element in spite of their discrepancies in accuracy.     

黄土地基中大直径超长桩受力特性的非线性有限元分析

基于通用有限元软件ANSYS对黄土地基中大直径超长桩受力特性进行探讨,通过改变桩长、桩径和桩土模量比等因素对其承载性能与沉降变形特性进行了研究。结果表明:黄土地基中大直径超长桩基的荷载-沉降曲线呈缓变型,没有明显拐点,且改变桩长、桩径和桩土模量比等因素对其曲线形式影响较小。桩长、桩径和桩土模量比的改变对其极限承载力的提高和减小沉降的能力有所不同,因此在设计超长桩基时需综合考虑桩土模量及合理的长径比。     

Strain-based finite element for the natural frequencies of cylindrical shells

The free-vibration natural frequencies of complete cylindrical shells, having different end conditions, and cylindrical panels have been investigated. The finite element method is used in which a strain-based cylindrical shell element is employed. This element satisfies the exact representation of rigid-body modes of displacements and all components of strains are assumed to be independent insofar as it is allowed by the compatibility equations. The element has only external degrees of freedom, five at each corner node, to avoid difficulties associated with higher-order elements. The stiffness and mass matrices are obtained using numerical integrations by the deployment of Gauss-Legendre quadrature points.     

Experimental research and finite element analysis of plate-cone cylindrical reticulated shell

为研究板锥网壳结构的实际承载能力和破坏全过程，了解结构的受力性能和整体刚度，对板锥柱面网壳结构进行模型试验研究。对试验模型的细部构造进行设计，确定上弦节点、下弦节点、支座节点、锥体成形及连接构造。对两纵边支承的试验模型在正常荷载工况和破坏荷载工况下进行加载试验，并采用ANSYS软件对试验模型进行非线性有限元分析。结果表明：板锥柱面网壳的整体刚度大，在正常荷载模式下，结构的变形很小，最大竖向位移与跨度的比值为1/3787，弦杆的受力主要是沿拱轴方向传递；在破坏荷载模式下，锥体的节点板连接处率先发生局部屈曲，之后焊点破坏，结构丧失承载能力。有限元与试验所得承载力最大误差为11%，破坏模式基本一致，所用有限元分析方法可靠。     

板锥柱面网壳结构的试验研究与有限元分析

为研究板锥网壳结构的实际承载能力和破坏全过程,了解结构的受力性能和整体刚度,对板锥柱面网壳结构进行模型试验研究。对试验模型的细部构造进行设计,确定上弦节点、下弦节点、支座节点、锥体成形及连接构造。对两纵边支承的试验模型在正常荷载工况和破坏荷载工况下进行加载试验,并采用ANSYS软件对试验模型进行非线性有限元分析。结果表明：板锥柱面网壳的整体刚度大,在正常荷载模式下,结构的变形很小,最大竖向位移与跨度的比值为1/3787,弦杆的受力主要是沿拱轴方向传递;在破坏荷载模式下,锥体的节点板连接处率先发生局部屈曲,之后焊点破坏,结构丧失承载能力。有限元与试验所得承载力最大误差为11%,破坏模式基本一致,所用有限元分析方法可靠。     

某高炉炉壳设计与弹性有限元分析

从高炉炉壳分段、材质的选用、炉壳厚度的确定及炉壳上开孔等方面对炉壳的设计进行了分析,用有限元分析软件对高炉炉壳做了弹性有限元应力分析,给出了炉壳炉腰段应力简化计算方法,为设计中如何确定炉壳直段的厚度提供了指导。     

Large deflection elastoplastic analysis of thin shells

Results are presented and some modifications made to problems posed in an earlier paper by the authors on the extension of the semi-loof element to the analysis of shell structures involving instabilities, snap-through and material nonlinearities. In this paper, by adopting a more refined method for solving problems of plasticity, in conjunction with a subincremental technique, more accurate results are obtained. The second-order Runge-Kutta method employed in this study shows significant improvement in the accuracy of the streesses in the shell as compared to the case when only the simple point-slope method of Euler is used. The detailed computational procedure for elastoplastic analysis of shell problems is presented in a way that can readily be incorporated into standard computer packages. Results obtained for large deflection analysis of plastic shells of different geometries and boundary conditions are compared with the available solutions and show very good agreement.     

导流隧洞进水口结构非线性有限元分析

对龙滩导流隧洞进水结构进行三维有限元分析,求得整体结构的应力、位移,并确定结构中的薄弱环节.针对薄弱环节进行二维有限元分析,确定钢筋应力,裂缝开展情况.在此基础上对现有的设计做出评价,并提出相应的建议.     

A simplified method for elastic large deflection analysis of plates and stiffened panels due to local buckling

A computational model for analysis of local buckling and postbuckling of stiffened panels is derived. The model provides a tool that is more accurate than existing design codes, and more efficient than nonlinear finite element methods. Any combination of biaxial in-plane compression or tension, shear, and lateral pressure may be analysed. Deflections are assumed in the form of trigonometric function series. The deformations are coupled such that continuity of rotation between the plate and the stiffener web is ensured, as well as longitudinal continuity of displacement. The response history is traced using energy principles and perturbation theory. The procedure is semi-analytical in the sense that all energy formulations are derived analytically, while a numerical method is used for solving the resulting set of equations, and for incrementation of the solution. The stress in certain critical points are checked using the von Mises yield criterion, and the onset of yielding is taken as an estimate of ultimate strength for design purposes.     

复合材料层合板的层间应力有限元分析

本文研究复合材料层合板的层间应力,以经典板理论为基础,考虑横向剪切变形和层间相互挤压,构造每一铺层与层间胶层的位移场,采用有限元方法,应用广义势能原理确定位移场中的待定系数,从而确定层合板的位移场和应力场。采用ANSYS计算,计算结果显示,这种解法克服了经典层合板理论的缺点,提高了层间应力的计算精度。     

Deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion

A three-dimensional reinforced concrete (RC) deteriorating beam finite element for nonlinear analysis of concrete structures under corrosion is presented in this study. The finite element formulation accounts for both material and geometrical nonlinearity. Damage modelling considers uniform and pitting corrosion and includes the reduction of cross-sectional area of corroded bars, the reduction of ductility of reinforcing steel and the deterioration of concrete strength due to splitting cracks, delamination and spalling of the concrete cover. The beam finite element is validated with reference to the results of experimental tests carried out on RC beams with corroded reinforcement. The application potentialities of the proposed formulation are shown through the finite element analysis of a statically indeterminate RC beam and a three-dimensional RC arch bridge under different damage scenarios and corrosion penetration levels. The results indicate that the design for durability of concrete structures exposed to corrosion needs to rely on structural analysis methods capable to account for the global effects of local damage phenomena on the overall system performance.