Shallow shell finite element for the large deflection geometrically nonlinear analysis of shells and plates

An investigation into the large deflection, geometrically nonlinear behaviour of shells is carried out in the present paper. The finite element method is used in conjunction with linearised incrementation and the Newton-Raphson iterative technique.The finite element used is based on independent strain assumptions insofar as it is allowed by the compatibility equations. Strain-displacement relationships based on shallow shell formulation are used and applied to an element having three principal curvatures. The resulting element has the only essential external degrees of freedom, satisfies the exact requirement of strain free rigid body modes of displacements and can be used for the representation of cylindrical, spherical and hyperbolic paraboloid shells.Complex load-deflection curves are obtained for cylindrical and spherical shells by incrementing loads as well as deflections. The relative behaviour of cylindrical and spherical panels having the same overall dimensions are also discussed in terms of stiffness, instability and snap-through phenomena.     

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。     

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。     

箱梁桥自振分析的非协调实体退化壳元法

桥梁结构的自振特性对研究其在风荷载和地震荷载作用下的动力响应具有重要意义,其分析精度取决于结构质量和刚度分布特性的准确计算。根据质量等效原理推导了非协调实体退化板壳元的一致质量矩阵,并采用逆迭代法求解了箱梁桥的固有频率和振型。实体退化板壳元可精确描述箱梁桥质量分布,便于同实体单元连接,对不同板厚的箱梁桥均适用。非协调位移的引入使其更适合描述箱梁桥各构件的变形特性。算例表明:单元可显著提高箱梁桥动力特性分析的效率,可获得满意的计算精度。     

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.     

将弧长法应用于结构的几何非线性有限元分析

首先介绍了弧长法的发展及基本理论，随后根据笔者的研究，对其中的几个问题提出了相应的参考意见，最后给出了几个算例。     

组合肋壳几何非线性分析

提出了一种球面组合肋壳截面形式,基于非线性有限元理论,采用空间梁单元和等厚曲边壳单元,考虑空间结构的几何非线性影响,推导了T．L坐标系下组合肋壳非线性单元刚度矩阵。分别讨论了在不同矢跨比、不同荷载作用、不同边界条件下组合肋壳的极限承载力和失稳形态。由大量算例得到了非线性极限承载力与线性极限承载力的比值为0．66及不同情况下结构承载力变化趋势,组合肋壳的极限承载力比混凝土壳承载力提高20％。     

An improved treatment of mixed interpolation functions in eight-node assumed natural strain shell element for vibration analysis

In this article, we investigate the vibration analysis of plates and shells, using an eight-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The natural frequencies of plates and shells are presented, and the forced vibration analysis of plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve the eight-node shell element for free and forced vibration analysis, a new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner–Mindlin theory, which directly addresses the transverse shear deformation without a shear correction factor, is adopted for the development of a new eight-node assumed strain shell element with rotary inertia effect. In order to validate the finite element numerical solutions, the reference solutions of plates based on the first-order shear deformation theory are presented. Results of the present theory show good agreement with the reference solutions. In addition, the effect of damping is investigated on the forced vibration analysis of plates and shells.     

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.     

Beam and shell element model for advanced analysis of steel structural members

Plastic zone method of advanced analysis, which uses shell elements to model the entire structure, is the most accurate method available to predict the ultimate strength and behavior of steel frames. The disadvantage of such full shell plastic zone models is that it is computationally expensive and hence its use is limited to small structures. Beam elements in commercial finite element packages can model residual stress and capture spread of plasticity, but cannot model local buckling of plates that the member is made up of, which leads to unloading and failure in steel frames. A hybrid model using shell elements only in the regions vulnerable to elastic or inelastic local buckling and beam elements in other locations could overcome this limitation of full beam element model. The issues in using this hybrid model are, knowing a priori the location and length of the shell element region and connecting the beam and shell regions without any artificial stress concentrations or incompatible displacements. In this study, in addition to addressing these issues, the hybrid model is systematically evaluated by studying its performance in structural elements. It is seen that the hybrid model strength predictions has an average error of only 0.91% but requires on an average 83% less computational time when compared to the full shell plastic zone models.     

Beam and shell element model for advanced analysis of steel structural members

Plastic zone method of advanced analysis, which uses shell elements to model the entire structure, is the most accurate method available to predict the ultimate strength and behavior of steel frames. The disadvantage of such full shell plastic zone models is that it is computationally expensive and hence its use is limited to small structures. Beam elements in commercial finite element packages can model residual stress and capture spread of plasticity, but cannot model local buckling of plates that the member is made up of, which leads to unloading and failure in steel frames. A hybrid model using shell elements only in the regions vulnerable to elastic or inelastic local buckling and beam elements in other locations could overcome this limitation of full beam element model. The issues in using this hybrid model are, knowing a priori the location and length of the shell element region and connecting the beam and shell regions without any artificial stress concentrations or incompatible displacements. In this study, in addition to addressing these issues, the hybrid model is systematically evaluated by studying its performance in structural elements. It is seen that the hybrid model strength predictions has an average error of only 0.91% but requires on an average 83% less computational time when compared to the full shell plastic zone models.     

有限元节点自由度自动编号的简捷算法

阐述了单元定位向量是一种重要的数据结构，而节点自由度编号是形成单元定位向量的基础，介绍了一种简单高效的节点自由度编号算法，并用C语言正确地实现了该算法，以供参考借鉴。     

Thermal analysis of FRP chimneys using consistent laminated shell element

Due to their high corrosion and chemical resistance, fiber reinforced plastic (FRP) materials are increasingly being used in the construction of industrial chimneys. The design of a chimney is governed by wind loads as well as thermal loads resulting from the differences among the ambient, the operating and the curing temperatures. This study involves an investigation for the thermal stresses induced in angle-ply laminated FRP chimneys, using an in-house developed laminated shell element model. The finite element model is verified by performing thermal analysis of a number of plate and shell problems and comparing the results to those available in the literature. An extensive parametric study is then conducted using the shell element model to identify the parameters which significantly affect thermal stresses induced in FRP chimneys.The study indicates that the thermal stresses are only affected by the inclination of the lamina plies, the percentage of fibers content and the through thickness temperature distribution. Analyses also show that localized cracks in the direction perpendicular to the fibers are expected to occur due to the thermal loads. Finally, thermal stress values that can be used in the design of FRP chimneys, when cracking is considered, are presented as function of the through thickness temperature distributions.     

An oriented finite element model for shearwall analysis

Generally, loadbearing wall structures exhibit some regularity along the height. This regularity is exploited by cutting the building into typical slices. Each slice is obtained from the assemblage of basic structural units. The finite element method supports the calculation of the boundary stiffness matrices of these components which are stored in a user-defined structural library. Evaluation of structural response is based on a frontal process. The resulting program is runable on a minicomputer at low cost. Torsion of a model core illustrates the application of the method.     

自适应模型缩放非线性动力分析方法

提出一种基于模型损伤的自适应模型降阶动力分析方法。该方法在动力分析的每个分析步中根据损伤分布和损伤程度自适应地定义和调整模型子区域的缩放属性。针对模型缩小子区域,采用模态综合方法对其进行动力缩聚;针对模型放大子区域,采用精细化单元替换原有单元,最终形成混合坐标空间内的结构运动方程,通过求解缩减自由度之后的运动方程来提高计算效率。最后通过一个20层钢框架来验证该方法的有效性和适用性,数值结果表明,自适应模型缩放动力分析方法能够在满足模拟精度要求的同时,显著地提高非线性动力分析的计算效率。     

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.     

钢筋混凝土框架变梁异型节点的有限元分析

运用通用有限元分析软件ANSYS,对变梁异型节点在梁端施加正反对称荷载作用时,节点区内混凝土的裂缝发展和破坏形态进行分析,由分析结果可以看出,节点区内裂缝发展都经历初裂、通裂、极限和破坏四个阶段,且随着梁高差的不断加大,变梁异型节点以小核芯区剪切破坏为主。     

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。     

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.