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。     

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.     

Buckling analysis design of steel frames

Steel design codes do not provide sufficient information for the efficient design of steel structures against out-of-plane failure, and what is provided is often overly conservative. The method of design by buckling analysis (DBA) specified in one code corrects this situation for beams, but the extension of this method to columns is only referred to, while there is no guidance on how to apply this method to the design of beam-columns and frames.Beam DBA uses the design code formulation for the member nominal design strengths in terms of the section moment capacities and the maximum moments at elastic buckling, accurate predictions of which may be determined by computer programs. Column DBA is similar, in that it uses the design code formulation for the column nominal design strengths in terms of the section compression capacities and accurate predictions of the elastic buckling.However, design codes do not provide formulations for the direct buckling design of beam-columns, but instead use the separate results of beam design and column design in interaction equations. The further extension to frames is not directly possible, because frames are not designed as a whole (except through the rarely used methods of advanced analysis), but as a series of individual members. This paper shows how the method of DBA can be used to design beam-columns and frames as well as beams and columns. Two example frames are designed and very significant economies are demonstrated when the DBA method is used.     

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。     

Geometrically and materially nonlinear finite element analysis of thin-walled frames: Numerical studies

This paper deals with the finite element analysis of free-form beams and frames undergoing large elastoplastic deformations. A mixed hybrid model proposed previously implemented and tested on a series of well selected examples representing a broad range of circumstances in non-linear beam and frame analysis.     

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.     

一种能够考虑复杂加载历史的RC框架单元模型

本文提出的单元模型把框架结构构件看作由分布弹塑性梁子单元、节点滑移子单元和剪切子单元等三个在节点上串联的子单元组成。着重介绍了分布塑性梁子单元柔度矩阵的建立过程,该柔度矩阵是在梁端塑性区域平均刚度假定和修正TAKEDA恢复力模型的基础上建立起来的。该单元模型能够考虑非线性变形随复杂加载历史在端部关键受力区域的逐步扩展和反弯点位置的移动,整个推导过程力学概念明确,所获得的柔度矩阵为对称矩阵,便于数值计算。计算结果与试验结果比较表明,本文提出的分布塑性梁单元模型可以较好地反映试件的滞回性能。     

基于杆系离散单元法的单层网壳结构屈曲行为研究

离散单元法因适合处理大位移、非线性和非连续等问题而逐渐被应用于结构工程中,但采用离散单元法进行结构屈曲全过程分析还有待研究。为此,基于杆系离散单元法的基本理论和计算方法,提出离散元力控制法及离散元位移控制法,研究上述方法在结构弹性屈曲全过程分析中的特点及适用性,同时给出离散元位移控制法（力控制法不需要单独处理）对不同荷载工况的处理方法及离散元法在进行结构弹性屈曲分析时的计算流程。采用Fortran语言自编程序,对典型算例进行弹性屈曲全过程分析,与传统方法相比,该方法无需组集刚度矩阵,对几何非线性问题不需特殊处理即可模拟结构的屈曲行为,更具优越性,并通过结果对比,验证了离散单元法在单层网壳结构弹性失稳全过程分析中的有效性。     

Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method

Differential quadrature element method (DQEM) for buckling analysis of stiffened circular cylindrical panels subjected to axial uniform compressive stresses is presented for the first time. The methodology and procedures are worked out in detail. The circular cylindrical panel and the stiffeners are treated separately. Governing differential equations are derived based on the equilibrium of the panel and the stiffener, and on compatibility conditions along the interface of panel elements and stiffeners. Torsional stiffness of the stiffener is ignored. Circular cylindrical panels with a stringer stiffener or a chordwise stiffener are analyzed by the DQEM, and the results are compared with previously published data to verify the established methodology and procedures. Some new results are presented for the circular cylindrical panels with two orthogonal stiffeners.     

Nonlinear analysis of masonry-infilled steel frames with openings using discrete element method

Nonlinear numerical modeling of masonry-infilled frames is one of the most complicated problems in structural engineering field. This complexity is attributed to the existence of joints as the major source of weakness and material nonlinearities as well as the infill-frame interaction which cannot be properly modeled using the traditional finite element methods. Although there are many numerical studies available on solid masonry-infilled steel frames’ behavior, however, few researches have been conducted on infilled frames with openings. In this paper a two-dimensional numerical model using the specialized discrete element method (DEM) software UDEC (2004) is developed for the nonlinear static analysis of masonry-infilled steel frames with openings subjected to in-plane monotonic loading. In this model, large displacements and rotations between masonry blocks are taken into account. It was found that the model can be used confidently to predict collapse load, joint cracking patterns and explore the possible failure modes of masonry-infilled steel frames with a given location for openings and relative area. Results from the numerical modeling and previous experimental studies found in the literature are compared which indicate a good correlation between them. Furthermore, a nonlinear analysis was performed to investigate the effect of door frame on lateral load capacity and stiffness of infilled frames with a central opening.     

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。     

Geometric and material nonlinear analysis of three-dimensional steel frames

Results obtained through theoretical and empirical studies which examined the nonlinear behaviour of construction members enabled us to characterize the behaviour of construction systems under external effects more closely. The calculation methods that took into consideration the nonlinear behaviour of the construction members and the nonlinear effects of their geometrical variations had to be developed in order to evaluate these phenomena and to design structures according to their collapse load principle. In the presented study, a computer program was developed for the characterization of structural systems by taking into consideration the nonlinear conditions of material behaviours under increasing loads and by considering the second-order effects. A matrix-replacement method was used as the basis for developing the program, which takes into consideration the effects of axial forces on the stiffness of the member by using the stability functions and the effects of plastic hinges by systematically changing the stiffness matrix in each occurrence of the plastic hinges. In the study, based on the results obtained from the examples, which were solved by the developed program, it was identified that the program could yield rapid and reliable results depending on the user-defined values (number of nodes, error limit for the iteration) and it is observed that the results are consistent with the literature. The obtained results in this study have contributed to capability of converting two dimensional analyses to three-dimensional analysis of stability functions developed.     

使用非线性有限元法对张力膜结构找形分析

首先介绍了张力膜结构找形分析的基本原理,然后讨论非线性有限元法中的几种索单元和膜单元力学模型,并建立相应的几何方程、物理方程和平衡方程,最后提出以极小曲面作为找形分析的最终平衡状态。     

Buckling analysis of structural steel frames with inelastic effects according to codes

Steel building frames are often analyzed for stability in an elastic way, while most of their columns behave inelastically at the buckling stage. Most column design provisions allow for inelastic behavior, but overall inelastic stability analysis is rarely performed. In this study the analysis philosophy is centered on the overall frame stability and its true safety factor. As many columns show inelastic behavior at the buckling stage, the proposed procedure takes due consideration of this fact. Once the overall buckling factor for the frame is obtained, individual column effective length factors, and their true slenderness ratios are computed, and used in the design relationships. This procedure circumvents the use of design nomographs and numerous formulas proposed in the past to alleviate their shortcomings. The procedure proposed based on the overall safety factor concept is an iterative one. It starts with a stability analysis and gradually modifies the structural properties to take account of inelasticity and eventually converges to the final buckling factor and mode shape. Any type of lateral restraint can be exactly modeled and taken into consideration without the need for approximate simplifying assumptions. The design philosophy proposed herein is that all columns must have their design parameters as related to buckling capacity must be derived from a single buckling analysis valid for the whole structure, and not considered separately and isolated from the rest of the structure as is currently practiced. Examples are worked out to illustrate the procedure and the results are compared to those of others.     

Buckling of frames braced by flexural bracing

This paper investigates the buckling of multistory frames braced by vertical beams. The sectional properties of the frames and the bracing beam are assumed to vary linearly along the height; the axial forces in the columns and the bracing beam are also assumed to linearly change along the height. A relationship between the buckling load and the bracing rigidity is established. The threshold rigidity for the vertical bracing beam which is just enough to make the frames buckle in a non-sway mode is obtained. The result may be used as a rational basis for classifying sway frames and non-sway frames after taking the influence of initial imperfections and lateral loads into account.     

薄柔截面构件屈曲铰及钢框架破坏机构分析

对H形薄柔截面构件组成的钢框架结构的极限承载性能及变形性能进行研究。首先对H形薄柔截面钢构件的破坏机制、承载能力、变形及耗能能力等特性进行总结,表明薄柔截面构件延性虽弱,在抗震设计中仍可以被用于耗散能量。针对薄柔截面构件的承载和变形特性,阐述屈曲铰的特征和实现条件。通过引入屈曲铰,对薄柔截面构件钢框架的非线性发展过程进行数值分析。分析结果表明,由“弱延性”构件组成的超静定框架可以实现非线性变形发展条件下的内力重分布,并使框架结构表现出一定的延性。基于结构的最终破坏机构模型,对薄柔构件利用屈曲铰模型,采用极限状态分析法预测框架结构的极限承载能力,并通过2个框架试验验证该方法的可行性。     

Design of tapered member portal frames

Non-uniform steel frames, incorporating tapered or haunched members, have proved to be economical solutions for warehouses and factory buildings over a wide range of spans. Design rules, however, deal only with uniform member frames and therefore attempts have been made to convert the non-uniform frame into an equivalent uniform frame. One such method appears in the AISC Specification for the Design of Steel Buildings^(l) but it is relatively complex and of limited application.A simpler and more general procedure, based on a parametric study and using a limit state interaction equation, is presented. In the study, elastic instability computer programs were used and changes were made to the values of the principal variables. The results were subjected to an analysis of variance and equations of best fit were obtained for the conversion to an equivalent uniform frame. At this stage of the research program only completely symmetrical taper member frames have been investigated. The proposed conversion enables the designer to use all the currently available design aids dealing with the effective length factors of uniform members. The method is illustrated by two numerical examples.     

Simplified nonlinear progressive collapse analysis of welded steel moment frames

In this study, two nonlinear analysis methods are proposed that can be used for a simplified but accurate evaluation of progressive collapse potential in welded steel moment frames. To this end, the load-resisting mechanism of the column-removed double-span beams in welded steel moment frames was first investigated based on material and geometric nonlinear parametric finite element analysis. A simplified tri-linear model for the vertical resistance versus chord rotation relationship of the double-span beams was developed. The application of the developed model to energy-based nonlinear static progressive collapse analysis was then proposed. The relationship between the gravity loading and the maximum dynamic chord rotation or the concept of collapse spectrum was also established for a quick assessment of the maximum deformation demands.     

Finite element analysis of creep for plane steel frames in fire

Steel is widely used for the construction of bridges, buildings, towers, and other structures because of its great strength, light weight, ductility, and ease of fabrication, but the cost of fireproofing is a major disadvantage. Therefore, the resistance of a steel structure to fire is a significant subject for modern society. In the past, for simplification, creep behavior was not taken into account in research on the resistance of a steel structure to fire. However, it was demonstrated that the effect of creep is considerable at temperatures that commonly reach 600°C and should not be neglected in this context. In this paper, a co-rotational total Lagrangian finite element formulation is derived, and the corresponding numerical model is developed to study the creep behavior of plane steel frames in fire conditions. The geometric nonlinearity, material nonlinearity, high temperature creep, and temperature rate of change are taken into account. To verify the accuracy and efficiency of the numerical model, four prototypical numerical examples are analyzed using this model, and the results show very good agreement with the solutions in the literature. Next, the numerical model is used to analyze the creep behavior of the plane steel frames under decreasing temperatures. The results indicate that the effect of creep is negligible at temperatures lower than 500°C and is considerable at temperatures higher than 500°C. In addition, the heating rate is a critical factor in the failure point of the steel frames. Furthermore, it is demonstrated that the deflection at the midpoint of the steel beam, considering creep behavior, is approximately 13% larger than for the situation in which creep is ignored. At temperatures higher than 500°C, the deformed steel member may recover approximately 20% of the total deflection. The application of the numerical model proposed in this paper is greatly beneficial to the steel industry for creep analysis, and the numerical results make a significant contribution to the understanding of resistance and protection for steel structures against disastrous fires.