钢筋砼框架非线性分析的简化单元模式

介绍一种用于钢筋混凝土框架二阶弹塑性分析的简化单元模式。它考虑了轴力的二阶效应、横截面的塑化和塑性区长度等非线性因素的影响。利用杆件截面的弯矩—曲率关系,可以直接由弹性杆件的转角—位移方程建立单元的非线性刚度矩阵。经与试验结果比较,说明计算结果是正确的。     

Multi-snap-through and dynamic fracture based on Finite Particle Method

Using the recently proposed Finite Particle Method (FPM), we present the post-buckling analysis of space trusses considering both geometric and material nonlinearities and member fracture. The FPM models the space truss with finite separated particles. Since every particle is considered to be in dynamic equilibrium, the static and dynamic analysis can be unified to the same procedure. Particles are free to separate from each other with FPM, which is advantageous in the simulation of member fracture. Fictitious motion procedures are developed in the particle internal force calculations to handle strong geometric nonlinearity without iterative correction and stiffness matrix calculation. The material nonlinearity is accounted for by tracing a complete stress–strain relationship including elastic and inelastic buckling, yielding, post-buckling, unloading and reloading. The fracture criterion and fracture model of the FPM are developed to simulate member fracture. Phenomena of multi-snap-through and dynamic fracture during the post-buckling range of two classic space trusses are obtained using present method. Corresponding results are verified by comparisons of numerical simulation results and energy conservation studies.     

A computer method for nonlinear inelastic analysis of 3D semi-rigid steel frameworks

This paper presents an efficient computer method for inelastic and large deflection analysis of steel space frames with non-linear flexible joint connections, based on the most refined type of second order inelastic analysis, the plastic zone analysis. The method employs modeling of structures with only one element per member, which reduces the number of degree of freedom involved and the computational time. Gradual yielding of cross-sections is modeled using the nonlinear inelastic force strain relationships, and then using the flexibility approach the elasto-plastic tangent stiffness matrix and equivalent nodal loads vector of 3-D beam-column element is developed. The method ensures also that the plastic bending moment is nowhere exceeded once a full plastified section develops. A zero-length rotational spring element is used for incorporating the connection flexibility into the element tangent stiffness matrix and equivalent nodal forces. The combined effects of material, geometric and connection behaviour nonlinearity sources are simulated into an object oriented computer program automatically. This program was used to study the ultimate response of several steel frames, which have been studied previously by other researchers. The example of computations and the comparisons made have proved the robustness, accuracy and time saving of the proposed analysis method.     

Nonlinear inelastic response history analysis of steel frame structures using plastic-zone method

A beam–column element formulation and solution procedure for nonlinear inelastic analysis of planar steel frame structures under dynamic loadings is presented. The spread of plasticity is considered by tracing the uniaxial stress–strain relationship of each fiber on the cross section of sub-elements. An elastic perfectly-plastic material model with linear strain hardening is employed for deriving a nonlinear elemental stiffness matrix, which directly takes into account geometric nonlinearity and gradual yielding. A solution procedure based on the combination of the Hilber–Hughes–Taylor method and the Newton–Raphson method is proposed for solving nonlinear equations of motion. The nonlinear inelastic time-history responses predicted by the proposed program compare well with those given by the commercial finite element package known as ABAQUS. Shaking table tests of a two-story steel frame were carried out with an aim to clarify the inelastic behavior of the frame subjected to earthquakes generated by the proposed program. A more practical analysis method for seismic design can be developed by comparing it with the presented frames for verification.     

Simplified amplification factors representing material and geometric inelasticity in frame instability

An approach for assessing the inelastic, in-plane, collapse load of framed structures using amplification factors is extended to a broader range of material inelasticity. This manual method is based on the amplification factor approach for elastic, rectangular frames in the Canadian steel design code, but allows for material and geometric nonlinearity of both rectangular and non-rectangular frames on a consistent basis. Improved accuracy is achieved with a linear variation of the incremental amplification factor between a lower limit at the onset of inelastic behaviour and an upper limit at which plastic collapse occurs. A method is demonstrated for notionally separating the effects of material and geometric nonlinearity in experimental measurements or advanced finite element analyses. This is used for validating the proposed inelastic models for a steel frame and a reinforced concrete frame.     

空间支撑钢框架结构的三重非线性分析

为了探讨三维结构的高等分析方法,本文将有限单元法与梁柱法相结合,建立了空间支撑钢框架结构的三重非线性分析方法,该法综合考虑了几何、材料和连接非线性效应。文中基于非线性连续介质力学理论和考虑剪切效应的稳定插值函数建立的严格三维梁柱单元刚度矩阵,包含了轴向、剪切、双向弯曲与扭转及其各耦合效应。三维单元简化塑性区模型可模拟塑性扩展,利用单元两端抗转弹簧和考虑支撑效应的节点域剪切变形模型来模拟连接非线性。使用包括几何、材料和连接非线性的数值算例来检验本文方法和所编计算机程序的可行性、有效性与精确度。算例表明,利用本文方法,每个构件只需一个单元即可准确预测三维结构的极限荷载与失稳模态,可提高结构非线性空间性能的分析效率。     

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。     

钢筋混凝土框架全过程分析的非线性简化单元及其应用

本文根据框架结构在加载过程中表现出来的塑性铰形成机理，介绍了一种用于钢筋混凝土框架非线性分析的简化单元模式。它考虑了轴力的二阶效应、横截面自开裂后的塑化和塑性区长度等非线性因素对结构的影响。此外，在分析中也考虑了钢筋锚固滑移和节点刚域的影响。经与试验结果比较，说明用本文模式对钢筋混凝土试验框架进行非线性有限元分析所得的计算结果是正确的。     

火灾下钢结构的性能与高等分析

本提出了一种改进的模型用于真实火灾下结构的性能分析。其主要特点是用非线性有限元模拟构件，反映结构整体非线性的影响。对真实火灾采用多区域及热辐射模型进行了模拟，对瞬态热传导采用有限元法进行了计算。采用边界面理论来考虑塑性沿构件截面的连续性。对承受局部火灾的半连续框架、多高层及大跨拱形析架采用了基于性能的分析方法。其中对梁跨度，火源位置对火势的蔓延对结构的影响进行了分析。最后对大跨屋面结构在非对称热力作用下的权限状态进行了分析。     

高强钢焊接箱形柱力学性能研究(Ⅱ)：二阶非弹性分析

高强钢的焊接残余应力分布和普通钢材的有较大差异,现有的切线模量和刚度退化函数不适合用于高强钢焊接箱形截面的二阶非弹性分析。而精炼塑性铰模型通过切线模量和刚度退化函数可合理考虑残余应力的影响和塑性渐进发展,达到与塑性区模型相近的精度。基于此,提出适合高强钢焊接箱形截面的二阶非弹性分析方法。通过稳定函数考虑单元二阶效应,基于杆端部转动引起的构件弯曲及其导致的轴向应变,考虑弯曲效应。在精炼塑性铰模型中,采用高强钢焊接箱形截面的残余应力统一分布模型,通过截面分析法构建不同强度等级的焊接箱形截面切线模量计算公式。同时,分析轴力和弯矩共同作用下的渐进屈服对箱形截面刚度退化的影响,从而建立可模拟截面塑性发展的刚度退化函数。结合塑性铰的产生与发展对平衡微分方程解的影响,建立梁柱单元的弹塑性刚度矩阵。结果表明,所提出的二阶非弹性分析方法可准确分析高强钢焊接箱形截面轴压构件的力学性能,可应用于高强钢框架结构设计,为二阶非弹性分析方法的工程应用提供参考。     

Nonlinear inelastic time-history analysis of truss structures

This paper presents the nonlinear inelastic time-history analysis of truss structures including both geometric and material nonlinearities. The geometric nonlinearity is considered based on an updated Lagrangian formulation, while the material nonlinearity is captured by tracing an empirical stress–strain relationship in the elastoplastic range. The presented truss model is capable of capturing several failure modes of member such as buckling, yielding, inelastic post-buckling, unloading, and reloading. An incremental-iterative solution scheme based on the Newmark method and the Newton–Raphson method is adopted for solving the nonlinear equations of motion. A computer program is developed to predict the nonlinear inelastic responses of truss structures. Numerical examples are presented to demonstrate the capabilities of the proposed program in capturing the nonlinear responses of space truss structures under earthquake loadings.     

考虑节点域变形效应的空间支撑钢框架结构二阶弹塑性分析

详细推导了基于非线性连续介质力学理论和考虑剪切效应的稳定插值函数所建立的严格三维梁柱单元虚功增量方程和切线刚度方程, 该方程包含了轴向、剪切、双向弯曲与扭转及其各耦合效应。提出的三维单元简化塑性区模型可模拟塑性扩展。建立了考虑支撑效应的节点域剪切变形模型, 该模型可更真实地反映节点域的变形影响。使用包括几何、材料非线性和节点域变形影响的数值算例来检验本文方法和所编计算机程序的可行性、有效性与精确度。算例表明: 利用该程序, 每个构件只需一个单元即可准确预测三维结构的极限荷载与失稳模态, 可提高结构非线性空间性能的分析效率。该程序可用于三维结构的非线性全过程分析, 为建立高层钢结构的高等分析方法奠定了基础。     

基于刚体准则的空间框架弹塑性非线性分析方法

基于刚体准则,采用二阶改进塑性铰模型,构建了空间弹塑性梁单元及其弹塑性刚度矩阵,建立了高效简洁的非线性增量迭代方法,可有效分析截面屈服产生的有限转动、二阶效应等柔性空间钢框架结构材料与几何非线性耦合效应。对于受初始力平衡的单元,随着单元的刚体转动与移动,其初始平衡力在当前状态下应保持大小不变,仅方向随单元做刚体转动,而实际结构的变形可以视为较大的刚体位移与较小的自然变形(弹性或非弹性)的组合。将此刚体准则植入增量迭代法,在预测阶段采用通过了刚体运动检验的弹塑性矩阵,从而合理确定迭代初始方向;在修正阶段使用刚体准则计算单元结点力,保证了计算精度。对三个典型柔性框架结构所做分析表明,本文方法能够准确预测结构的极限承载力值与塑性铰发展过程。对于空间框架结构,每根杆件仅需划分一个单元,极大提高了计算效率、降低了计算成本。与塑性区法、纤维元法以及考虑截面翘曲的修正切线刚度法等相比,本文提出的方法具有物理概念明确、单元划分少、刚度矩阵简单、分析过程简洁、计算精度与效率高等显著特点,适于工程应用。     

Large deflection inelastic analysis of space trusses using generalized displacement control method

This paper presents the large deflection inelastic analysis of space truss structures including both geometric and material nonlinearities. The geometric nonlinearity is considered, based on an updated Lagrangian formulation, while the material nonlinearity is accounted for by tracing a complete stress–strain relationship in the elastoplastic range. The nonlinear equilibrium equations are solved using an incremental-iterative scheme based on the generalized displacement control method. This algorithm can accurately trace the equilibrium path of nonlinear problems with multiple limit points and snap-back points. A computer program is developed to predict the inelastic post-buckling behavior of space trusses. Numerical results obtained from the developed program are compared with those reported in the literature to demonstrate the accuracy of the proposed procedure.     

张弦空间结构的非线性分析

运用非线性有限元基本理论研究张弦空间结构的非线性特征。针对5个张弦空间结构工程,研究结构的几何非线性、材料非线性和边界条件的状态非线性特征,揭示其基本力学特性。分析表明:张弦空间结构的刚性构件体系贡献了结构的线性刚度,结构的变形协调使拉索应力刚化进而增大结构的几何刚度;对索施加初始预拉力可以增大结构几何刚度,但不影响结构总刚度增量的变化规律;结构总刚度的非线性部分随荷载步的改变而更新,结构分析须先确定结构所处的荷载工况;结构材料进入塑性后表现为结构总切线刚度中线性部分的降低,当结构达到弹塑性极限承载力时表现为结构材料失效。基于张弦结构的自平衡特性,当张弦空间结构滑动支座滑移达到滑程时,结构的边界条件转变为相应的铰支座或弹性支座。通过屋盖结构支座附近同位置且同方向的下部支承结构体系的刚度与屋盖邻支座区域杆件体系刚度的比较,可方便准确地对屋盖单独模型进行屋盖结构在实际工作环境中边界条件的模拟。     

空间钢框架结构的改进塑性区模型

为探讨三维结构的高等分析方法 ,给出了基于非线性连续介质力学理论和考虑剪切效应的稳定插值函数所建立的严格三维梁柱单元切线刚度方程 ,并提出了基于三维单元改进塑性区模型的双重非线性刚度方程。在方程中考虑了轴向位移、弯曲位移和扭转位移的耦合效应 ,使用包括几何与材料双重非线性的数值算例来验证本文方法和计算机程序的可行性、有效性与精确度。利用该程序 ,每个构件只需一个单元即可准确预测三维结构的极限承载力与失稳模态 ,可提高结构非线性空间性能的分析效率。     

Analytical model for the preliminary design of a single-storey multi-bay steel frame under horizontal and vertical loads

Many complicated analytical methods have been proposed to predict the effects of the geometric nonlinearity of a single-story multi-bay steel frame and the material nonlinearity of its steel members. However, some structural engineers have difficulty in understanding the complicated methods and applying them in designing steel structures. Therefore, this study has been performed to provide a simplified analytical model that is only applicable in the preliminary design stage. Using the simplified analytical model, structural engineers can easily predict the storey drift, maximum allowable loads, and bracing stiffness of a single-storey multi-bay steel frame. The application feasibility of the simplified model is verified by performing a two-dimensional finite element analysis.     

New method of inelastic buckling analysis for steel frames

In general, the concept of bifurcation stability cannot be used to evaluate the critical load of typical steel frames that have geometric imperfections and primary bending moment due to transverse loads. These cases require a plastic zone or plastic hinge analysis based on the concept of limit-load stability instead. However, such analyses require large computation times and complicated theories that are unsuitable for practical designs. The present paper proposes a new method of inelastic buckling analysis in order to determine the critical load of steel frames. This inelastic analysis is based on the concept of modified bifurcation stability using a tangent modulus approach and the column strength curve. Criteria for an iterative eigenvalue analysis are proposed in order to consider the primary bending moment as well as the axial force by using the interaction equation for beam-column members. The validity and applicability of the proposed inelastic buckling analysis were evaluated alongside elastic buckling analysis and refined plastic hinge analysis. Simple columns with geometric imperfections and a four-story plane frame were analyzed as benchmark problems. The results show that the proposed inelastic buckling analysis suitably evaluates the critical load and failure modes of steel frames, and can be a good alternative for the evaluation of critical load in the design of steel frames.     

Seismic analysis of inelastic moment‐resisting frames Part I: Modified force analogy method for end offsets

An analytical method of performing inelastic structural dynamic analysis based on the force analogy method to study real moment‐resisting frames with plastic hinge offsets from member ends and rigid panel zones is proposed. New stiffness matrices used in the force analogy method for members with two ends being rigid are theoretically derived using the unit displacement method. Through static condensation, each term in the stiffness matrices is found to be modified simply through multiplying by a scale factor. This is an enhancement to the original force analogy method or other conventional methods, where the condensed form reduces the size of the structural problem by eliminating the unnecessary additional degrees of freedom that must be placed at the plastic hinges. But more importantly, this is a significant improvement on other conventional methods where the present inelastic analysis procedure is more of a theoretical nature rather than numerical. Numerical simulation for seismic analysis is performed on a single degree of freedom system, and the results show that plastic hinge end offsets have significant effects on the seismic response and therefore they should be carefully considered in dynamic analysis. The companion paper further discusses the influence of panel zone deformation on the dynamic response based on the method proposed in this part of the research. Copyright © 2007 John Wiley & Sons, Ltd.