Slepian simulation of distributions of plastic displacements of earthquake excited shear frames with a large number of stories

The object of this study is a stationary Gaussian white noise excited plane multistory shear frame with a large number of rigid traverses. All the traverse-connecting columns have finite symmetrical yield limits except the columns in one or more of the bottom floors. The columns behave linearly elastic within the yield limits and ideally plastic outside these without accumulating eigenstresses. Within the elastic domain, the frame is modeled as a linearly damped oscillator. The white noise excitation acts on the mass of the first floor making the movement of the elastic bottom floors simulate a ground motion that interacts with the structure above the bottom floors. As in a recent work by the authors, the paper is about application of the so-called Slepian model simulation, but in this paper supplemented by a simplification principle that allows a manageable calculation for the considered type of elasto-plastic oscillator also when it has a large number of elasto-plastic columns.     

Equivalent linearization of MDOF systems under external Poisson white noise excitation

Equivalent linearization (EQL) techniques are developed and evaluated for multidimensional systems under external Poisson white noise excitation. Especially, a simulation strategy for the calculation of the linearization coefficients is proposed. The methods are illustrated by several examples that have been treated under Gaussian white noise excitation in the literature. It is shown that EQL for MDOF systems under Poisson white noise excitation is able to deal with problems of nearly the same dimension as under Gaussian white noise excitation.     

Probabilistic analysis of truss structures with uncertain parameters (virtual distortion method approach)

A new approach for probabilistic characterization of linear elastic redundant trusses with uncertainty on the various members subjected to deterministic loads acting on the nodes of the structure is presented. The method is based on the simple observation that variations of structural parameters are equivalent to superimposed strains on a reference structure depending on the axial forces on the elastic modulus of the original structure as well as on the uncertainty (virtual distortion method approach). Superposition principle may be applied to separate contribution to mechanical response due to external loads and parameter variations. Statically determinate trusses dealt with the proposed method yields explicit analytic solution in terms of displacements while redundant trusses have been studied by means of an asymptotic expansion exhibiting explicit dependence on parameter fluctuations. Probabilistic characterization of the response may then be obtained both for statically determinate and statically indeterminate stochastic trusses.     

First passage failure of quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations

The first passage failure of multi-degree-of-freedom (MDOF) quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations in the case of external resonance is studied. First, a stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations using generalized harmonic functions is reviewed briefly. Then, a backward Kolmogorov equation governing the conditional reliability function and a Pontryagin equation governing the conditional mean of the first passage time are established from the averaged Itô equations, respectively. The conditional reliability function, and the conditional probability density and conditional mean of the first passage time are obtained from solving these equations together with suitable initial condition and boundary conditions. The comparison between the analytical results and those from Monte Carlo simulation for an example shows that the proposed method works very well. It is also shown by using Monte Carlo simulation that the reliability of the system in the case of external resonance is much lower than that in the non-resonant case.     

Variability response functions for effective material properties

The variability response function (VRF) is a well-established concept for efficient evaluation of the variance and sensitivity of the response of stochastic systems where properties are modeled by random fields that circumvents the need for computationally expensive Monte Carlo (MC) simulations. Homogenization of material properties is an important procedure in the analysis of structural mechanics problems in which the material properties fluctuate randomly, yet no method other than MC simulation exists for evaluating the variability of the effective material properties. The concept of a VRF for effective material properties is introduced in this paper based on the equivalence of elastic strain energy in the heterogeneous and equivalent homogeneous bodies. It is shown that such a VRF exists for the effective material properties of statically determinate structures. The VRF for effective material properties can be calculated exactly or by Fast MC simulation and depends on extending the classical displacement VRF to consider the covariance of the response displacement at two points in a statically determinate beam with randomly fluctuating material properties modeled using random fields. Two numerical examples are presented that demonstrate the character of the VRF for effective material properties, the method of calculation, and results that can be obtained from it.     

Substructuring in the implicit simulation of single point incremental sheet forming

This paper presents a direct substructuring method to reduce the computing time of implicit simulations of single point incremental forming (SPIF). Substructuring is used to divide the finite element (FE) mesh into several non-overlapping parts. Based on the hypothesis that plastic deformation is localized, the substructures are categorized into two groups: the plastic—nonlinear—substructures and the elastic—pseudo-linear—substructures. The plastic substructures assemble a part of the FE mesh that is in contact with the forming tool; they are iteratively updated respecting all nonlinearities. The elastic substructures model the elastic deformation of the rest of the FE mesh. For these substructures, the geometrical and the material behaviour are assumed linear within the increment. The stiffness matrices and the internal force vectors are calculated at the beginning of each increment then they are statically condensed to eliminate the internal degrees of freedom (DOF). In the iteration process the condensed stiffness matrices for the elastic substructures are kept constant. The condensed internal force vectors are updated by the multiplication of the condensed stiffness matrices and the displacement increments. After convergence, any geometrical and material nonlinearity for the elastic substructures are nonlinearly updated. The categorization of substructures in plastic and elastic domains is adapted during the simulation to capture the tool motion. The resulting, plastic and condensed elastic, set of equations is solved on a single processor. In an example with 1600 shell elements, the presented substructuring of the SPIF implicit simulation is 2.4 times faster than the classical implicit simulation.     

多自由度Duffing系统受演变随机激励的非平稳响应

用等效线性化法将受演变随机激励的非线性多自由度Ｄｕｆｆｉｎｇ系统等效为线性时变系统,用虚拟激励法来求解该时变系统的非平稳响应。具有计算简单、精确、效率高的特点。该演变随机激励的谱密度不局限于白噪声和过滤白噪声,各激励之间可以存在相位差。该方法的计算精度由Ｍｏｎｔｅ－Ｃａｒｌｏ法得以验证。     

板柱结构矩形弹性板弯曲精确解法

板柱结构是工程中经常采用的受力体系,但至今尚无一种精确解法分析板中内力分布。将板柱结构矩形板的弯曲划分为广义静定和广义超静定二类。对于前者利用静力平衡条件确定柱支反力后撤去柱支座,柱支条件下板的弯曲即转换为四边自由矩形板在原荷载和柱支反力共同作用下的弯曲。挠度表达式采用了新的通解形式,其变形曲线符合四边自由边界所限定的变形特征,并采用组合特解,即特解同时满足平衡微分方程,自由边界上剪力分布条件及自由角点上作用力条件,从而可以利用四边边界条件和柱支座处的位移条件直接求解。对于广义超静定弯曲需要利用叠加法求解。这种解法可以分析板柱结构在任意柱支条件下和任意荷载作用下板的弯曲。通过逆向分析验证法真实地说明了本解法具有很高的计算精度。     

White noise excited non-ideal elasto-plastic oscillator

Summary Two sets of 50 samples of the displacement response of the top traverse relative to the second traverse of an experimental shear frame with three traverses subject to white noise base shaking of two different intensities have been recorded at Institut für Allgemeine Mechanik in 1995, and are in file available for analysis. The column connection between the two top traverses were made of aluminum with a linear-elastic non-ideal plastic behavior, and the columns were therefore renewed after each experiment. The two other connections were made of steel with a purely linear-elastic behavior. By use of the measured displacement-retaining force relation for the aluminum connection the plastic displacement responses were isolated from the sample records. From the obtained samples of plastic displacement records various distributions were estimated as well as the time development of the variance of the plastic displacement process.This paper presents a determination of the experimentally estimated statistical properties of the plastic response by use of Slepian model process theory as the basis for a numerical simulation algorithm. Solely the given defining parameters of the experimental frame are used in the calculations, i.e. the given displacement-retaining force relations, the traverse masses, the modal damping ratios for the vibrations within the elastic domain, and the two white noise excitation intensities, all as measured.First the Slepian model process method is applied to a single degree of freedom oscillator with linear-elastic non-ideal plastic displacement restoring force relation. The method is based on a direct generalization of the Slepian model process method that quite successfully has been developed for the linear-elastic ideal-plastic oscillator. Next the method is modified to be applicable on an oscillator of more than one degree of freedom. Applied to the experimental frame the calculations give excellent predictions of the main distributional properties of the plastic displacement process.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday Prologue. The modeling of the random vibration behavior of elasto-plastic structures subject to earthquake excitation is a topic of stochastic mechanics that among many other topics has been in the focus of the research activities at Institut für Allgemeine Mechanik, Technische Universität Wien under the leadership of Prof. Franz Ziegler. He and his coworkers have contributed to the development both by theory and by experimental investigations reported in several publications of which only some few are listed in the reference list of this paper [1]–[6].     

A statically determinate truss model for thin shells: Two-surface analysis (bending theory)

This paper presents a simple scheme for analysing shells subject to the Kirchhoff–Love hypothesis. The method combines a previously developed, statically determinate truss model with the static-geometric analogy of elastic thin shell theory. In this way, both in-plane and flexural mid-surface actions are obtained by simply repeating the elementary computations performed on an essentially ‘membrane’ truss.     

4X框架木箱结构内力计算方法研究

目的 以重型包装运输用木质框架结构为研究对象,解决木质框架结构内力求解困难的问题。方法 利用解析法,以4X框架结构为例,分别以经验简化静定桁架与无简化超静定桁架进行求解;基于ANSYS软件建立经验简化静定桁架、无简化超静定桁架、梁模型、梁杆组合模型及实体模型,并进行对比分析。结果 有限元求解结果与解析法结果具有高度的一致性;经验简化静定桁架的最大轴力超过无简化超静定桁架的最大轴力15%;梁模型、梁杆组合模型及实体模型的计算结果与无简化超静定桁架的计算结果一致。结论 经验法对框架结构的简化往往会导致比较大的误差,可能导致过包装设计或欠包装设计。梁杆组合模型和实体模型建模过程比较复杂,选用梁单元对木箱用框架结构进行数值计算分析,不仅计算精度高,分析处理快捷,而且对复杂工况具有较好的适应性。     

实腹式型钢混凝土异形柱框架刚度与承载力试验研究

通过2榀实腹式配钢的型钢混凝土(SRC)异形柱框架的低周反复加载试验,获得其破坏特征和荷载-位移滞回曲线,分析其刚度和承载力。结果表明,实腹式配钢的SRC异形柱框架具有良好的抗震性能,破坏机制为梁铰机制;刚度退化由快到慢,呈现出较好的规律性;对SRC异形柱框架的弹性层刚度进行计算,结果与试验结果符合较好;承载力衰减随加载位移的增加而增大,但当位移小于5#x00394;_y时,同级位移下承载力衰减较小;实腹式SRC异形柱框架的层间受剪承载力可采用柱底塑性铰法进行计算。     

Experiments with elasto-plastic oscillator

Plastic displacements of a Gaussian white noise excited three degrees of freedom non-ideal elasto-plastic oscillator are measured in laboratory experiments and the plastic displacements are compared to computer simulated results for the corresponding ideal elasto-plastic oscillator. The comparative analysis leads to an equivalent ideal plastic yield limit that gives good coincidence between the simulated distributions and the experimentally determined distributions.     

Finite three-point bending of a fiber-reinforced beam with a step

Summary Using the theory of ideal fiber-reinforced composite materials, an equilibrium solution was obtained for the finite three-point bending of a beam which has a central step on its bottom surface. The beam is axially reinforced by fibers and simply supported by fixed roller fulcrums. It was found that the exact solution reached by the rule of trial and error is statically and kinematically admissible only for a linear elastic (or quasielastic) shear response. The equilibrium condition of the portion of the beam corresponding to the step edge is reduced to a Fredholm type integral equation of the second kind with respect to the curvature radius of the uppermost fiber.With 5 Figures     

弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法

提出了一种新的计算弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法，它是一种时域复模态分析方法。利用此方法获得了弹性-粘弹性复合结构在白噪声、滤过白噪声等典型平稳随机激励下随机响应的各阶谱矩的解析表达式，分析了粘弹性对各阶谱矩的影响。此计算方法简便、易用，无论单自由度或多自由度系统均适用，为进一步研究弹性-粘弹性复合结构在随机激励下的可靠性打下良好基础。     

Non-parametric system identification from non-linear stochastic response

An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable processing of records of the stochastic response. The stiffness estimation is based on a local iterative procedure, which compares the elastic energy at mean-level crossings with the kinetic energy at the extremes. The damping estimation is based on a generic expression for the probability density of the energy at mean-level crossings, which yields the damping relative to white noise intensity. Finally, an estimate of the noise intensity is extracted by estimating the absolute damping from the autocovariance functions of a set of modified phase plane variables at different energy levels. The method is demonstrated using records obtained by numerical simulation.     

高层框架-斜交网格结构协同受力性能研究

高层框架-斜交网格结构是由高层斜交网格结构和框架结构组成的双抗侧力体系。采用理论推导和数值模拟的方法研究了该体系处于弹性和弹塑性状态下楼层水平剪力分配规律。针对高层斜交网格结构和框架结构协同工作变形特点,提出结构体系的弹性平面简化分析模型,进一步推导出结构侧向变形和剪力计算公式,并研究了结构处于弹性阶段时的剪力分配规律;采用非线性静力推覆法对结构体系在弹塑性阶段的变形特性、刚度退化和剪力分配规律进行了研究。结果表明:高层斜交网格结构和框架结构的协同工作性能良好,结构在弹性阶段,结构刚度的特征值及荷载分布对其剪力分配影响较大;结构进入塑性阶段,斜柱刚度退化速率较快,楼层剪力存在重分配现象。     

部分组合框架-钢板剪力墙边框柱设计方法研究

该文通过对部分组合框架—薄钢板剪力墙结构的试验,发现其内嵌钢板破坏顺序为初始对角屈服、统一屈服和应变硬化三个阶段。引入部分组合柱后,有效改善了传统钢柱的弯扭失稳破坏模式,部分组合框架柱破坏模式为柱顶和柱底形成塑性铰的强度破坏。基于“强框架、弱墙板”的设计理念,该文根据叠加原理确定了统一屈服阶段和应变硬化阶段部分组合柱内力计算原则,提出了适用于部分组合框架-薄钢板剪力墙框架柱的设计方法。通过有限元验证表明:该设计方法能够有效地预测底层受压柱的破坏模式及其塑性铰出现的位置,能够为合理的钢板墙边框柱设计提供理论依据。     

Y形高强钢组合偏心支撑框架结构基于性能的塑性设计方法研究

Y形高强钢组合偏心支撑框架结构（YEBF）的耗能梁段采用屈服点较低的钢材,框架梁、柱采用高强度钢材,采用高强钢可有效减小构件截面,节约钢材,降低造价。现行设计规范中偏心支撑结构基于弹性理论进行设计,采用内力放大系数的方法保证结构在罕遇地震下耗能梁段进入塑性,其他构件保持弹性,结构的弹塑性变形可能过于集中而出现薄弱层。该文提出了采用基于性能设计方法（PBPD）设计剪切屈服型耗能梁段YEBF结构（S-YEBF）,以目标位移和理想的整体破坏模式为作为预测和控制结构弹塑性受力状态的性能目标,保证结构在罕遇地震作用下各层耗能梁段均能参与耗能,使结构层间侧移角分布趋于均匀,避免出现薄弱层。根据PBPD方法设计了多层S-YEBF结构,对其1/2缩尺模型进行了振动台试验以评估其抗震性能。通过非线性静力推覆分析和动力时程分析对比了分别采用PBPD方法和传统设计方法设计的10层S-YEBF结构算例的抗震性能。结果表明:采用PBPD方法设计的S-YEBF结构具有良好的抗震性能,结构呈较为理想的整体破坏模式,在罕遇地震作用下,各层耗能梁段均参与耗能,层间侧移角沿结构高度方向分布较均匀;与传统设计相比,PBPD方法设计的S-YEBF结构层间侧移角分布更均匀,并且可节省一定的钢材;PBPD设计方法可以为S-YEBF结构的工程设计提供参考。