基于位移频响函数灵敏度分析的模型修正

针对频响函数灵敏度分析法进行模型修正时,由于一阶近似固有的局限性,很难直接迭代得到正确收敛结果的问题,提出了频响函数灵敏度拟合函数进行基于模型修正的结构损伤识别方法。首先,采用模态参与变异系数准则选取激励点位置、频率响应有效独立法结合距离系数-有效独立法选取测点位置;然后,综合考虑频响函数对修正参数变化的灵敏度和频响函数的相关性,选择一个合理的频率点;最后,拟合随参数变化的频响函数灵敏度函数曲线,引入新的中间设计参数,从而建立中间设计参数的频响函数灵敏度方程组,通过求解中间设计参数的改变量来求解修正参数的改变量。三自由度质量—弹簧和二维桁架系统的数值算例验证了所提出方法的可行性;数值算例表明,该方法具有较高的计算效率和识别精度,也对随机噪声具有鲁棒性,同时有效地避免了灵敏度方程组数值平衡导致的收敛问题。     

Tikhonov方法在不适定模型修正中的应用

数值建模和分析在结构动态设计中应用广泛,为获取准确的计算模型,基于参数灵敏度有限元修正技术得到迅速发展。然而,参数灵敏度矩阵病态性和修正目标函数方程组的不适定性,造成最小二乘直接法难以得到稳定的物理解。为此,对灵敏度矩阵的病态和模型优化方程组的不适定性进行研究,以铁道车辆6自由度离散模型和有限元支架模型为载体,采用Tikhonov正则化方法分别完成了超定系统和欠定系统仿真模型的参数修正。从而,解决了病态不适定系统中最小二乘直接法无稳定物理解的缺陷。参数修正后的模型准确反应了实际结构的尺寸差别和质量,这表明该方法具有实际的应用价值。     

计算结构非线性地震峰值响应的等价线性化模型

多自由度体系的等价线性化方法是预测结构的非线性地震峰值响应的有效方法。单自由度等价线性化模型是该方法的基础。该文在前人研究的基础上,从定性和定量的两个方面综合分析了结构周期、延性系数以及恢复力模型等因素对单自由度等价线性化模型的影响,并通过对大量地震动记录下动力弹塑性分析结果的拟合回归,提出了能够综合反映各方面参数影响的单自由度等价线性化模型。与现有代表性的等价线性化模型相比,该文模型所反映的参数最为全面,预测峰值位移的平均相对误差最小,且略偏于保守。     

各向异性层合板壳的弹塑性分析

用最小二乘配点法对各向异性层合扁薄壳体的弹塑性弯曲问题进行分析。文中以双五次样条函数为位移试函数,采用弹塑性增量理论和由Hill推广的Huber-Mises屈服准则,把材料塑性变形的影响作为等效荷载处理,从而使推出的基本迭代公式为一常系数线性代数方程组,然后用变步长增量加载和初应力法求解。算例证明该法收敛快、精度高,是一种简便、经济的分析方法。     

地震作用下冷弯薄壁型钢结构房屋弹塑性位移简化计算研究

针对地震作用下冷弯薄壁型钢结构房屋弹塑性位移的简化计算,基于层间剪切模型和冷弯薄壁型钢组合墙体的恢复力模型,对2层~7层冷弯薄壁型钢结构房屋进行弹塑性时程分析。通过对滞回耗能沿楼层高度分布规律的研究,确定了冷弯薄壁型钢结构房屋薄弱楼层的位置;研究了楼层屈服剪力系数、楼层数、结构自振周期和不同地震记录对弹塑性层间位移增大系数的影响;通过大量参数统计分析,提出了冷弯薄壁型钢结构房屋弹塑性层间位移增大系数与楼层屈服剪力系数和楼层数的定量关系,为罕遇地震作用下冷弯薄壁型钢结构房屋弹塑性位移验算提供依据。     

0.01～961.78℃分温区90国际温标的传播不确定度方程

通过直接对内插方程求导,获得了0.01~961.78℃分温区的传播不确定度方程。其灵敏度系数的基本结构与内插方程相同,仍然是组成原内插方程的基础函数的线性组合,但组合系数不同,且仍是一分段函数。     

求解二进制二次规划问题的一种连续化方法

本文提出了一种求解二进制二次规划问题的连续化方法。首先利用NCP函数方法,将二进制变量转化为等价的非光滑方程,再用凝聚函数法对其进行光滑化处理,从而把原来的组合优化问题转化成了一般的可微非线性规划问题。通过对一些标准考题进行计算,表明了该连续化方法的可行性、高效性以及稳定性。     

非黏滞阻尼系统频响函数灵敏度分析的改进计算方法

频响函数灵敏度分析是实现频域梯度优化算法的基础。随着各类高阻尼复合材料的广泛应用,黏性阻尼模型假设已不能准确描述其耗能特性。卷积型非黏滞阻尼模型的阻尼力与质点速度的时间历程相关,能够更准确地描述黏弹性材料的阻尼特性。利用复模态叠加法和直接微分法推导出不考虑高阶模态影响的频响函数灵敏度表达式;基于非黏滞阻尼系统矩阵与模态间的关系,提出适用于非黏滞阻尼系统频响函数灵敏度求解的一阶近似法和二阶近似法;通过数值算例验证了提出方法的有效性和准确性。结果表明,与传统方法相比,该改进的计算方法兼顾了计算精度和效率,为实现具有高阻尼性能复合材料结构的动力分析奠定了基础。     

基于能量平衡的基础隔震结构地震响应预测及优化设计法研究

为了能快速准确地预测基础隔震结构隔震层响应的上限值,针对隔震层设置滞回型阻尼器的基础隔震结构建立地震能量平衡方程,根据等价往复滞回次数下限值经验公式提出考虑等价往复滞回次数降低的地震响应预测法。给出了预测式的推导过程,分析了阻尼量较大时等价往复滞回次数降低的现象,通过非线性时程分析验证了该预测法的准确性。分析了最优总剪力系数设计的剪力降低效果。利用总剪力降低率和位移降低率的线性组合构建优化设计目标函数,在此基础上提出能够考虑剪力和位移不同侧重需求的优化设计法。通过对6层钢框架基础隔震结构进行优化设计和时程分析验算,验证了优化设计法的可行性与高效性。     

平稳随机激励下非黏滞阻尼系统功率谱密度函数的灵敏度分析EI北大核心CSCD

功率谱密度(power spectral density,PSD)函数的灵敏度分析是实现结构系统在随机激励下梯度优化算法的基础。区别于黏性阻尼模型假设阻尼力正比于瞬时速度,非黏滞阻尼模型的阻尼力与质点的时间历程相关,因而能够更准确地描述黏弹性材料的耗能特性。针对卷积型非黏滞阻尼系统PSD函数的灵敏度求解问题,利用虚拟激励法(pseudo-excitation method,PEM)将平稳随机激励下非黏滞阻尼系统的随机响应问题等效转化为确定性的简谐响应问题;利用直接微分法推导出PSD函数的灵敏度表达式;分别引入基于复模态的一阶、二阶近似法和基于实模态的迭代法构建PSD函数的灵敏度算法;通过数值算例比较三种方法的计算精度和效率。结果表明,迭代法更适合大规模非黏滞阻尼系统PSD函数的灵敏度求解。     

Topology optimization of material‐nonlinear continuum structures by the element connectivity parameterization

The application of the element density‐based topology optimization method to nonlinear continuum structures is limited to relatively simple problems such as bilinear elastoplastic material problems. Furthermore, it is very difficult to use analytic sensitivity when a commercial nonlinear finite element code is used. As an alternative to the element density formulation, the element connectivity parameterization (ECP) formulation is developed for the topology optimization of isotropic‐hardening elastoplastic or hyperelastic continua by using commercial software. ECP varies the stiffness of zero‐length linear elastic links that connect design domain‐discretizing finite elements. Unloading was not considered. But the advantages of ECP in material‐nonlinear problems were demonstrated: considerably simple analytic sensitivity calculation using a commercial code and simple link stiffness penalization regardless of nonlinear material behaviour. Copyright © 2006 John Wiley & Sons, Ltd.     

Voigt–Reuss topology optimization for structures with nonlinear material behaviors

This work is directed toward optimizing concept designs of structures featuring inelastic material behaviours by using topology optimization. In the proposed framework, alternative structural designs are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain. Since two or more materials are permitted to simultaneously occupy local regions of the design domain, small-strain integration algorithms for general two-material mixtures of solids are developed for the Voigt (isostrain) and Reuss (isostress) assumptions, and hybrid combinations thereof. Structural topology optimization problems involving non-linear material behaviours are formulated and algorithms for incremental topology design sensitivity analysis (DSA) of energy type functionals are presented. The consistency between the structural topology design formulation and the developed sensitivity analysis algorithms is established on three small structural topology problems separately involving linear elastic materials, elastoplastic materials, and viscoelastic materials. The good performance of the proposed framework is demonstrated by solving two topology optimization problems to maximize the limit strength of elastoplastic structures. It is demonstrated through the second example that structures optimized for maximal strength can be significantly different than those optimized for minimal elastic compliance. © 1997 John Wiley & Sons, Ltd.     

三种非线性梁柱单元的研究及单元开发

罕遇地震作用下混凝土梁柱构件易进入塑性阶段而发生弹塑性损伤,正确地模拟结构进入非线性状态后的力学行为对评价结构的抗震安全性具有重要的意义.通过面向对象语言编制了基于宏观单元的结构弹塑性分析软件平台MESAP,增加了三种非线性梁柱单元:基于刚度法纤维单元、基于柔度法纤维单元及基于柔度法的塑性铰单元.通过算例分析三种非线性...     

Discontinuity in sensitivity of elastoplastic bifurcation loads of finite dimensional symmetric structures

A detailed discussion is presented on discontinuity in elastoplastic bifurcation load factor and its design sensitivity coefficients of symmetric finite dimensional structures subjected to symmetric proportional loads. Due to the discontinuity of the design sensitivity coefficients with respect to the design variables, verification of the analytical design sensitivity coefficients by comparing with the results by a finite difference approach can show only local accuracy of the results which is not sufficient if the method of design sensitivity analysis is applied to optimum design problems. It is shown in the example of a simple column that the approach of tracing the yield points in conjunction with the interpolation technique is shown to be most effective for finding continuously varying bifurcation load factor and the design sensitivity coefficients which are valid in wide range of the design variables.     

Applications of a reduction method for reanalysis to nonlinear dynamic analysis of framed structures

 This paper is concerned with the nonlinear dynamic analysis of framed structures using a reduction method recently proposed by the authors. The reduction method is originally devised for structural static reanalysis and has been applied in optimal design of structures to speed up the design process. For nonlinear dynamic analysis of framed structures, the incremental or iterative equations of motion can be transformed into an algebraic system of equations if appropriate integration methods such as Newmark's method are used to integrate the equations of motion. The resulting algebraic system, referred to as the effective system in this paper, changes during the simulation for a nonlinear dynamic problem. Therefore, from the point of view of solving systems of equations, a nonlinear dynamic problem is very similar to an optimal design problem in that the system of equations changes for both types of problems. Hence, any reanalysis technique can be readily applied to carry out a nonlinear dynamic analysis of structures. As demonstrated from the presented numerical examples, the response obtained by the adopted reduction method is as accurate as that obtained by the Cholesky method, and as estimated from the operation counts involved in the method, it is more efficient than the Cholesky method when the half-band width is greater than about 50. Received 23 March 2000     

Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling

Design of reinforced concrete structures is governed by the nonlinear behavior of concrete and by its different strengths in tension and compression. The purpose of this article is to present a computational procedure for optimal conceptual design of reinforced concrete structures on the basis of topology optimization with elastoplastic material modeling. Concrete and steel are both considered as elastoplastic materials, including the appropriate yield criteria and post‐yielding response. The same approach can be applied also for topology optimization of other material compositions where nonlinear response must be considered. Optimized distribution of materials is achieved by introducing interpolation rules for both elastic and plastic material properties. Several numerical examples illustrate the capability and potential of the proposed procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of the stressed state of a circular thin-walled cylinder under complex loading and with nonlinear hardening of the material

The generalized differential equations of plastic flow for a material with nonlinear hardening are derived using the Prager kinematic model. An example of numerical analysis for stress variation under elastoplastic deformation of a thin-walled cylinder of a structural carbon steel is given for different elastoplastic material models. Translated from Problemy Prochnosti, No. 3, pp. 58–65, May–June, 2009.     

Elastoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models

The paper presents results on the elastoplastic analysis of compact and thin-walled structures via refined beam models. The application of Carrera Unified Formulation (CUF) to perform elastoplastic analysis of isotropic beam structures is discussed. Particular attention is paid to the evaluation of local effects and cross-sectional distortions. CUF allows formulation of the kinematics of a one-dimensional (1D) structure by employing a generalized expansion of primary variables by arbitrary cross-section functions. Two types of cross-section expansion functions, TE (Taylor expansion) and LE (Lagrange expansion), are used to model the structure. The isotropically work-hardening von Mises constitutive model is incorporated to account for material nonlinearity. A Newton–Raphson iteration scheme is used to solve the system of nonlinear algebraic equations. Numerical results for compact and thin-walled beam members in plastic regime are presented with displacement profiles and beam deformed configurations along with stress contour plots. The results are compared against classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory, reference solutions from literature, and three-dimensional (3D) solid finite element models. The results highlight: (1) the capability of the present refined beam models to describe the elastoplastic behavior of compact and thin-walled structures with 3D-like accuracy; (2) that local effects and severe cross-sectional distortions can be detected; (3) the computational cost of the present modeling approach is significantly lower than shell and solid model ones.     

基于参数二次规划与精细积分方法的动力弹塑性问题分析

给出了将参数二次规划方法与精细积分方法相结合进行结构弹塑性动力响应分析的一条新途径。基于参变量变分原理与有限元参数二次规划方法建立了动力弹塑性问题的求解方程,方法对于关联与非关联问题的求解在算法上是完全一致的。对于动力非线性方程求解则进一步采用了被线性问题分析所广泛采用的精细积分方法,推导了方法在动力弹塑性问题求解上的算法列式。所给出的数值算例在验证本文理论与算法的同时,进一步证实了精细积分方法在动力学分析中所具有的各种良好性态。