区间桁架结构有限元分析的区间因子法

研究了具有区间参数的桁架结构在区间力作用下的有限元分析方法。利用区间因子法,桁架结构材料物理参数、几何尺寸和外荷载均可表达为其区间因子和其确定性量的乘积,进而结构的位移和应力响应也可表达成区间因子们的函数。利用区间算法,推导出了结构位移和应力响应的上、下限和均值的计算表达式。通过算例,分析了结构参数和外荷载的不确定性对结构响应的影响,并验证了模型和方法的合理性与可行性。该方法的优点是能够反映结构某一参数的不确定性对结构响应的影响。     

Interval spectral stochastic finite element analysis of structures with aggregation of random field and bounded parameters

This paper presents the study on non‐deterministic problems of structures with a mixture of random field and interval material properties under uncertain‐but‐bounded forces. Probabilistic framework is extended to handle the mixed uncertainties from structural parameters and loads by incorporating interval algorithms into spectral stochastic finite element method. Random interval formulations are developed based on K–L expansion and polynomial chaos accommodating the random field Young's modulus, interval Poisson's ratios and bounded applied forces. Numerical characteristics including mean value and standard deviation of the interval random structural responses are consequently obtained as intervals rather than deterministic values. The randomised low‐discrepancy sequences initialized particles and high‐order nonlinear inertia weight with multi‐dimensional parameters are employed to determine the change ranges of statistical moments of the random interval structural responses. The bounded probability density and cumulative distribution of the interval random response are then visualised. The feasibility, efficiency and usefulness of the proposed interval spectral stochastic finite element method are illustrated by three numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

不均匀随机参数桁架结构的随机反应分析

以随机荷载作用下的不均匀随机参数桁架结构为研究对象,提出了求解结构反应数字特征的矩法。从结构有限元方程出发,推导出结构刚度矩阵对各单元的弹性模量、横截面积以及各节点坐标的导数,进一步导得结构位移反应对各随机参数的敏度。利用随机变量函数的矩法,导出了结构位移反应的均值和方差,依据单元位移应力的转换表达式,分析了应力反应的均值和方差。算例表明,结构反应的方差取决于各随机参数的分散性和参数间的相关性。     

Non-Deterministic Structural Response and Reliability Analysis Using a Hybrid Perturbation-Based Stochastic Finite Element and Quasi-Monte Carlo Method

The random interval response and probabilistic interval reliability of structures with a mixture of random and interval properties are studied in this paper. Structural stiffness matrix is a random interval matrix if some structural parameters and loads are modeled as random variables and the others are considered as interval variables. The perturbation-based stochastic finite element method and random interval moment method are employed to develop the expressions for the mean value and standard deviation of random interval structural displacement and stress responses. The lower bound and upper bound of the mean value and standard deviation of random interval structural responses are then determined by the quasi-Monte Carlo method. The structural reliability is not a deterministic value but an interval as the structural stress responses are random interval variables. Using a combination of the first order reliability method and interval approach, the lower and upper bounds of reliability for structural elements, series, parallel, parallel-series and series-parallel systems are investigated. Three numerical examples are used to demonstrate the effectiveness and efficiency of the proposed method.     

Interval static displacement analysis for structures with interval parameters

In this paper, a new method to solve the uncertain static displacement problem of structures with interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even if an optimum scheme is adopted when there are many uncertain parameters. With the interval mathematics, the interval finite element equation is developed. Based on the perturbation and the interval extension, the upper and lower bounds of the static displacements are obtained, in which the sharp bounds are guaranteed by the interval calculation operators. Two numerical examples, a box cantilever beam and an automobile frame, are given to illustrate the validity of the present method. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparison of static response of structures using convex models and interval analysis method

In this paper, by combining the finite element analysis and non‐probabilistic convex models, we present the numerical algorithm of non‐probabilistic convex models and interval analysis method for the static displacement of structures with uncertain‐but‐bounded parameters. Under the condition of the box or interval vector determined from the ellipsoid of the uncertain‐but‐bounded structural parameter vector, by comparing the numerical algorithm of non‐probabilistic convex models and the interval analysis method in the mathematical proof and the numerical example, we can see that the width of the maximum or upper and minimum or lower bounds on the static displacement yielded by the numerical algorithm of non‐probabilistic convex models is tighter than those produced by the interval analysis method. Copyright © 2003 John Wiley & Sons, Ltd.     

随机-区间型天线结构有限元及可靠性分析

构建了对随机-区间混合型天线结构的有限元及可靠性分析模型,提出了一种新的处理不确定性因素的结构有限元分析方法,给出了结构保精度和保强度两工况的概率描述。同时考虑了结构的物理参数、几何参数的随机性和作用风载荷的区间性。首先将随机变量固定,利用区间因子法求得结构位移和应力响应的区间范围,然后在区间内任意点处利用随机因子法求结构响应的随机分布范围。构造了天线反射面位移响应和结构单元应力响应不确定变量的数字特征计算公式,进而得到结构各响应量的可靠性指标。对一8m口径天线结构进行了分析,分析结果表明文中所提方法具有合理性和可行性。     

Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials

An extended multiscale finite element method is developed for small-deformation elasto-plastic analysis of periodic truss materials. The base functions constructed numerically are employed to establish the relationship between the macroscopic displacement and the microscopic stress and strain. The unbalanced nodal forces in the micro-scale of unit cells are treated as the combined effects of macroscopic equivalent forces and microscopic perturbed forces, in which macroscopic equivalent forces are used to solve the macroscopic displacement field and microscopic perturbed forces are used to obtain the stress and strain in the micro-scale to make sure the correctness of the results obtained by the downscale computation in the elastic-plastic problems. Numerical examples are carried out and the results verify the validity and efficiency of the developed method by comparing it with the conventional finite element method.     

A Hybrid Method for Structural System Reliability‐Based Design Optimization and its Application to Trusses

Most research studies on structural optimum design have focused on single‐objective optimization of deterministic structures, while little study has been carried out to address multi‐objective optimization of random structures. Statistical parameters and redundancy allocation problems should be considered in structural optimization. In order to address these problems, this paper presents a hybrid method for structural system reliability‐based design optimization (SRBDO) and applies it to trusses. The hybrid method integrates the concepts of the finite element method, radial basis function (RBF) neural networks, and genetic algorithms. The finite element method was used to compute structural responses under random loads. The RBF neural networks were employed to approximate structural responses for the purpose of replacing the structural limit state functions. The system reliabilities were calculated by Monte Carlo simulation method together with the trained RBF neural networks. The optimal parameters were obtained by genetic algorithms, where the system reliabilities were converted into penalty functions in order to address the constrained optimization. The hybrid method applied to trusses was demonstrated by two examples which were a typical 10‐bar truss and a steel truss girder structure. Detailed discussions and parameter analysis for the failure sequences such as web‐bucking failure and beam‐bending failure in the SRBDO were given. This hybrid method provides a new idea for SRBDO of trusses. Copyright © 2015 John Wiley & Sons, Ltd.     

一种基于静力位移测量值的车辐式屋盖结构索力识别方法

该文从车辐式张拉屋盖结构的组成特点出发,提出了一种基于静力位移测量值的索力识别方法。首先通过测量屋盖结构的几何位形,建立有限元模型。然后给真实结构施加特定荷载并测量加载点位移。给有限元模型施加同样的荷载并计算其位移。通过比较计算和实测的位移值,修正并迭代有限元模型中拉索的预应力;当计算位移与实测位移一致时就获得了拉索的真实内力。该方法只需要测量加载的自由度所对应的位移,能够在通用有限元软件ANSYS上进行索力识别,计算结果准确。     

随机参数智能桁架结构振动控制中主动杆的优化配置

该文研究压电智能桁架结构振动主动控制中结构物理参数，作用荷载和控制力同时具有随机性时，压电主动杆的最优配置和增益优化问题，采用智能结构的状态空间模型建立了以最大耗散能准则来基础的目标函数，建立了具有动应力，动位移可靠约束的主动杆的优化配置和增益优化模型，对结构动力响应的数字特征进行了推导，并通过一智能桁架结构的优化配置计算，说明该优化配置模型的合理性和有效性。     

结构静力分析的区间摄动有限元法

基于新的区间参数系统响应界值的评估方法,推导了基于Taylor展开的区间摄动有限元法和区间参数摄动有限元法的高阶求解方法。并提出了一种新的区间摄动有限元法,该方法将刚度矩阵的逆矩阵用一系列Neumann展开级数来表示,最终得到结构响应摄动量的上下界限,是对结构响应鲁棒性的一种直接评估,因此称之为区间鲁棒摄动有限元法。比较了三种区间摄动有限元法的计算精度和计算效率。算例结果表明:区间鲁棒摄动有限元法具有较好的精度,能够适用于大型航空航天结构的不确定分析和优化。     

风荷激励下天线结构的随机振动分析

研究随机天线结构的风激随机振动响应问题。考虑天线结构物理参数、几何尺寸和结构阻尼的随机性,在基于随机因子法对结构进行动力特性分析的基础上,从结构风激随机振动响应在频域上的表达式出发,利用求解随机变量函数矩的方法和求解随机变量数字特征的代数综合法,导出了随机天线结构在风荷激励下位移响应均方值和应力响应均方值的均值、方差和变异系数的计算表达式。以8米口径天线为例,分析了结构物理参数、几何尺寸和阻尼的随机性对天线结构风激位移响应均方值和应力响应均方值随机性的影响。     

基于ANSYS的离心复合校准装置桁架结构分析

在离心复合校准装置极限载荷工况下,为确定桁架强度满足离心复合校准应用需求,对桁架结构进行有限元分析和试验验证。利用ANSYS有限元分析软件,设计仿真过程,完成对该种离心转臂式桁架结构,从结构组成、模型建立、网格划分、载荷约束设置等程序描述整个分析过程。通过分析结果云图,确定桁架受力结果符合机械结构要求。经线加速度计校准试验测试对结构分析结果进行验证,结果表明：桁架的结构强度满足使用要求,变形量与实测值接近,结构分析结果与实际应用测试值相符合,分析结果可靠。此桁架分析过程和验证方式可为类似桁架分析提供参考。     

非线性间隙杆单元的特性及其迭代算法

螺栓与栓孔之间间隙引起的非弹性变形是栓接结构产生挠度的一个重要原因.该文根据有限元的基本方法,建立了有间隙拉压杆单元,能够模拟有间隙栓接结构的力学行为,并准确计算出连接节点处间隙引起的结构的非弹性变形,并针对间隙单元的特点提出了基于剩余荷载系数增量理论的迭代求解方法.该文提出的计算方法为贵州省正安县桑坝大桥施工过程中拱...     

压电主动杆位置和增益在随机智能桁架结构振动控制中的优化

对结构物理参数、几何尺寸、作用荷载和控制力同时具有随机性时 ,随机压电智能桁架结构中主动杆的配置位置和闭环控制系统增益进行了优化 ,基于系统最小储存能 ,构建了具有动应力、动位移可靠性约束的主动杆配置和控制增益的优化模型 ;并对结构动力响应的数字特征进行了推导。通过算例 ,验证了该优化配置模型的合理性和有效性 ,获得了若干有意义的结论。     

Fixed-point iteration to nonlinear finite element analysis. Part II: Formulation and implementation

The finite element formulation and implementation of the Fixed-Point Iteration (FPI) to linear/nonlinear structural static or dynamic analysis are developed. The direct and tangent formulations are presented and compared with the Newton–Raphson method (NRM). ‘Modified’ FPI algorithms have also been derived. A graphical interpretation of the method is introduced and suggested to call the FPI ‘the Saw method’. Mixing both the FPI and NRM is shown to be possible and may be useful in some applications. The overall strategies, iterative algorithms, and the appropriate norm convergence criteria necessary to implant the FPI into existing finite element programs are also included in the development. The superiority of the FPI over the NRM as seen from the development and the formulation lies in three major factors. First, the existing assembly process of element matrices is eliminated completely from the nonlinear finite element analysis. Secondly, the Gauss elimination or Crout's method is also eliminated. In the finite element terminology, this means that nonlinear structural static or dynamic responses can he obtained without recourse to the inverse of the structural stiffness matrix. Thirdly, the FPI can also be applied equally to linear structural analysis. Hence, the assembly process and the programming and storage associated with it can be removed from the existing finite element programs. While the FPI can solve problems that the NRM can, it will also be able to handle some engineering problems where the latter cannot. Buckling problems and problems where the force–displacement curve changes curvature are examples where the FPI is expected to be efficient.     

Quantum-Inspired Evolutionary Algorithm for Topology Optimization of Modular Cabled-Trusses

This article proposes an alternative optimization framework applied to topology optimization of modular lightweight cabled-truss structures. These structures are described as a system of intrinsically positioned cables and triangular bar formations jointed at their ends by hinged connections to form a rigid framework. The optimized topologies are determined through a stochastic discrete optimization procedure that uses ground structure approach, nonlinear finite element analysis, and quantum-inspired evolutionary algorithms. The optimization searches for optimal mass reduction with minimal losses in stiffness, such relation, is expressed by the stiffness-to-mass ratio parameter. Nonlinear finite element analysis is used to evaluate the static structural response. In order to decrease computation time, kinematically instable and structurally invalid individuals are filtered before evaluation. Modular design approach is taken into consideration to reduce the number of design variables and increase the productibility of cabled-trusses. Symmetric structural response is desired since in several mechanical applications forces can assume different directions during the working cycle. A modular ground structure with 300 elements is optimized, and optimal truss and cabled-truss topologies are compared. Complementary analyses comprise the investigation of the structural performance under different number of modules and slenderness ratios. The results indicate that the proposed optimization framework leads to optimized structures. In addition, it was observed that cabled trusses presented significant improvements in structural performance when compared with trusses.     

Uncertain static plane stress analysis with interval fields

Uncertain static plane stress analysis of continuous structure involving interval fields is investigated in this study. Unlike traditional interval analysis of discrete structure, the interval field is adopted to model the uncertainty, as well as the dependency between the physical locations and degrees of variability, of all interval system parameters presented in the continuous structures. By implementing the flexibility properties of some common structural elements, a new computational scheme is proposed to reformulate the uncertain static plane stress analysis with interval fields into standard mathematical programming problems. Consequently, feasible upper and lower bounds of structural responses can be effectively yet efficiently determined. In addition, the proposed method is adequate to deal with situations involving one‐dimensional and two‐dimensional interval fields, which enhances the pertinence of the proposed approach by incorporating both discrete and continuous structures. In addition, the proposed computational scheme is able to establish the realizations of the uncertain parameters causing the extreme structural responses at zero computational cost. The applicability and credibility of the established computational framework are rigorously justified by various numerical investigations. Copyright © 2016 John Wiley & Sons, Ltd.