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A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

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Acta Mechanica Sinica 2016年第5期32卷 941-958页

作者： Zheng Lv zhiping qiu Institute of Solid Mechanics Beihang University

In this paper, a direct probabilistic approach（DPA） is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random *** proposed method has the advantage of obtaining the response＇s moments directly from the initial conditions and statistical characteristics of the corresponding external excitations. First, the response＇s moment equations are directly derived based on a DPA, which is completely independent of the It？/filtering approach since no specific assumptions regarding the correlation structure of excitation are *** solving them under Gaussian closure, the response＇s moments can be obtained. Subsequently, a multiscale algorithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo（MC） simulation gives good ***, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.

关键词： Direct probabilistic approach Nonlinear dynamic system Nonstationary random process Response’s moments Multiscale algorithm

Modified perturbation method for eigenvalues of structure with interval parameters

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Science China(Physics,Mechanics & Astronomy) 2015年第1期58卷 75-83页

作者： WANG Chong qiu zhiping Institute of Solid Mechanics Beihang University

In overcoming the drawbacks of traditional interval perturbation method due to the unpredictable effect of ignoring higher order terms,a modified parameter perturbation method is presented to predict the eigenvalue intervals of the uncertain structures with interval *** the proposed method,interval variables are used to quantitatively describe all the uncertain *** order perturbations in both eigenvalues and eigenvectors are fully *** retaining higher order terms,the original dynamic eigenvalue equations are transformed into interval linear equations based on the orthogonality and regularization conditions of *** eigenvalue ranges and corresponding eigenvectors can be approximately predicted by the parameter combinatorial *** with the Monte Carlo method,two numerical examples are given to demonstrate the accuracy and efficiency of the proposed algorithm to solve both the real eigenvalue problem and complex eigenvalue problem.

关键词： interval perturbation method uncertain parameters higher order terms eigenvalue parameter combinatorial ap-proach

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

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Acta Mechanica Sinica 2006年第3期22卷 265-276页

作者： zhiping qiu Xiaojun Wang Institute of Solid Mechanics Beijing University of Aeronautics and Astronautics Beijing 100083 China

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

关键词： Impulsive response Interval analysis method Convex model Uncertain-but-bounded impulse

A direct-variance-analysis method for generalized stochastic eigenvalue problem based on matrix perturbation theory

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Science China(Technological Sciences) 2014年第6期57卷 1238-1248页

作者： qiu zhiping qiu HeChen Institute of Solid Mechanics Beihang University

It has been extensively recognized that the engineering structures are becoming increasingly precise and complex,which makes the requirements of design and analysis more and more *** the uncertainty effects are indispensable during the process of product ***,iterative calculations,which are usually unaffordable in calculative efforts,are unavoidable if we want to achieve the best *** uncertainty effects into consideration,matrix perturbation methodpermits quick sensitivity analysis and structural dynamic re-analysis,it can also overcome the difficulties in computational *** to the situations above,matrix perturbation method has been investigated by researchers worldwide ***,in the existing matrix perturbation methods,correlation coefficient matrix of random structural parameters,which is barely achievable in engineering practice,has to be given or to be assumed during the computational *** has become the bottleneck of application for matrix perturbation *** this paper,we aim to develop an executable approach,which contributes to the application of matrix perturbation *** the present research,the first-order perturbation of structural vibration eigenvalues and eigenvectors is derived on the basis of the matrix perturbation theory when structural parameters such as stiffness and mass have *** the first-order perturbation of structural vibration eigenvalues and eigenvectors with the probability theory,the variance of structural random eigenvalue is derived from the perturbation of stiffness matrix,the perturbation of mass matrix and the eigenvector of baseline-structure *** the Direct-VarianceAnalysis(DVA)method is developed to assess the variation range of the structural random eigenvalues without correlation coefficient matrix being *** feasibility of the DVA method is verified with two numerical examples(one is trusssystem and the other is wing struct

关键词： matrix perturbation theory generalized stochastic eigenvalue problem structure with random parameter direct variance analysis

Parameter vertex method and its parallel solution for evaluating the dynamic response bounds of structures with interval parameters

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Science China(Physics,Mechanics & Astronomy) 2018年第6期61卷 62-74页

作者： zhiping qiu PengBo Wang Institute of Solid Mechanics Beihang University Beijing 100191 China

In this article, we propose a parameter vertex method to determine the upper and lower bounds of the dynamic response of structures with interval parameters, which can be regarded as an extension of the matrix vertex method proposed by qiu and Wang. The matrix vertex method requires considerable computation time and encounters the dependency problem in practice,thereby limiting its application in engineering. The proposed parameter vertex method can avoid the dependency problem, and the number of possible vertex combinations in the proposed method is significantly less than that in the matrix vertex *** parameter vertex method requires that each matrix element in the dynamic differential equation is monotonic with respect to the uncertain parameter, and that the dynamic response reaches its extreme value when the uncertain parameter is at its *** further reduce the runtime, both vertical and transversal parallel algorithms are introduced and integrated into the parameter vertex method to improve its computational efficiency. Two numerical examples are presented to demonstrate the proposed method combined with both parallel algorithms. The performances of the two parallel algorithms are thoroughly studied. The parameter vertex method combined with parallel algorithm can be used for large-scale computing.

关键词： parameter vertex method dynamic response interval parameter parallel algorithm upper and lower bounds

Transient aeroelastic responses and flutter analysis of a variable-span wing during the morphing process

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Chinese Journal of Aeronautics 2013年第6期26卷 1430-1438页

作者： Huang Ren qiu zhiping Institute of Solid Mechanics Beihang University

To investigate the transient aeroelastic responses and flutter characteristics of a variablespan wing during the morphing process,a novel frst-order state-space aeroelastic model is *** time-varying structural model of the morphing wing is established based on the Euler-Bernoulli beam theory with time-dependent boundary conditions.A nondimensionalization method is used to translate the time-dependent boundary conditions to be *** time-domain aerodynamic forces are calculated by the reduced-order unsteady vortex lattice *** morphing parameters,i.e.,wing span length and morphing speed,are of particular interest for understanding the fundamental aeroelastic behavior of variable-span wings.A test case is proposed and numerical results indicate that the flutter characteristics are sensitive to both of the two morphing *** could be noticed that the aeroelastic characteristics during the wing extracting process are more serious than those during the extending process at the same morphing speed by transient aeroelastic response *** addition,a faster morphing process can get better aeroelastic performance while the mechanism comlexity will arise.

关键词： Galerkin methods Morphing aircraft Time-varying systems Transient aeroelastic Unsteady vortex lattice method Variable-span wing

The need for introduction of non-probabilistic interval conceptions into structural analysis and design

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Science China(Physics,Mechanics & Astronomy) 2016年第11期59卷 90-92页

作者： zhiping qiu Lei Wang Institute of Solid Mechanics Beihang University

With the growing complexity of engineering structures and the severity of their service environments,the uncertainties related to material properties,external loads,boundary conditions,measurement noises,etc.,have *** greatly influences structural safety,and hence,it is necessary to completely understand all the uncertainties involved when tackling analysis and design issues[1].

关键词：设计问题结构分析概率区间不确定性分析工程结构材料性能边界条件测量噪声

A symplectic finite element method based on Galerkin discretization for solving linear systems

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Applied Mathematics and Mechanics(English Edition) 2023年第8期44卷 1305-1316页

作者： zhiping qiu Zhao WANG Bo ZHU Institute of Solid Mechanics School of Aeronautic Science and EngineeringBeihang UniversityBeijing 100083China

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic *** the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy ***,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be *** single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian ***,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference *** the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta *** results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

关键词： Galerkin finite element method linear system structural dynamic response symplectic difference scheme

Interval analysis of transient temperature field with uncertain-but-bounded parameters

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Science China(Physics,Mechanics & Astronomy) 2014年第10期57卷 1959-1966页

作者： WANG Chong qiu zhiping Institute of Solid Mechanics Beihang University

Based on the traditional finite volume method, a new numerical technique is presented for the transient temperature field prediction with interval uncertainties in both the physical parameters and initial/boundary conditions. New stability theory applicable to interval discrete schemes is developed. Interval ranges of the uncertain temperature field can be approximately yielded by two kinds of parameter perturbation methods. Different order Neumann series are adopted to approximate the interval matrix inverse. By comparing the results with traditional Monte Carlo simulation, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed model and methods.

关键词： finite volume method temperature field prediction interval uncertainties stability theory parameter perturbationmethod