Response of Systems with Uncertain Parameters to Stochastic Excitation

Jensen, Héctor A.; Iwan, W. D.

doi:10.1061/(asce)0733-9399(1992)118:5(1012)

Cited by 111 publications

(38 citation statements)

References 9 publications

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“…These methods have been naturally extended to assess the reliability of structures involving random parameters. For instance, in Reference [11] the reliability is assessed by the level crossing theory after the statistical quantities have been gained by the orthogonal polynomial expansion method. The similar methodology, to directly employ the level crossing theory after gaining the statistical quantities with the random perturbation, is widely used as well, say, in References [12,13].…”

Section: Introductionmentioning

confidence: 99%

Dynamic response and reliability analysis of structures with uncertain parameters

Chen

2004

Numerical Meth Engineering

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SUMMARYAn original approach for dynamic response and reliability analysis of stochastic structures is proposed. The probability density evolution equation is established which implies that incremental rate of the probability density function is related to the structural response velocity. Therefore, the response analysis of stochastic structures becomes an initial-value partial differential equation problem. For the dynamic reliability problem, the solution can be derived through solving the probability density evolution equation with an initial value condition and an absorbing boundary condition corresponding to specified failure criterion. The numerical algorithm for the proposed method is suggested by combining the precise time integration method and the finite difference method with TVD scheme. To verify and validate the proposed method, a SDOF system and an 8-storey frame with random parameters are investigated in detail. In the SDOF system, the response obtained by the proposed method is compared with the counterparts by the exact solution. The responses and the reliabilities of a frame with random stiffness, subject to deterministic excitation or random excitation, are evaluated by the proposed method as well. The mean, the standard deviation and the reliabilities are compared, respectively, with the Monte Carlo simulation. The numerical examples verify that the proposed method is of high accuracy and efficiency. Moreover, it is found that the probability transition of structural responses is like water flowing in a river with many whirlpools, showing complexity of probability transition process of the stochastic dynamic responses.

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Section: Introductionmentioning

confidence: 99%

Dynamic response and reliability analysis of structures with uncertain parameters

Chen

2004

Numerical Meth Engineering

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“…During the last decades, the engineering community acknowledged the importance of uncertainties on the performance of structures and engineering systems in general (Jensen and Iwan, 1992;Bulleit, 2008). Uncertainty quantification provides metrics to study the relationship between imprecisely prescribed model inputs and the model's predictions (Papadrakakis et al, 2005).…”

Section: Modeling Of Uncertaintiesmentioning

confidence: 99%

Computational Structural Engineering: Past Achievements and Future Challenges

Plevris

Tsiatas

2018

Front. Built Environ.

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PAST ACHIEVEMENTS AND CURRENT TRENDSComputational methods are computer-based methods used to numerically solve mathematical models that describe physical phenomena. The purpose of computational modeling is to study the behavior of complex systems by means of computer simulations and it can be used to make predictions of the system's behavior under different conditions, often for cases in which intuitive analytical solutions are not available (Nature, 2018). Computational methods have emerged in engineering during the 1960s. Since then, structural engineers have been leaders in technological solutions to engineering analysis and design problems. The evolution of electronic computers together with the tremendous increase of computational power has triggered the continuous development of computational methods. Rapid advances in computer hardware have had a profound effect on various engineering disciplines. The applications are numerous and cover a broad field of engineering branches including civil, mechanical, naval, electrical, aerospace, material, biomolecular, among others. Computational structural engineering has evolved as an insightful blend combining both structural analysis and computer science.Among all computational methods, the Finite Element Method (FEM) and the Boundary Element Method (BEM) are the most prevalent ones. Both methods exhibit unique characteristics as well as advantages and disadvantages. The FEM, as a simulation tool, enables sophisticated methods of computational mechanics, computer technology and applied mathematics. It has been broadly adopted in scientific research and engineering applications and it can be considered as the most popular method used for structural analysis, tackling linear and nonlinear problems of systems with various geometries, material properties and loads (Reddy, 2005). In FEM, the solution domain is subdivided into a finite number of elements. Each element approximately reproduces the behavior of a small region of the body it represents, but continuity between the elements is only enforced in an overall minimum energy sense. The FEM is especially suitable for problems with complex geometries, but the whole-body discretization scheme that is utilized inevitably leads to a large number of finite elements and, thus, increased computational cost. Although Professor R. Clough coined the term "Finite Element Method" in his pioneer work dated back in 1960 (Clough, 1960), the answer to the question "who invented FEM in everyday use?" is possibly M. Jonathan (Jon) Turner at Boeing who generalized and perfected the Direct Stiffness Method, and convinced his company to commit resources to it, over the period 1952 -1964(Felippa, 2017. The FEM obtained its real impetus in the 1960s and 1970s by the developments of pioneers J. H. Argyris, R. W. Clough, H. C. Martin, O. C. Zienkiewicz and their co-workers who evolved the method and applied it to a wide range of structural problems and applications.In the years since its first use, FEM has grown and developed into a standard...

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“…The reliability sensitivity curves with the forcing frequency (Ω) are depicted in Figs. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In order to find the variation of reliability sensitivity, in figures there are some key points in x direction (Ω), those are (1-γ) u ωx , u ωx , (1＋γ) u ωx , (1-γ) u ωy , u ωy and (1+γ) u ωy .…”

Section: Numerical Examplementioning

confidence: 99%

“…One is failure research on the basis of the responses (displacement, stress, etc.) of system [7][8][9][10][11][12][13][14]. The other is failure research on the basis of the relation between natural frequency and forcing frequency of general systems at resonance and non-resonance [15,16].…”

Section: Introductionmentioning

confidence: 99%

Vibration reliability sensitivity analysis of general system with correlation failure modes

Zhang

Zhao

2011

J Mech Sci Technol

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The vibration problem of the general system is the main object of research. The material properties and geometry of general system are random parameters because of the manufacturing environment, technical conditions, manufacturing and installation errors, multiphase materials, features and other factors. According to the relation criterion that the difference between the natural frequency and the driving frequency of general systems is not beyond a specific value, the vibration reliability mode and vibration reliability of general systems are defined considering the correlation of the multi-order natural frequency and the random characteristics of structure size and material, and the vibration reliability analysis method for avoiding the resonant is carried out. The second-order joint failure probability is obtained by using the numerical integration method. Based on the reliability design theory and sensitivity analysis method, the vibration reliability sensitivity of the general system with correlation failure modes is extensively discussed and a numerical method for vibration reliability sensitivity design is presented. The variation regularities of vibration reliability sensitivity are obtained and the effects of random parameters on vibration reliability of the general system are studied. The presented method provided the theoretic basis for the reliability design of the general system. A numerical example demonstrated that the proposed method is effective.

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Response of Systems with Uncertain Parameters to Stochastic Excitation

Cited by 111 publications

References 9 publications

Dynamic response and reliability analysis of structures with uncertain parameters

Dynamic response and reliability analysis of structures with uncertain parameters

Computational Structural Engineering: Past Achievements and Future Challenges

Vibration reliability sensitivity analysis of general system with correlation failure modes

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