Dynamic response sensitivity of inelastic structures

Zhang, Yan; Kiureghian, Armen Der

doi:10.1016/0045-7825(93)90151-m

Cited by 144 publications

(61 citation statements)

References 15 publications

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“…The reliability of nonlinear problems involving a large number of random variables can be solved efficiently by either first-or second-order reliability methods combined with the direct differentiation method for the evaluation of the derivatives (see [18], [19]) or by selected simulation approaches, including subset simulation [8], spherical subset simulation [20] and recently the asymptotic sampling method [21]. First/second order reliability methods using direct differentiation require alterations at the FE code level, while simulation approaches may be easily coupled with a "black-box" FE code.…”

Section: Reliability Analysis In High Dimensionsmentioning

confidence: 99%

Reliability updating in geotechnical engineering including spatial variability of soil

Papaioannou

Straub

2012

Computers and Geotechnics

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At geotechnical sites, deformation measurements are routinely performed during the construction process. In this paper, it is shown how information from such measurements can be utilized to update the reliability estimate of the geotechnical site at future construction stages. A recently proposed method for Bayesian updating of the reliability is successfully applied in conjunction with a stochastic nonlinear geotechnical finite element model. Therein, uncertainty in the soil material properties is modelled by non-Gaussian random fields. The structural reliability evaluations required for the Bayesian updating are carried out by means of subset simulation, an efficient adaptive Monte Carlo method. The approach is demonstrated through an application to a sheet pile wall at a deformation-sensitive geotechnical construction site.

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Section: Reliability Analysis In High Dimensionsmentioning

confidence: 99%

Reliability updating in geotechnical engineering including spatial variability of soil

Papaioannou

Straub

2012

Computers and Geotechnics

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“…At each time step, after convergence of the incrementaliterative response computation, the consistent response sensitivities are calculated. According to the Direct Differentiation Method (DDM) (see [3][4][5][6][7][8]), this requires the analytical differentiation of the finite element numerical scheme for response computation with respect to the sensitivity parameter θ in order to obtain the "exact" or "consistent" sensitivities of the computationally simulated system response. After spatial discretization using the finite element method, the equations of motion of a structural system, accounting for both material and geometric nonlinearities, take the form of the following nonlinear matrix differential equation:…”

Section: Finite Element Response Sensitivity Analysismentioning

confidence: 99%

“…Then, we differentiate Equation (4) with respect to θ using the chain rule of differentiation and recognizing that (i.e., the structure inelastic resisting force vector depends on θ both implicitly, through , and explicitly), which yields the following response sensitivity equation at the structure level (see [3][4][5]): …”

Section: Finite Element Response Sensitivity Analysismentioning

confidence: 99%

“…This formulation represents a general class of one-step implicit integration algorithms, containing the well-known Newmark-β and Wilson methods (see [3][4][5][6][7][8]). In the case of the Newmark-β method [24], the integration coefficients are given by:…”

Section: Finite Element Response Sensitivity Analysismentioning

confidence: 99%

“…Finite element response sensitivities are also invaluable for gaining deeper insight into the effects and relative importance of the various geometric, material, and loading parameters defining the structure and its loading environment. Sensitivity analysis formulations have been developed for displacement-based finite element models [3][4][5] and, recently, for force-based frame elements [6,7]. The advantages gained in response analysis by using finite element formulations more advanced than the classical displacement-based formulation can be further extended to the realm of response sensitivity analysis [8].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite element response sensitivity analysis using three‐field mixed formulation: general theory and application to frame structures

Barbato

Zona

Conte

2006

Numerical Meth Engineering

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SUMMARYThis paper presents a method to compute response sensitivities of finite element models of structures based on a three-field mixed formulation. The methodology is based on the Direct Differentiation Method (DDM), and produces the response sensitivities consistent with the numerical finite element response. The general formulation is specialized to frame finite elements and details related to a newly developed steelconcrete composite frame element are provided. DDM sensitivity results are validated through the forward Finite Difference Method (FDM) using a finite element model of a realistic steel-concrete composite frame subjected to quasi-static and dynamic loading. The finite element model of the structure considered is constructed using both monolithic frame elements and composite frame elements with deformable shear connection based on the three-field mixed formulation. The addition of the analytical sensitivity computation algorithm presented in this paper extends the use of finite elements based on a three-field mixed formulation to applications that require finite element response sensitivities. Such applications include structural reliability analysis, structural optimization, structural identification, and finite element model updating.KEY WORDS: Hu-Washizu functional; three-field mixed finite element formulation; material constitutive parameters; finite element response sensitivity; steel-concrete composite beam.

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Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method

Ebrahimian

Astroza

Conte

2015

Earthq Engng Struct Dyn

108

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Summary This paper presents a novel nonlinear finite element (FE) model updating framework, in which advanced nonlinear structural FE modeling and analysis techniques are used jointly with the extended Kalman filter (EKF) to estimate time‐invariant parameters associated to the nonlinear material constitutive models used in the FE model of the structural system of interest. The EKF as a parameter estimation tool requires the computation of structural FE response sensitivities (total partial derivatives) with respect to the material parameters to be estimated. Employing the direct differentiation method, which is a well‐established procedure for FE response sensitivity analysis, facilitates the application of the EKF in the parameter estimation problem. To verify the proposed nonlinear FE model updating framework, two proof‐of‐concept examples are presented. For each example, the FE‐simulated response of a realistic prototype structure to a set of earthquake ground motions of varying intensity is polluted with artificial measurement noise and used as structural response measurement to estimate the assumed unknown material parameters using the proposed nonlinear FE model updating framework. The first example consists of a cantilever steel bridge column with three unknown material parameters, while a three‐story three‐bay moment resisting steel frame with six unknown material parameters is used as second example. Both examples demonstrate the excellent performance of the proposed parameter estimation framework even in the presence of high measurement noise. Copyright © 2015 John Wiley & Sons, Ltd.

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Dynamic response sensitivity of inelastic structures

Cited by 144 publications

References 15 publications

Reliability updating in geotechnical engineering including spatial variability of soil

Reliability updating in geotechnical engineering including spatial variability of soil

Finite element response sensitivity analysis using three‐field mixed formulation: general theory and application to frame structures

Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method

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