Direct differentiation method for response sensitivity analysis of a bounding surface plasticity soil model

SummaryThis 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.

In this paper, the mean-centered first-order second-moment (FOSM) method is employed to perform probabilistic push-over analysis (POA) of structural and/or soil-structure systems. Approximations of first and second statistical moments (FSSMs) of engineering demand parameters (EDPs) of structural and/or geotechnical systems with random material parameters are computed based on finite-element (FE) response and response sensitivity analysis (RSA) results. The FE RSA is performed accurately and efficiently by using the direct differentiation method (DDM) and is employed to evaluate the relative importance (RI) of the various modeling material parameters in influencing the variability of the EDPs. The proposed approximate methodology is illustrated through probabilistic POA results for nonlinear inelastic FE models of: (1) a three-story reinforced-concrete (RC) frame building and (2) a soil-foundation-structure interaction system consisting of a RC frame structure founded on layered soil. FSSMs of EDPs computed through the FOSM method are compared with the corresponding accurate estimates obtained via Monte Carlo simulation. Results obtained from exact (or local) and averaged (or global) response sensitivities are also compared. The RI of the material parameters describing the systems is studied in both the deterministic and probabilistic sense, and presented in the form of tornado diagrams. Effects of statistical correlation between material parameters are also considered and analyzed by the FOSM method. A simple approximation of the probability density function and cumulative distribution function of EDPs due to a single random parameter at a time (while all the other parameters are fixed to their mean values) is also proposed. Conclusions are drawn on both the appropriateness of using local RSA for simplified probabilistic POA and on the application limits of the FOSM method. It is observed that the FOSM method combined with the DDM provides accurate estimates of FSSMs of EDPs for low-to-moderate level of inelastic structural or system behavior and useful qualitative information on the RI ranking of material parameters on the structural or system response for high level of inelastic behavior.

Response sensitivity studies of a cable-stayed bridge with shape memory alloy damping system considering temperature effects

Sensitivity analysis of the dynamic response of a frame. Part I: Direct differentiation method

Design sensitivity analysis of dynamic response of nonviscously damped systems

SummaryResponse sensitivity is an essential component to understanding the complexity of material and geometric nonlinear finite element formulations of structural response. The direct differentiation method (DDM), a versatile approach to computing response sensitivity, requires differentiation of the equations that govern the state determination of an element and it produces accurate and efficient results. The DDM is applied to a force‐based element formulation that utilizes curvature‐shear‐based displacement interpolation (CSBDI) in its state determination for material and geometric nonlinearity in the basic system of the element. The response sensitivity equations are verified against finite difference computations, and a detailed example shows the effect of parameters that control flexure–shear interaction for a stress resultant plasticity model. The developed equations make the CSBDI force‐based element available for gradient‐based applications such as reliability and optimization where efficient computation of response sensitivities is necessary for convergence of gradient‐based search algorithms. Copyright © 2016 John Wiley & Sons, Ltd.

A two-stage approach based on residual force vector and response sensitivity analysis is proposed for structural damage identification in this study. Local damage is represented by a perturbation in the elemental stiffness parameter of the structural finite element model. Primarily, the difference between the virtual residual force vector of an intact and damaged structure is used to localize the damage. Then, a response sensitivity-based method is adopted to identify the perturbation of the stiffness parameter (i.e., the extent of the local damage) from the measured dynamic responses. Numerical simulations are conducted to identify both single and multiple structural damages under sinusoidal or impulsive excitation. The proposed approach gives satisfactory results with artificial measurement noise.

ESA: Expert structural analysis for engineers

Effect of buckling-restrained brace model parameters on seismic structural response

Presented is a detailed case study on structural Finite Element (FE) modeling and Modal Pushover Analysis (MPA) of a 14-story office building instrumented for seismic response investigation. The system identification tool was used to identify the structural dynamic properties, including the natural periods of vibration of the structure and level of critical damping based on seismic data recorded during small seismic ground motions. A series of FE models were created to improve the modeling technique. The final corrected FE model was refined and calibrated to match the identified structural natural periods. It was found that a FE model can be calibrated to give a good prediction of earthquake response. Using the calibrated FE model, the structural seismic behavior has been examined using the MPA procedure. In the MPA procedure, an improved analysis based on structural dynamic theory with invariant force distributions was used to generate the push loads. Four recorded ground acceleration time histories were used as input data for the MPA procedure. Five sets of push forces, corresponding to the effective earthquake forces from the first five modal expansions, were applied to the FE model. The final MPA results were combined from these five push-over cases using the Square-Root-of-Sum-of-Squares (SRSS) rule and the Complete Quadratic Combination (CQC) rule to get the total response. The MPA results were also compared with the Incremental Dynamic Analysis (IDA). It is found that the MPA and IDA results are reasonably matched. The MPA procedure is an improved tool for estimating seismic demands on buildings. Using the MPA procedure, the structural behavior can be examined during seismic loading and future performance of the building during damaging earthquakes can be predicted.

The present paper develops an enhanced response sensitivity approach for parameter identification of nonlinear time-delay systems from the time-domain data. Accurate and rapid identification of the time-delay system’s parameters is the key to achieve effective control and synchronization, especially for the delay parameters. The work of this paper is mainly threefold. Firstly, taking a general nonlinear time-delay system as the investigated object, the characteristics of the nonlinear time-delay system are introduced, and the response sensitivity analysis with respect to the system parameters is derived. Then, the problem of parameter identification is modeled as a nonlinear least-squares optimization function. To this end, a novel iteration-based approach is developed to solve such problem, and the ill-posed situation is tackled by Tikhonov regularization. Besides, the trust-region constraint is implemented to enhance the convergence of the algorithm. Finally, the feasibility of the proposed approach is verified by two numerical examples and a real electronic circuit experiment. The results proved that the proposed approach can identify parameters of nonlinear time-delay systems accurately, robustly and effectively.

Parameters affecting laterally loaded piles in frozen soils by an efficient sensitivity analysis method

Sensitivity analysis of eigenmodes and dynamic responses for intelligent structures

Finite Element Response Sensitivity Analysis of Steel Frames Equipped with Buckling-Restrained Braces

This research article presents the design and analysis of a displacement amplification mechanism based on a microelectromechanical system (MEMS). The mechanism, compared to generic displacement mechanisms, is smaller and capable of amplifying input displacement by a factor of 6.8. Finite element analysis (FEA) is performed with commercial software Intellisuite using the extended finite element method (XFEM) technique to verify the analytical results from mathematical models. Kinematic response and kinematic sensitivity analysis of the amplification mechanism are computationally carried out to predict the effect of different geometric parameters on the performance of the proposed mechanism. The analysis predicts that length and angle of flexure are the two key geometric parameters significantly affecting the amplification factor (AF), with length having a direct relationship and angle of flexure having an inverse relationship. A significant increase in the AF is seen for a flexure length up to 550 μm and angle below 5°. Based on the sensitivity analysis, the design is optimized, and geometric parameters are finalized. Modal analysis and dynamic simulations, including direct-integration transient and steady-state modal analysis, are performed on the mechanism under the application of 25 g. The mechanism can be integrated with any conventional actuating mechanism in a microsystem where the amplification of a small displacement at the output is desired.