Journal of Engineering Mechanics

A sample-based evaluation of Sobol’ sensitivity indices is discussed in this paper relying on Kernel Density Estimation (KDE) for achieving computational efficiency. The foundation of the approach is the definition of an auxiliary probability density function (PDF) for the vector of model parameters (i.e., random variables representing system input). The sensitivity index for each input can be then expressed through the marginal density related to this auxiliary joint PDF. The efficient estimation of the indices for all model parameters is ultimately facilitated by simulating first a single sample-set from the joint PDF and then utilizing this information to approximate all marginal distributions of interest through KDE. The same sample set is used for all approximations whereas this set is further exploited to improve the accuracy of the estimation of the integrals defining the sensitivity indices. An extension to facilitate calculation of higher order indices and total sensitivity indices is also examined. Once the sample set is generated, the computational burden of the approach is small and practically independent of the dimension of the model parameters. This makes the proposed approach particularly attractive for applications for which such samples are readily available (or can be efficiently obtained), as it can provide sensitivity information with small overall computational cost.

This research studies a substructure finite element model updating approach that requires vibration data from only part of a large structure (i.e., a substructure). The residual structure is condensed using a limited number of dominant modal coordinates, whereas the substructure model remains at high resolution. To update the condensed model, physical parameters in the substructure and modal parameters of the residual structure are chosen as optimization variables; minimization of modal dynamic residuals from the eigenvalue equations in structural dynamics is chosen as the optimization objective. An iterative linearization procedure is adopted for efficiently solving the optimization problem. The proposed substructure model updating approach is validated with 1D, 2D, and 3D examples.

This paper presents an exploration of noncollinear Timoshenko beam structures for attenuating the stress waves generated from impulsive transient loadings. Due to the existence of the noncollinear segments, flexural waves are generated in addition to the longitudinal waves. Furthermore, the resulting waves are dispersive and thus provide higher potential for the attenuation of the stress waves. Symmetric patterns are found to be more appropriate for increasing the stress-wave attenuation capacity, as these patterns can eliminate bending stress effects at the boundary of the structures. More generally, an adaptive optimization methodology is developed to find the most efficient layout of the noncollinear stress-wave attenuators (NSWAs). This methodology uses genetic algorithms (GA), coupled with an explicit finite-element (FE) method for analyzing the wave-propagation behavior of the structures. The developed methodology is capable of updating the FE model of each trial solution, as the geometric characteristics of the solutions are evolving during the optimization procedure. Through this evolutionary design process, the attenuation capacity of the noncollinear structures is observed to be a complex function of the number of noncollinear segments and the relative wavelength associated with the transient loading. In addition, the results show that the single-material noncollinear structures are not effective for attenuating the amplitudes of transient pulse loadings with longer durations, such as blast waves. Most interestingly, however, by incorporating geometric and material discontinuities, bimaterial NSWAs are found to provide impressive levels of attenuation within compact geometries. Although much analytical and experimental validation remains, designs along these lines could help to initiate a paradigm shift from hardening of structures for blast protection towards a protective systems design approach featuring creative management of stress wave propagation.

This paper studies the flexural performance of sandwich panels composed of a soft polyurethane foam core and glass-fiber-reinforced polymer (GFRP) skins. A robust numerical model is developed to predict the full load-deflection and strain responses of the panel. It is based on equilibrium and strain compatibility and accounts for the excessive shear deformation and material nonlinearity of the core. It also accounts for geometric nonlinearity in the form of localized deflection of the loaded skin using the principals of beam-on-elastic foundation and the change in core thickness due to its softness. The model incorporates various failure criteria, namely core shear failure, core flexural tension or compression failure, compression skin crushing or wrinkling, or tensile rupture of skin. The model has the advantage of being able to isolate quantitatively the individual contributions of flexure, shear, and localized skin deformations, to overall deflection. A parametric study is performed to examine the effects of core density and skin thickness on panel behavior. It is shown that as the core density increases from 32 to $192{\mathrm{kg}/\mathrm{m}}^3$, the contribution of shear to overall deflection reduces from about 90 to 10%. It also appears that the optimal core density of the sandwich panels is within 96 to $128{\mathrm{kg}/\mathrm{m}}^3$, which represents the lowest density necessary to achieve the highest ultimate strength and stiffness.

The Transitional Markov chain Monte Carlo (TMCMC) method is a widely used method for Bayesian updating and Bayesian model class selection. The method is based on successively sampling from a sequence of distributions that gradually approach the posterior target distribution. The samples of the intermediate distributions are used to obtain an estimate of the evidence, which is needed in the context of Bayesian model class selection. The properties of the TMCMC method are discussed and the following three modifications to the TMCMC method are proposed: (1) The sample weights should be adjusted after each MCMC step; (2) a burn-in period in the MCMC sampling step can improve the posterior approximation; and (3) the scale of the proposal distribution of the MCMC algorithm can be selected adaptively to achieve a near-optimal acceptance rate. The performance of the proposed modifications is compared with the original TMCMC method by means of three example problems. The proposed modifications reduce the bias in the estimate of the evidence, and improve the convergence behavior of posterior estimates.

This study sought to illuminate the turbulence-induced changes in the aerodynamic correlation structure on a stationary/oscillating rectangular prism. A forced-vibration system was used with a model instrumented with 66 pressure transducers. The study included the effects of the turbulence intensity, turbulence integral scale, and structural motion on the spanwise and streamwise correlation (or coherence) of integrated aerodynamic quantities (lift force or torsional moment) and pressures. These effects are discussed based on the stationary model tests, the oscillating model tests in the low to the high reduced velocity ranges, which are characterized as three different aerodynamic regimes. In general, the turbulence scale effects are more significant than those of the turbulence intensity. Larger turbulence scale usually leads to larger spanwise correlation of aerodynamic quantities on stationary models, but the results of the oscillating model tests in the low reduced velocity range indicate a reversal of this trend. In the high reduced velocity range, the self-excited force exhibited correlation coefficients greater than 0.95 for every incident flow in the entire spanwise separation range considered (2.4 times the deck width), which supports the assumption common in analytical modeling of fully correlated self-excited forces. Typically, the lift force correlation is larger than that of the torsional moment. The self-excited force correlation values were far larger than those of any velocity components and significantly larger than those of the buffeting force. Spanwise correlation of the buffeting force showed exceptional similarity between stationary and oscillating model tests. The spanwise correlation of the total wind-induced force (a combination of the self-excited and buffeting forces) has a value between those of the self-excited and buffeting cases, individually.

In this paper, the authors address the issue of determining the size of a representative volume element (RVE) in the case of nonlinear random composites with either elastoplastic or elasto-viscoplastic phases. In such a case, the general form of the effective constitutive behavior is not known in advance and the response must be evaluated either by direct numerical computations on the RVE or by an appropriate approximation scheme. Previous methodologies for determining the size of RVE usually rely on analyzing the convergence of the RVE response computed numerically with respect to its size. In the present work, the convergence of parameters related to an incremental homogenization scheme is analyzed with respect to (1) the size of the RVE; and (2) statistical convergence related to microstructure realizations. For that purpose, an incremental homogenization method is combined with a statistical convergence analysis of parameters related to the matrix phase only. The advantage is that the range of parameters to be identified is much narrower than for a general empirical constitutive law. Once identified and once the convergence analysis is performed with respect to both size of RVE and statistical realizations, the macroscopic constitutive law can be readily used for structure calculations. The methodology is illustrated by analyzing two-dimensional microstructures with randomly distributed cylindrical elastic rigid fibers embedded in an elastoplastic or elasto-viscoplastic matrix. For these materials, the existence of an RVE is demonstrated for sizes of RVE corresponding to 17–18 and 14–15 times the diameter of the inclusions, respectively.

Historically, structural health monitoring (SHM) has relied on fixed sensors, which remain at specific locations in a structural system throughout data collection. This paper introduces state-space approaches for processing data from sensor networks with time-variant configurations, for which a novel truncated physical model (TPM) is proposed. The state-space model is a popular representation of the second-order equation of motion for a multidegree of freedom (MDOF) system in first-order matrix form based on field measurements and system states. In this mathematical model, a spatially dense observation space on the physical structure dictates an equivalently large modeling space, i.e., more total sensing nodes require a more complex dynamic model. Furthermore, such sensing nodes are expected to coincide with state variable DOF. Thus, the model complexity of the underlying dynamic linear model depends on the spatial resolution of the sensors during data acquisition. As sensor network technologies evolve and with increased use of innovative sensing techniques in practice, it is desirable to decouple the size of the dynamic system model from the spatial grid applied through measurement. This paper defines a new data class called dynamic sensor network (DSN) data, for efficiently storing sensor measurements from a very dense spatial grid (very many sensing nodes). Three exact mathematical models are developed to relate observed DSN data to the underlying structural system. Candidate models are compared from a computational perspective and a truncated physical model (TPM) is presented as an efficient technique to process DSN data while reducing the size of the state variable. The role of basis functions in the approximation of mode shape regression is also established. Two examples are provided to demonstrate new applications of DSN that would otherwise be computationally prohibitive: high-resolution mobile sensing and BIGDATA processing.

A generally applicable algorithm for the iterative generation of data ensembles to efficiently create accurate computational mechanics reduced-order models (ROMs) for use in computational approaches to approximate inverse problem solutions is presented and numerically evaluated. The ROM approach considered is based on identifying the optimal low-dimensional basis to be used within a Galerkin weak-form finite-element (FE) method to provide substantially reduced computational cost while maintaining accuracy relative to that of a (traditional) full-order FE model. Furthermore, proper orthogonal decomposition is used to derive the ROM basis from a set of response fields (i.e., snapshots) generated a priori with full-order FE analyses. Therefore, the set of full-order FE analyses used to create the ROM directly affects the accuracy/generalization of the ROM. The core hypothesis of the algorithm presented is that maximizing the diversity, as defined in a measurable sense, of the full-order models (FOM) used to create the ROM will improve the accuracy of the ROM over a range of input system parameters. Based on an initial (small) set of snapshots, the algorithm uses snapshot correlation to quantify the snapshot diversity with respect to the system input parameters. Then the algorithm iteratively applies surrogate-model optimization to identify the next set(s) of system input parameters to be evaluated with full-order analyses to create additional so-called optimal snapshots. Although generally applicable to a variety of physical processes, the ROM approach with the iterative snapshot generation algorithm is presented within the context of the steady-state dynamic solid mechanics of heterogeneous media. Two simulated case studies are then presented involving forward analysis and inverse characterization of semilocalized Young’s modulus distributions in structural components as could be relevant to nondestructive evaluation problems. The iterative snapshot generation algorithm is shown to produce ROMs that can accurately estimate displacement response fields over a wide range of material parameters and that are substantially more accurate than ROMs created from randomly generated snapshot sets. Moreover, the accurate generalization of the iteratively generated ROMs is shown to be sufficient to consistently produce accurate inverse characterization solution estimates with a fraction of the computational expense that would be required to do so with full-order analyses.

There are many occasions in structural health monitoring (SHM) on which collected data sets contain missing observations. Such instances may occur as a result of failed communications or packet losses in a wireless sensor network or as a result of sensing and sampling methods—for example, mobile sensing. By implementing modified expectation and maximization steps, structural identification using expectation maximization (STRIDE) is capable of processing data in these circumstances and is the first modal identification technique to formally accept data with missing observations. This paper presents the STRIDE algorithm, a statistical perspective of missing data, and new STRIDE equations that account for missing observations. Expectation step (E-step) equations are given explicitly for both partially observed time steps and those not fully observed. The maximization step (M-step) provides state-space parameter updates in terms of available observations and missing-data state-variable statistics. This paper also discusses the performance and convergence behavior of STRIDE with missing data. Finally, two applications are presented to exemplify common use in network reliability and mobile sensing, both using data collected at the Golden Gate Bridge. This paper proves that sensor network data containing a significant amount of missing observations can be used to achieve a comprehensive modal identification. A successful real-world identification with simulated mobile sensors quantifies the preservation of spatial information, establishing the benefits of this type of network and emphasizing a line of inquiry for future SHM implementations.

In structural dynamics, direct integration algorithms are commonly used to solve the temporally discretized differential equations of motion. Numerous research efforts focused on the stability and accuracy of different integration algorithms for linear elastic structures. However, investigations of those properties applied to nonlinear structures are limited. Systematic Lyapunov stability and accuracy analyses of several direct integration algorithms for nonlinear structural dynamics are presented. These integration algorithms include the implicit methods of the Newmark family of integration algorithm and the TRBDF2 algorithm, and the explicit methods of operator-splitting (OS) algorithms. Two versions of the OS algorithms, using initial and tangent stiffness formulations, are investigated. The latter one is shown to possess similar stability properties to the implicit Newmark integration. Some arguments of stability regarding these direct integration algorithms from past studies are found to be groundless. An approach that enables performing the stability analysis numerically is proposed. It transforms the stability analysis to a problem of convex optimization. In addition, accuracy of the previously discussed five integration algorithms is investigated using a geometrically nonlinear test problem, in which acceptable amounts of period elongation and amplitude decay were evident.

A nonlinear vibration absorber exploiting the pinched hysteresis of mixed wire ropes made of NiTiNOL and steel is proposed. The mixed wire ropes are assembled in a mechanical device which, by bending them, provides the restoring force to the oscillating mass. The assembly of mixed wire ropes, subject to cyclic end displacements, gives rise to a pinched force-displacement behavior due to the simultaneous occurrence of interwire friction and phase transformations. A modified Bouc-Wen model is adopted to represent the pinched hysteresis while the differential evolutionary (DE) algorithm is employed to identify the constitutive parameters that reproduce the experimental force-displacement cycles. The DE algorithm is also utilized to optimize the restoring force of the absorber toward mitigation of the dynamic response of the main structure to external disturbances of various magnitudes. The pinched hysteresis provides an equivalent damping ratio and resonance frequency, which tend to become almost constant in a given oscillation amplitude range, thus overcoming detrimental detuning problems typical of other nonlinear absorbers. The absorber performance is evaluated in the context of a multistory steel building model mounted on a shaking table. The comparison between controlled and uncontrolled responses shows a very good attenuation performance within the design frequency bandwidth.