Journal of Engineering Mechanics

Various model updating approaches relying on solving nonconvex optimization problems have been developed; however, few of them can reach the global optimum. To obtain the global optimum, the real sum-of-squares optimization algorithm (SOSOA) was proposed to minimize the modal dynamic residuals of proportionally damped structural systems by recasting the nonconvex optimization into a convex optimization. However, this algorithm becomes inefficient for model updating of nonproportionally damped systems with complex-valued eigenvalues and eigvenvectors. This study proposes a model updating approach that exploits and adapts a complex SOSOA to minimize the modal dynamic residuals of nonproportionally damped systems. Numerical considerations unique to using the adapted complex SOSOA to update medium- or large-scale structural models are discussed. Finite-element models of three nonproportionally damped structures—including a base-isolated shear building, a frame building implemented with a tuned mass damper, and a frame building implemented with buckling-restrained braces—are updated to demonstrate that the adapted complex SOSOA finds the global optimum while being orders of magnitude more computationally efficient and far less demanding of computer memory than the real SOSOA.

Salt layers and domes have been used to store hydrocarbons and to dispose of nuclear wastes. One of the most important properties of rock salt is its good deformability, which can neutralize the deviatoric stress and heal damage. Structural stability is one crucial requirement in salt cavern design and construction. Various criteria and methods have been proposed for salt cavern design and stability analysis. This paper investigated the advantages and limitations of various stability criteria. The results suggest that the stability criterion proposed by De Vries et al. is the most suitable approach for stability analysis. However, the effects of the stress path and history are not considered in this criterion. To overcome this shortcoming and to integrate effects of the stress path and history within the criterion, an updatable dilatancy criterion is proposed. In the proposed dilatancy criterion, a representative parameter is defined based on the healing and damage that occurred in a previous cycle of loading and unloading, which takes into account the stress path and history and their effects on the behavior of rock salt in subsequent cycles. The new criterion gives deeper insight into the strength of rock salt based on previous damage-healing background, and is useful in appropriate design and operation of salt cavern.

This study develops stability conditions for general tensegrity regarding the three stability criteria (e.g., prestress stability, general stability, and super stability) based on an energy approach. The coupling relations of specific nodal degrees of freedom caused by the rigid bodies are described by a set of constraint functions and incorporated into the potential energy function by the Lagrangian multiplier method. Stiffness matrices of general tensegrity systems are derived from the augmented potential energy function. It shows that the stability of general tensegrity can be evaluated through the stiffness matrices expressed in the constrained motion space generated by the constraint functions. Elegant formulations are developed for the evaluation of the three types of stability conditions for general tensegrity systems. Moreover, it turns out that the formulations developed in this study will degenerate into those for the stability analysis of classic tensegrity if no rigid bodies exist in the system, which indicates that the proposed approach is a general framework for the stability analysis of any type of tensegrity systems.

Energy harvesting from vortex-induced vibrations (VIV) is gaining more attention in many applied cases. This paper studied the nonlinear dynamics of a tunable VIV-based energy harvester. The energy harvester structure consists of a base-clamped cylinder having an adjustable mass (the tuner) which enables the system to actively synchronize with vortex-shedding frequencies. The Euler-Bernoulli beam theory and the extended Hamilton’s principle are used to extract the nonlinear partial differential equations of the distributed model for the cylinder, tuner motion, harvested voltage, and fluctuated lift force. The reduced-order model of the system of equations is derived via the Galerkin method using modified mode shapes. The method of multiple time scales is employed to obtain the approximated analytical solution of the 1:1 internal resonance of the lumped parameter system. The dynamical response of the system is shown by investigating various parameters of the harvester. Additionally, the locus of the points at which the higher orbits of harvested voltage occur is specified for the tuner equilibrium position. The results show the proposed design significantly increases energy harvesting performance by a factor of 900%. This paper is offered as a contribution towards energy harvester design and optimization with the goal of capturing higher energy orbits.

A recent comparative study revealed that the commonly offered experimental validations of peridynamics and phase-field fracture models have been insufficient because they involved only nondistinctive experiments, i.e., experiments that can be closely fitted by different models that at the same time give very different predictions in important practical applications. The comparisons showed that the peridynamic and phase-field models are incapable of simulating a set of 11 distinctive experiments—experiments that are critical for assessing the accuracy of different models and are representative of fracture behavior of engineering structures. Practical applications would be helped by common adoption of a model index that would compare the predictive capability of various fracture models quantitatively. Proposed here for further discussion is an example of a possible numerical index, the m-Index, which attempts to characterize how well the optimal calibration of model parameters can match the experimental evidence, such as the fracture patterns, measured response curves, size effect, and crack-parallel stress effect. Included are only the distinctive experiments. As an example, the m-Index is here calculated for a set of seven fracture models whose performance was previously compared with 11 distinctive experiments. This previous comparison of seven models is here extended to an eighth model, proposed as a fresh improvement of peridynamics. The choice of distinctive experiments is one of the subjects calling for further discussion. Despite inevitable imperfections, a widely adopted index for appraising new material models would mitigate waste of researchers’ effort and grant funds, as well as the space in scientific journals and conference programs.

A novel quadrature element for performing plane stress elastoplastic analysis is introduced in this paper. Differing from the popular finite-element method, the quadrature-element method (QEM) first evaluates the integration in the weak-form statement of the problem by an integral quadrature scheme, and then approximates the differentiation at the discrete integration points by the differential quadrature analog. As a result, the QEM avoids construction of shape functions and obtains higher-order elements easily by just increasing the order of integration. The usage of higher-order elements leads to more accurate solutions and coarser geometric meshes without detriment to the computational scale because the number of degrees of freedom is maintained. In addition, the element nodes in the QEM are the same as the integration points that possess physical meanings such as strains and stresses, which is crucial in the elastoplastic analysis for determining the elastic/plastic state of the nodes. A straightforward elastoplastic quadrature-element formulation is developed. Incremental-iterative and return mapping solution schemes are adopted to implement the quadrature element for the elastoplastic analysis. Numerical examples are presented to demonstrate the effectiveness and high accuracy of the proposed approach.

We consider the problem of modeling heterogeneous materials where microscale dynamics and interactions affect global behavior. In the presence of heterogeneities in material microstructure it is often impractical, if not impossible, to provide quantitative characterization of material response. The goal of this work is to develop a Bayesian framework for uncertainty quantification (UQ) in material response prediction when using nonlocal models. Our approach combines the nonlocal operator regression (NOR) technique and Bayesian inference. Specifically, additive independent identically distributed Gaussian noise is employed to model the discrepancy between the nonlocal model and the data. Then, we use a Markov chain Monte Carlo (MCMC) method to sample the posterior probability distribution on parameters involved in the nonlocal constitutive law and associated modeling discrepancies relative to higher-fidelity computations. As an application, we consider the propagation of stress waves through a one-dimensional heterogeneous bar with randomly generated microstructure. Several numerical tests illustrate the construction, enabling UQ in nonlocal model predictions. Although nonlocal models have become popular means for homogenization, their statistical calibration with respect to high-fidelity models has not been presented before. This work is a first step in this direction, focused on Bayesian parameter calibration.

Gaussian processes (GPs) are a popular technique for global metamodeling applications. Their objective in such settings is to establish an efficient and globally accurate approximation of the response surface of computationally expensive simulation models. When developing such GPs, the design of (simulation) experiments (DoE) plays an important role in reducing the required number of model runs for obtaining accurate approximations. Sequential (adaptive) selection of experiments can provide significant advantages, especially when the response surface is characterized by localized nonlinearities. Such adaptive DoE strategies for global metamodeling applications typically focus on minimizing the predictive GP variance, representing an exploration strategy, while recent developments have additionally considered the reduction of the GP bias obtained through cross validation, representing an exploitation strategy. While significant focus has been placed on the definition of appropriate adaptive DoE criteria, computational challenges still exist that limit the widespread adoption of adaptive DoE techniques—for example, related to the additional computational demand for identifying the optimal new experiment(s) or the necessity to establish proper schemes to combine exploration and exploitation strategies. To address these specific challenges, this research investigates two new adaptive DoE formulations. The first one focuses on the approximation of the popular integrated mean square error (IMSE) DoE criterion. The computationally demanding GP predictive variance update (after addition of each candidate experiment), required in the original IMSE formulation, is replaced by an approximation based on the current predictive variance and the domain of influence that surrounds each new experiment. The approximation is established through a parametric formulation that leverages the GP kernel to describe the aforementioned domain, with characteristics that are progressively calibrated across the GP training stages, to minimize the discrepancy between the actual and the approximated IMSE. The second formulation establishes a multicriteria search for simultaneously identifying multiple Pareto optimal experiments that balance exploration and exploitation objectives, replacing conventional strategies that establish a weighted combination of these objectives to promote a single DoE selection criterion.

This paper presents the development of a steel-climbing bicycle robot integrated with an ultrasonic sensing device towards autonomous thickness measurement of steel bridge members. The bicycle-like robot has two magnetic wheels controlled by two independent steering actuators, which navigates on various steel surfaces (flat, curved, rough, concave, and convex). The compact ultrasonic sensing device is capable of high-voltage pulse excitation, filtering/amplification of the received ultrasonic signal, and high-speed analog-to-digital conversions (up to 80 MHz). Along with the ultrasonic sensing device, the robot carries a dual element transducer, an automatic gel couplant dispenser, a position tracking sensor, and a camera. A mounting/retrieving mechanism of the transducer is designed to ensure the reliable contact of the transducer on steel surfaces. The camera view assists an operator to safely navigate the robot to measurement locations, properly dispense gel couplant, and firmly press the transducer on a measurement surface. The automated robot localization provides accurate thickness measurement locations, which are mapped real-time in three-dimensional (3D) space together with the robot’s travel path. We validate the performance of the developed system in several indoor and outdoor tests. Weblink to a supplementary video demonstrating the robot’s maneuverability and ultrasonic thickness measurements is available in the Data Availability Statement of this article.

The purpose of this paper is to develop a unified elastoplastic model for describing both monotonic and cyclic behaviors of natural structured clay–structure and crushable sand–structure interfaces based on the bounding surface plasticity and the critical state concept with three features: (1) a more general yield surface with two shape parameters is adopted to improve the prediction of the shear yield and the critical state of the soil–structure interface, (2) the degradation of bounding surface size and the adhesive normal stress is introduced into the model to consider the shear strength reduction of natural structured clay–structure interface, and (3) the grain breakage effect on the behavior of crushable sand–structure interface is considered by incorporating the location of the critical-state line with the broadening of grain-size distribution induced by grain breakage. Then, explicit simulation schemes with substepping and error control are established for simulating interface shear tests under constant volume, constant normal load, and constant normal stiffness conditions. Finally, comparisons between experimental and numerical results indicate that the unified soil–structure interface model is able to not only predict the state-dependent monotonic stress–strain behavior of structured clay–structure or crushable sand–structure interfaces, but also reproduce the cyclic accumulative contraction and stabilization, as well as the stress degradation observed in both structured clay–structure and crushable sand–structure interfaces.