Journal of Engineering Mechanics

Abstract

Combined influence of temperature and mechanical deformations define the resulting contact stresses, heat flow, and rolling loss at the tire–pavement contact. In this study, the thermomechanical coupling of a hyperviscoelastic tire with a deformable pavement layer revealed the impact and extent of temperature influence on the hysteretic loss of a rolling tire. A scheme to predict the three-dimensional contact stress distribution was established that incorporated the thermomechanical interaction between a rolling hyperviscoelastic truck tire and a deformable pavement layer. The fully coupled thermal-stress model addressed two distinct yet intertwined perspectives: (1) establishing a thermomechanical database and prediction tool to generate contact stresses as inputs for pavement structural design, and (2) quantifying the associated rolling loss at the tire–pavement interaction that relates to tire design configurations and environmental impacts. Differences in the resulting contact stresses and rolling energy loss were observed between imposing uniform and nonuniform temperature profiles. Both the range and magnitudes of stresses throughout the tire–pavement contact imprint changed drastically as varying temperature profiles were implemented. Ranking the influence of thermal boundary conditions, the ambient temperature induced the highest impact on the dissipation energy and change in contact stress distribution, followed by the road and inner tire surface conditions. Moreover, the global hysteretic loss within the tire as myriad temperature profiles were imposed did not change significantly; however, the creep dissipation observed within the contact imprint revealed a higher disparity.

Practical Applications

In this study, a finite-element model was established to simulate a free-rolling truck tire over a pavement layer and determine the combined influence of temperature and loading on the three-dimensional contact stresses and hysteretic loss. The thermomechanical interaction between the truck tire and pavement layer impacted both the range and magnitude of the contact stresses, wherein differences were observed between imposing uniform and nonuniform temperature profiles. Particularly, the ambient temperature had the highest impact on the contact stress distribution and dissipation energy, in contrast to the level of influence from the pavement surface temperature and internal tire air temperature. In lieu of complex models, nonlinear regression equations were developed as a simple means to generate three-dimensional contact stress inputs for pavement analysis. Future model improvements and considerations may include other rolling conditions, such as braking, accelerating, or cornering conditions; temperature-dependent tire-inflation pressure and interface friction; influence of air and sun through convection and radiation along with daily temperature cycles; and a viscoelastic asphalt pavement layer.

A new method for conversion of the distributed strain measurements to crack opening displacements (CODs) in structural elements is introduced. A hybrid approach involving theoretical and experimental strain distribution at the crack location was employed to formulate the conversion equation. The objective was to find a simple deterministic equation for practical field application that quantifies crack opening displacements directly from distributed strain measurements. The viability of the method was accomplished by experiments involving a 15-m steel beam with prefabricated flaws. A Brillouin scattering–based optical fiber sensor system was employed for distributed measurement of strains along the length of the 15-m-long beam. Two fiber Bragg grating (FBG)–based displacement sensors were also used for direct measurement of crack opening displacements at the locations of the flaws. The process involved defining and computing the bond length, which is the segment of the optical fiber affected by the presence of the crack. The distributed strain was integrated over the bond length for describing the crack opening displacements. In developing the method, it was necessary to also perform direct tension tests of the optical fiber for the acquisition of the mechanical properties. The proposed method takes into account the elastic and elastoplastic stages of deformations in the optical-fiber coating and the influence of plastic phenomena on the bond length.

The $l_1$-norm regularized inverse methods have been suggested as a means to quantify and localize spatially sparse damage from a set of identified natural frequencies. Thus far, damage has been interpreted as changes in stiffness without any appreciable associated changes in mass. In seeking to generalize $l_1$-norm-based inverse methods to encompass damage that produces significant changes in both mass and stiffness, this paper finds that sparsity is too weak a prior to uniquely solve the associated underdetermined inverse problem. However, when damage is defined by local reductions to stiffness and mass, then the addition of a nonnegative constraint when combined with sparsity can yield physically meaningful solutions. This work proposes a two-step model-updating method to obtain sparse and nonnegative solutions. The findings and proposed method were verified using two numerical models: a shear beam and a four-level plane frame. The proposed methodology was experimentally validated using vibration data taken from a four-level bolted steel frame subjected to multiple damage scenarios.

In general, the response of a system coupled with a vibration absorber is obtained by incorporating only elastic analysis under different loading conditions. However, the elastoplastic analysis is carried out for blast-resistant structures such as monolithic and composite sandwich panels. The present study delineates the nonlinear elastoplastic analysis of two steel plates sandwiched with mechanical elements (spring-dashpot-inerter)–based dynamic vibration absorber (DVA) subjected to a uniformly distributed blast load on one of its surfaces. The assembly of two steel plates interconnected with spring–dashpot elements is modeled as an equivalent two-degree-of-freedom (2DOF) system incorporating nonlinear elastoplastic material properties. The equivalent mass, resistance, and load are computed using transformation factors. The displacement response of the equivalent 2DOF system is compared with a finite element (FE)–based numerical model of the assembly. The influence of inserting an inerter between two plates is investigated by considering three configurations of dynamic vibration absorber and varying certain parameters such as stiffness, damping coefficient, and inertance. It was observed that in terms of deformation and force transmitted to the back plate, the configuration of the inerter in series with a dashpot element performed better than the simple spring–dashpot arrangement. The internal resistance of the front plate governs the performance of different configurations of DVA, which was demonstrated by changing the thicknesses of the plates. The influence of nonlinearity on the dynamics of the system was investigated.

The $N$-segment circular arch with rigid members and semirigid joints under external pressure is studied. The problem is formulated in coupled difference equations. An efficient initial value method is presented to solve the stability problem. The product of buckling pressure and $N$ tends to be that of the continuous elastic arch as $N\to \infty$. Critical buckling is mostly antisymmetric but may be symmetric at larger opening angles. Optimum shapes (for maximum critical pressure) are determined for both segmented and continuous circular arches.

When using the traditional multilayered shell element to perform material nonlinearity analysis of large structures, the computation time is often overwhelming because of the repeated updating and factorization of the large-size global stiffness matrix. This paper aims to provide an efficient and general solution to such problems. To this end, a novel flat multilayered shell model is proposed by adding additional inelastic degrees of freedom (IDOFs) to describe the inelastic behavior of elements and adopting the approximate Woodbury formula that is an efficient solution method based on matrix perturbation theory as a solver. In this way, the entire nonlinear solution process only needs to factorize a sparse matrix called approximate Schur complement, whose dimension is consistent with the IDOF number, instead of the global stiffness matrix. To avoid the performance degradation of the proposed approach due to the activation of too many IDOFs when performing material nonlinearity analysis on large reinforced concrete (RC) structures, an improved concrete constitutive model and a two-level sparseness strategy are further developed. These measures are helpful to numerically reduce the IDOF number of the RC multilayered shell model, thus saving the computational overhead of factorizing and constructing the approximate Schur complement matrix. The accuracy and efficiency of the proposed scheme are verified by numerical examples.

As already indicated by Galileo, the laws of rescaling for load-bearing structures do not follow the simple geometric proportion because the structural weight increases more than the structural capacity and can equally lead to an effective loss of stiffness. Developing the theory originally proposed by Stüssi, the structural capacity of various materials are compared on the basis of performance indexes, such as specific strength and specific stiffness. This highlights how the structural weight increases as a function of the service load for various static schemes, dictating a theoretical limit for the structural size. Worked examples are presented in the fields of civil, marine, and aerospace engineering. Solution-spun carbon nanotube fibers appear promising because they are sustainable green materials whose capacity is superior to the best steels and comparable with the state-of-the-art carbon and Kevlar fibers. It is expected that the continuous improvement of the production techniques can bring their performances close to the theoretical limit of the constituent carbon nanotubes (CNTs), allowing the construction of superstructures not even imaginable today with the currently available materials.

Abstract

Identification and monitoring of structural damage have a growing importance in the maintenance of aging structures. Specifically, an optimal sensor configuration capable of fully identifying structural damage is desired. One innovative approach is casting the optimal sensor placement problem as a decision-centric, utility-maximization framework. By choosing mutual information (or relative entropy) as the utility criteria, sensor placements are chosen to maximize information about structural damage parameters. To accelerate this optimal experimental design (OED) problem, we propose the parameterization of damage using binary variables and the corresponding integration of the Bernoulli prior into this Bayesian OED framework. By limiting the damage parameter design space, we can direct the computational effort toward optimizing over informative and practical structural damage scenarios. Additionally, we convert the OED problem into a convex optimization problem, ensuring that sensor placement solutions contain the maximum information. We evaluate our proposed modified OED framework using a deterministic damage estimator also informed by the Bernoulli prior. We quantify the performance of sensor placements using a mean-squared error (MSE) metric, and we show that optimally selected sensors outperform randomly selected sensors, in general. We also provide a potential heuristic in selecting a sensor budget through the consideration of utility.

Practical Applications

In this work, we present a theoretical framework that identifies a set of optimal locations for sensor placement for damage detection in large structures. Given a sufficiently defined finite element model of a structure, this framework can identify a set of optimal sensor placements. Then, physically placing any sensor that can measure field data (e.g., displacements or accelerations) at these positions will yield experimental data that is most informative about potential damage scenarios at key components. Sensors can include and are not limited to accelerometers, strain gauges, fiber optic sensors, and laser vibrometers, among others. Ideally, sensors should minimally interfere with the structure’s dynamics. Furthermore, any measurement data should be processed to displacements in the frequency domain to seamlessly fit in the theoretical framework with minimal modifications. We expect practitioners to use the framework to numerically model and design experimental sensor configurations before physically placing any sensors on a structure to minimize any experimental burden.

This study investigates the vertical profile of streamwise (longitudinal) velocity in an unsteady and nonuniform open-channel turbulent flow. In contrast to the previous works, a direct derivation for velocity distribution starting from Reynolds-averaged Navier-Stokes (RANS) equation has been shown. Due to unavailability of several expressions for unsteady flow to solve the governing equation, a few assumptions have been made. The proposed model contains the effect of secondary current, which is generally present in all types of open-channel flow. The resulting partial differential equation has been solved numerically. Validation has been done by comparing the model with available experimental data and an existing analytical model.

This technical note investigates the preparation of a phase space of two simple constitutive laws, von Mises (J2) and Drucker-Prager (DP) models, for deep neural networks with special attention to elastic and plastic data points. The phase space is referred to as a database describing the material behavior via data points instead of mathematical formulation. To examine the effect of the proportions of elastic and plastic data points on the prediction quality, two sets (for J2 and DP models) including three equal phase spaces with different proportions of elastic and plastic data points are considered. To make a fair comparison, the only difference in phase spaces is the proportion of elastic and plastic data points in each set. We further study two different data types for constitutive behaviors, the tensorial space and the invariant space (volumetric-deviatoric space). The Nash-Sutcliffe error (NSE) is calculated for an unbiased comparison of prediction with different phase spaces in both tensorial and volumetric-deviatoric spaces. The results reveal that the distribution of elastic and plastic points may affect the accuracy of prediction for simple constitutive laws (isotropic, elasto-perfect plastic) via artificial neural networks; when an equal portion of elastic and plastic data points are used, the more robust prediction is achieved in this study.