Relative Entropy Application to Study the Elastoplastic Behavior of S235JR Structural Steel

The main issue in this work is to study the limit functions necessary for the reliability assessment of structural steel with the use of the relative entropy apparatus. This will be done using a few different mathematical theories relevant to this relative entropy, namely those proposed by Bhattacharyya, Kullback-Leibler, Jeffreys, and Hellinger. Probabilistic analysis in the presence of uncertainty in material characteristics will be delivered using three different numerical strategies-Monte Carlo simulation, the stochastic perturbation method, as well as the semi-analytical approach. All of these methods are based on the weighted least squares method approximations of the structural response functions versus the given uncertainty source, and they allow efficient determination of the first two probabilistic moments of the structural responses including stresses, displacements, and strains. The entire computational implementation will be delivered using the finite element method system ABAQUS and computer algebra program MAPLE, where relative entropies, as well as polynomial response functions, will be determined. This study demonstrates that the relative entropies may be efficiently used in reliability assessment close to the widely engaged first-order reliability method (FORM). The relative entropy concept enables us to study the probabilistic distance of any two distributions, so that structural resistance and extreme effort in elastoplastic behavior need not be restricted to Gaussian distributions.

Thermal Contact Response of a Transversely Isotropic Magneto-Electro-Elastic Coating

The magneto-electro-elastic (MEE) medium is a typical intelligent material with promising application prospects in sensors and transducers, whose thermal contact response is responsible for their sensitivity and stability. An effective thermal contact model between a moving sphere and a coated MEE medium with transverse isotropy is established via a semi-analytical method (SAM) to explore its thermal contact response. First, a group of frequency response functions for the magneto-electro-thermo-elastic field of a coated medium are derived, assuming that the coating is perfectly bonded to the substrate. Then, with the aid of the discrete convolution-fast Fourier transform algorithm and conjugate gradient method, the contact pressure and heat flux can be determined. Subsequently, the induced elastic, thermal, electric and magnetic fields in the coating and substrate can be obtained via influence coefficients relating the induced field and external loads. With the proposed method, parametric studies on the influence of the sliding velocity and coating property are conducted to investigate the thermal contact behavior and resulting field responses of the MEE material. The sliding velocity and thermal properties of the coating have a significant effect on the thermal contact response of the MEE material; the coupled multi-field response can be controlled by changing the coating thickness between ~0.1 a0 and a0.

Stochastic Reliability-Based Design Optimization Framework for the Steel Plate Girder with Corrugated Web Subjected to Corrosion

This paper proposes the framework for reliability-based design optimization (RBDO) of structural elements with an example based on the corrugated web I-girder. It tackles the problem of topological optimization of corroding structures with uncertainties. Engineering restrictions follow a concept of the limit states (LS) and extend it for stability and eigenfrequency assessment. The reliability constraints include all the LS; they are computed according to first- and second-order reliability methods. The RBDO example minimizes the bridge girder cross-section while satisfying the structural reliability level for the ultimate and the serviceability limit states, stability, and eigenfrequency. It takes into consideration two uncorrelated random effects, i.e., manufacturing imperfection and corrosion. They are both Gaussian; the first of them is applied at assembly time, while the second is applied according to the time series. The example confronts three independent FEM models with an increasing level of detailing, and compares RBDO results for three concurrent probabilistic methods, i.e., the iterative stochastic perturbation technique (ISPT), the semi-analytical method, and the Monte Carlo simulation. This study proves that the RBDO analysis is feasible even for computationally demanding structures, can support automation of structural design, and that the level of detailing in the FEM models influences its results. Finally, it exemplifies that reliability restrictions for LS are much more rigorous than for their deterministic counterparts, and that the fastest ISPT method is sufficiently accurate for probabilistic calculations in this RBDO.

Modeling Full-Field Transient Flexural Waves on Damaged Plates with Arbitrary Excitations Using Temporal Vibration Characteristics

We propose an efficient semi-analytical method capable of modeling the propagation of flexural waves on cracked plate structures with any forms of excitations, based on the same group of vibration characteristics and validated by a non-contact scanning Laser Doppler Vibrometer (LDV) system. The proposed modeling method is based on the superposition of the vibrational normal modes of the detected structure, which can be applied to analyze long-time and full-field transient wave propagations. By connecting the vibration-based transient model to a power flow analysis technique, we further analyze the transient waves on a cracked plate subjected to different excitation sources and show the influence of the damage event on the path of the propagating waves. The experimental results indicate that the proposed semi-analytical method can model the flexural waves, and through that, the crack information can be revealed.

Approach of Pavement Surface Layer Degradation Caused by Tire Contact Using Semi-Analytical Model

New methods of degradations on the pavement’s surface, such as top-down cracking and delamination, caused by the repeated passage of heavy vehicles led to questions about the impact of the contact between the tire and the pavement. In fact, to increase the service life of the structures, future road design methods must have a precise knowledge of the consequences of the contact parameters on the state of stress and deformation in the pavement. In this paper, tractive rolling contact under the effect of friction is modeled by Kalker’s theory using a semi-analytical method (SAM). A tire profile is performed thanks to a digitization by fringes or a photogrammetry technique. The effect of rolling on the main surface extension deformations is then highlighted to study top cracking. At the end of the SAM calculation, contact areas are closed to 200 μdef, exceeding the allowable micro-deformation limit for the initiation of cracking. In addition, results on the main strain directions also give information on the direction of cracking (initiation of longitudinal or transverse cracks). The cracking then becomes evident, leading to a reduced service life.

Tip Pressure on Semicircular Specimens in Tapping Mode Atomic Force Microscopy in Viscous Fluid Environments

Tapping mode (TM) atomic force microscopy (AFM) in a liquid environment is widely used to measure the contours of biological specimens. The TM triggers the AFM probe approximately at the resonant frequencies and controls the tip such that it periodically touches the specimen along the scanning path. The AFM probe and its tip produce a hydrodynamic pressure on the probe itself and press the specimen. The tip to specimen size ratio is known to affect the measurement accuracy of AFM, however, few studies have focused on the hydrodynamic pressure caused by the effects of specimen size. Such pressure affects the contour distortion of the biological specimen. In this study, a semi-analytical method is employed for a semicircular specimen to analyze the vorticity and pressure distributions for specimens of various sizes and at various tip locations. Changes in pressure distribution, fluid spin motion, and specimen deformation are identified as the tip approaches the specimen. The results indicate the following: the specimen surface experiences the highest pressure when the specimen diameter equals the tip width; the vorticity between tip and specimen is complex when the tip is close to the specimen center line; and the specimen inflates when the tip is aligned with the specimen center line.

Tip Effect of the Tapping Mode of Atomic Force Microscope in Viscous Fluid Environments

Atomic force microscope with applicable types of operation in a liquid environment is widely used to scan the contours of biological specimens. The contact mode of operation allows a tip to touch a specimen directly but sometimes it damages the specimen; thus, a tapping mode of operation may replace the contact mode. The tapping mode triggers the cantilever of the microscope approximately at resonance frequencies, and so the tip periodically knocks the specimen. It is well known that the cantilever induces extra liquid pressure that leads to drift in the resonance frequency. Studies have noted that the heights of protein surfaces measured via the tapping mode of an atomic force microscope are ~25% smaller than those measured by other methods. This discrepancy may be attributable to the induced superficial hydrodynamic pressure, which is worth investigating. In this paper, we introduce a semi-analytical method to analyze the pressure distribution of various tip geometries. According to our analysis, the maximum hydrodynamic pressure on the specimen caused by a cone-shaped tip is ~0.5 Pa, which can, for example, pre-deform a cell by several nanometers in compression before the tip taps it. Moreover, the pressure calculated on the surface of the specimen is 20 times larger than the pressure without considering the tip effect; these results have not been motioned in other papers. Dominating factors, such as surface heights of protein surface, mechanical stiffness of protein increasing with loading velocity, and radius of tip affecting the local pressure of specimen, are also addressed in this study.