Journal of Engineering Mechanics

An analytical approach is presented to investigate the linear buckling of eccentrically stiffened functionally graded thin toroidal shell segments subjected to axial compression, lateral pressure, and hydrostatic pressure. On the basis of classical thin shell theory, the smeared stiffener technique and the adjacent equilibrium criterion, the governing equations of buckling of eccentrically stiffened functionally graded toroidal shell segments are derived. The functionally graded toroidal shell segments with simply supported edges are reinforced by a ring and stringer stiffener system on an external surface. The resulting equations in the case of compressive and pressure loads are solved directly. The obtained results show the effects of stiffeners and input factors on the buckling behavior of these structures. In this paper, the results are also compared with the solutions published in the literature for the specific cases of a toroidal shell.

In the present work, the flexural vibration of nonlocal Timoshenko beams under an initial stress is readdressed. The complete effect of the initial stress is taken into account in the basic formulation. The analytical solution presented herein is based on Eringen’s nonlocal elasticity theory. A numerical application of the corrected solution is carried out for a simply supported single-walled carbon nanotube (SWCNT). The comparative results show that the difference between the present corrected and the earlier solutions is not negligible.

This paper presents a unified approach to model the influence of fabric anisotropy and its evolution on both the elastic and plastic responses of sand. A physically based fabric tensor is employed to characterize the anisotropic internal structure of sand. It is incorporated into the nonlinear elastic stiffness tensor to describe anisotropic elasticity, and is further included explicitly in the yield function, the dilatancy relation, and the flow rule to characterize the anisotropic plastic sand response. The physical change of fabric with loading is described by a fabric evolution law driven by plastic strain, which influences both the elastic and the plastic sand behavior. The proposed model furnishes a comprehensive consideration of both anisotropic elasticity and anisotropic plasticity, particularly the nonlinear change of elastic stiffness with the evolution of fabric during the plastic deformation of sand. It offers a natural and rational way to capture the noncoaxial behavior in sand caused by anisotropy. It also facilitates easy determination of the initial anisotropy in sand based on simple laboratory tests and avoids the various arbitrary assumptions on its value made by many previous studies. The model predictions on sand behavior compare well with test data.

Laminated rubber, or elastomeric, bearings fatigue when subjected to repeated cycles of loading. Fatigue in these elements is characterized by the formation of cracks typically originating at the interface of the steel-rubber laminae at the outermost edge of the laminate then propagating at an inclination toward the center of the bearing under subsequent cycling. The presence of fatigue cracks alters the bulging surface of the rubber layers, thereby degrading the stiffness properties of the bearings. Past experimental studies have shown the stiffness degradation of laminated rubber bearings can be significant, i.e., reductions on the order of 20–30%. To date, much of the analytical and experimental research has been focused on the determination of the initiation of fatigue cracking to establish replacement schedules for elastomeric bearing components in aerospace and rail applications. However, in bridge applications elastomeric bearings are likely to fatigue while in service and the level of stiffness degradation could significantly affect the in-service performance and safety of the bridge. To develop an improved understanding of the impact of fatigue cracking on the stiffness degradation of elastomeric bearings, a modeling framework is proposed that builds on previous research to link cycles of loading to stiffness degradation. The modeling framework is implemented in a numerical routine to perform parametric and sensitivity studies to quantify the effect of parameters and factors variations on both the stiffness degradation and fatigue life of elastomeric bearings.

This paper presents a theoretical model for flat cavity expansion in elastic soil. By using the conformal mapping method, the nonaxisymmetric boundary value problem of flat cavity expansion is transformed from the original physical plane into the axisymmetric boundary value problem in the phase plane, which results in a series of closed-form solutions for the stress and displacement induced by the flat cavity expansion. These closed-form solutions are then validated by FEM and provide the basis for the interpretation of the list-off pressure of the flat dilatometer test. Subsequently, a closed-form solution for the list-off pressure in the flat dilatometer test is given. The suitability of the solution for the list-off pressure is validated by comparing the predictions with a series of field test data provided by previous scholars. Good agreement is achieved. The proposed theoretical model improves on the previous empirical method for the interpretation of the list-off pressure in the flat dilatometer test. It also provides a new method for analyzing the nonaxisymmetric cavity expansion problem, improves the theory framework of the conventional cavity expansion theory, and can be seen as an extension of the conventional cavity expansion theory.

This article describes an inverse method for the identification of heterogeneous anisotropic elastic parameters of plate structure from an incomplete modal response. Many efforts in this area have shown that derivatives of the displacement mode shapes or curvature mode shapes are much more sensitive to the heterogeneous parameter distribution of the structure when compared with the mode shapes themselves. Thus, the curvature mode shapes are used widely to quantify the material profile. Following this observation, a strategy based on the error in constitutive equation (ECE) function, which naturally incorporates this fact seamlessly into the identification procedure, is proposed. The identification problem is posed as an optimization problem in that the cost function measures the discrepancy in the constitutive equation, which connects kinematically admissible curvature/strains and dynamically admissible couples/stresses. The resulting system becomes an extended system with primary and Lagrangian variables as the unknown with penalized measurement as the forcing function. The material update then follows by way of constitutive discrepancy, and an explicit update formula is derived. Although the regularization resulting from ill-posedness is achieved through the penalization parameter associated with the modified ECE function, this also helped to incorporate the partial and corrupted data map in the reconstruction strategy. Finally, a few numerical examples are considered to show the applicability of the proposed scheme.

Damage detection for civil structures is limited by several factors including poor signal-to-noise ratios, a large number of unknown parameters, and a limited set of measured responses. Global vibration techniques that track modal parameters often remain insensitive to common forms of structural damage. Moreover, large sets of identified parameters make inverse problems ill-conditioned. To overcome some of these limitations, researchers have advanced substructure identification as a methodology to directly detect local stiffness changes using measured responses to improve damage detection and scalability in civil structures. This paper develops a substructure identification estimator that identifies the story stiffness of a shear building. Concurrent with the estimator derivation, identified parameter confidence intervals are developed and identification performance is predicted. Using the developed estimator, experimental testing is performed on a 3.66-m (12-ft) four-story steel structure subject to base excitation. Several structural configurations are tested where the story-level stiffness is decreased by loosening floor-level connections. These changes simulate damage and are mostly detected by substructure identification within computed confidence intervals. The substructure identified parameters are compared against modal measures and found to be more sensitive to damage. Furthermore, the estimator’s performance follows predictions from the error analysis and motivates future work with identification assisted by structural control.

An energy dissipation mechanism of abalone shells, called sacrificial bonds and hidden length, is simulated and proposed to develop new strategies for base isolation. The concept of integrating this novel energy dispersion mechanism into a conventional linear isolator is proposed. A systematic parametric study is performed to evaluate the influences of the properties of both the isolation layer and the structure on the structural seismic responses to a series of earthquake records. Using the insights gained from the parametric study, an optimization procedure for designing such a bio-inspired isolator is presented based on the multiobjective optimization approach. To demonstrate the advantages of this idea, the optimized bio-inspired isolation system is numerically investigated by first comparing it with the passive isolators such as a high-damping linear isolator and a lead rubber bearing system. The proposed isolator is found to have superior performance to conventional passive isolation systems, especially in cases of near-fault earthquakes. Furthermore, the bio-inspired passive isolator shows comparable performance to a semiactive isolation system under the selected earthquake excitations.

The rocking problem is applicable to a wide variety of structural and nonstructural elements. The current applications range from bridge pier and shallow footing design to hospital and data center equipment, even art preservation. Despite the increasing number of theoretical and simulation studies of rocking motion, few experimental studies exist. Of those that have been published, most are focused on a reduced version of the problem introducing modifications to the physical problem with the purpose of eliminating either sliding, uplift, or the three-dimensional (3D) response of the body. However, all of these phenomena may affect the response of an unrestrained rocking body. The intent of this work is to present a computer vision method that allows for the experimental measurement of the rigid body translation and rotation time histories in three dimensions. Experimental results obtained with this method will be presented to demonstrate that it obtains greater than 97% accuracy when compared against National Institute of Standards and Technology traceable displacement sensors. The work concludes with two example experimental studies of rigid body rocking measured with this method as proof of concept. The experimental results highlight important phenomena predicted in some state-of-the-art models for 3D rocking behavior.

Terrorist attacks are a growing threat worldwide. Explosive devices, the weapon of choice for a majority of these attacks, significantly threaten civilian and military personnel. Seismic ground motions are also associated with catastrophic structural failures, and due to their infrequency, seismic-resilient designs aim at protecting the life-safety of occupants. The area of structural control for seismic hazard mitigation is well-researched and similar strategies that safely concentrate deflection or safely dissipate energy on the global structure hold some merit in the face of blast loading. Although blast and seismic loading are two different phenomena from a fundamental physics perspective, base isolation, as one of the most robust and popular passive control technologies, has significant potential to mitigate damage from other impulsive sources such as blast. The goals of this study can be summarized as (1) demonstrating the potential for base isolation to protect from blast loads, and (2) improving the response of base-isolated structures under blasts without compromising seismic protection. Through numerical simulations of a low-rise structure, beneficial effects of using base isolation to reduce interstory drifts and absolute story accelerations seen in earthquake engineering were also observed for blast loading. Furthermore, the proposed supplemental control devices were able to maintain nominal base isolation performance under smaller excitations while restrict damaging base displacements under larger excitations. Both nonlinear bumpers and tuned-mass dampers were considered as supplemental devices, with the former enforcing safe maximum base displacements and the latter improving overall root-mean-square behavior.

Evaluating controllable damping designs typically requires simulation of the resulting inherently nonlinear closed-loop system because linear design strategies cannot always be reliably used. These analyses typically require many simulations, each a function evaluation in a parameter study or optimization. For complex structural models, these simulations can require significant computational resources. Further, complex structural models requiring repeated solutions of high-order Riccati equations for each function evaluation further exacerbate the computational burden. This paper demonstrates that a reduced-order model for designing the control strategy, resulting in a low-order control law, coupled with the full model of the original system, falls in the class of systems that are mostly linear but with very localized nonlinearities. For such systems, the authors have previously developed an approach that reduces the equations of motion to a low-order nonlinear Volterra integral equation that can be rapidly solved for each function evaluation. The proposed approach is evaluated using two numerical examples, a moderate-order seismically excited isolated building and a high-order wind-excited building, showing that exploiting the localized nature of the nonlinearities can speed up the computations by a factor of approximately 200, and further gains are achieved for the high-order example by basing the dynamic control strategies on reduced-order models but evaluating them with the full system model. The result is a strategy for complex structures that reduces the computation time for a typical controllable damping design parameter study from more than a year to less than a day, making these design studies computationally tractable.

Currently, empirical mode decomposition (EMD) has become a popular data-driven time-frequency analysis method for nonstationary and nonlinear data. However, it is still limited to univariate data due to the number and/or scale misalignment for multivariate data. A newly developed multivariate EMD (MEMD) scheme decomposes multivariate data simultaneously and thus leads to mode alignment and minimizes mode mixing. In addition, an improved amplitude and frequency modulation (AM-FM) decomposition algorithm presented here provides an estimation of a more meaningful instantaneous amplitude and frequency than the widely used Hilbert transform (HT). Both of these facilitate development of a time-frequency analysis framework for multivariate nonstationary and nonlinear data analysis. In this paper, MEMD-based scalogram and coscalogram, and instantaneous frequency spectra and cospectra are proposed to characterize a multivariate nonstationary process. The scalogram and instantaneous frequency spectra capture spectral evolution of each component while the coscalogram and instantaneous frequency cospectra reveal embedded intermittent correlation between two components. Compared with scale-based scalogram and coscalogram, frequency-based instantaneous frequency spectra and cospectra provide a more detailed portrait of multivariate data. The effectiveness of the proposed MEMD-based time-frequency analysis framework is demonstrated by numerical examples of a thunderstorm downburst and an earthquake ground motion. Also, the results from the MEMD-based approach are compared with those based on a continuous wavelet transform, which further reinforces the effectiveness of the proposed framework.

In this paper, an analytical model is developed to determine the torsional-flexural buckling load of a channel column braced by unevenly distributed batten plates. Solutions of the critical-buckling loads were derived for three boundary cases using the energy method in which the rotating angle between the adjacent battens was presented in the form of a piecewise cubic Hermite interpolation (PCHI) for unequally spaced battens. The validity of the PCHI method was numerically verified by the classic analytical approach for evenly battened columns and a finite-element analysis for unevenly battened ones, respectively. Parameter studies were then performed to examine the effects of loading eccentricities on the torsional-flexural buckling capacity of both evenly and unevenly battened columns. Design parameters taken into account were the ratios of pure torsional buckling load to pure flexural–buckling load, the number and position of battens, and the ratio of the relative extent of the eccentricity. Numerical results were summarized into a series of relative curves indicating the combination of the buckling load and corresponding moments for various buckling ratios.

Several existing methods on the extreme value estimation and signal simulation are reviewed in this study with evaluation of their performances in the simulation of the $r$ highest-order extreme values. The limitations of these methods are also discussed. Then, a new method to simulate the $r$ highest-order extreme values of a random process is presented with improvement to these limitations. Extreme value theory is involved in the estimation and Monte Carlo simulation is used in the numerical study. Estimation of the annual top 10 highest 10-min mean wind speeds is conducted for illustration. Results show that the top-order extreme values of the correlated random processes can be well simulated by the proposed method.

The aerodynamic forces on the cable and rivulet are usually determined by the quasi-steady method, which cannot take signature turbulence into account. Furthermore, the oscillation of the cable and rivulet might have significant effects on the aerodynamic forces. In this study, a series of wind tunnel tests were carried out to measure the wind pressures on a cable-rivulet test model, which can keep static and moving statuses utilizing a forced vibration system developed at Hunan University. Wind pressures measured on the test model surface were then used to integrate the drag and lift forces of the cable and rivulet. The results show that vertical vibration of the test model has little effect on the pressure distribution on the cable and rivulet and the mean wind pressures are not very sensitive to the vibration of test model. On the other hand, the oscillation of the rivulet on the cable surface seems to significantly amplify the fluctuating pressures. A sudden decrease of the lift coefficient was observed when the rivulet position is close to 60°, which indicates that classical galloping could be evoked. Eight aerodynamic derivatives of the cable and the rivulet were also identified based on the experimental data, and these aerodynamic derivatives can be further used to determine the unsteady self-excited aerodynamic forces on the cable and rivulet. Overall, this study shows that compared with the quasi-steady aerodynamic forces, the unsteady self-excited aerodynamic forces are more consistent with the exact values.

The theory of hydrodynamic phenomenon of the axisymmetric circular far-wake flow behind a sphere is revisited in this study by the generalized similarity solution of the governing momentum equations to obtain the solutions to the second order in respect of the inverse distance from the sphere center. In case of a laminar wake, the nonlinear equation is derived from the Navier–Stokes equations; while in case of a turbulent wake, it is obtained from the Reynolds averaged Navier–Stokes (RANS) equations and the eddy viscosity concept. The first-order Oseen-type linearization yields solutions well known in the literature, but the second-order solutions obtained in this study are novel.