Journal of Engineering Mechanics

Taking inspiration from the basic two-degree-of-freedom (2-DOF) models usually adopted to study base isolation (BI) and tuned mass damper (TMD), a unique main archetype 2-DOF model is here introduced to describe the behavior of general multi-degree-of-freedom (MDOF) frame systems, in which a stiffness discontinuity (disconnection), such as the one that can be identified in BI or TMD, may be inserted. With the aim to evaluate the dynamic enhancement following from such a discontinuity for the two masses of the model, two reference schemes (TMD scheme and BI scheme) are introduced and two particular mean gain parameters are associated with them. These represent the main subject of the parametric analyses presented in this work, based on variable mass and stiffness ratios. These analyses are carried out considering groups of earthquake records collected on the basis of a specific criterion (spectrum compatibility). The results of the parametric analyses are arranged by means of mean gain maps and surfaces that can be directly related to a reference response spectrum. The mean gain maps provide a description of the dynamic performance of the archetype model. In order to extend the results obtained for the archetype models to general MDOF frame systems, a specific equivalence procedure is then introduced. Using such an approach, it is possible to define values of mass and stiffness ratio for a general MDOF systems, and then to use the maps to design the characteristics of the disconnection. The results expressed by the mean gain maps have been confirmed by several simulations carried out with reference to a 6-story shear-type frame, thus showing some practical implications of the research.

The analytical models of two spherical grains contact interactions, typical for several classes of slip and sliding regimes in the experimental testing, are proposed. They analyze the cases for coupling or decoupling the frictional microslip and sliding displacements during the kinematically induced sphere translation along a straight trajectory or the force-induced motion from the initially activated contact zone under constant vertical loading. In the slip mode, the evolution of sphere center horizontal displacement obeys the Mindlin-Deresiewicz theory rules either for the force or kinematically induced transverse motions of the sphere. In the frictional sliding mode, it is demonstrated that for the kinematically induced transverse motion of the sphere, the contact tractions are fully governed by the coupled evolution of slip and sliding displacements. When the account for contact slip velocity and the rate of contact plane rotation is made, then the coupling of slip and sliding modes theoretically results in a simple scaling multiplier imposed on the overlap resulted from the sliding mode. It generates a driving force fluctuation and affects the evolution of contact tractions. For transverse sliding of the sphere under constant vertical load and driving force, the contact tractions are essentially governed by the conditions of static equilibrium and are independent of the displacements generated in the slip mode. In this case, the slip displacement provides only the additive term to the sliding displacement of the sphere center, not affecting contact tractions.

This work studied the coupled stretching and bending deformations of a through-thickness nonelliptical elastic inhomogeneity embedded in an infinite matrix within the context of Kirchhoff isotropic and laminated plate theory. The matrix was subjected to uniform remote membrane stress resultants and bending moments, and was also subjected to a concentrated rotational moment at any position. Our analysis, based on complex variable methods, indicated that when the nonelliptical shape of the inhomogeneity is suitably designed and when three specific conditions on the remote loading are met for a given set of material and geometric parameters characterizing the composite: (1) the elastic inhomogneity is harmonic, (2) the internal stress resultants inside the inhomogeneity are uniform and hydrostatic, and (3) the hoop membrane stress resultant and hoop bending moment on the matrix side are uniform along the inhomogeneity–matrix interface. A couple-loaded rigid harmonic inhomogeneity in the absence of remote loading and in the presence of a concentrated rotational moment at any position in the matrix was also obtained using a similar procedure.

Hydrated cement produces the strength and stiffness of concrete, a widely utilized infrastructural material. Estimation of elastic constants of hydrated cement, a heterogeneous material consisting of numerous constituents, is a complex problem. This paper presents a comprehensive multiscale micromechanical estimation methodology. X-ray diffraction (XRD) investigations along with Rietveld refinements were done to estimate the constituents of hydrated cement. Molecular dynamics investigations were carried out for each individual constituent to determine individual elastic constants. Micro computed tomography (microCT) investigations determined the porosity of the sample at different cross sections and also estimated the pore-size distributions. The Mori–Tanaka homogenization principle was used on the constituent elastic constants to estimate the final elastic constants of the hydrated cement, which were compared with values obtained from experimental investigations in the literature. The methodology demonstrated that consideration of tobermorite (all three phases) and jennite along with the estimated macroporosity can predict the overall stiffness of the cement paste with an error of about 8%.

Superficially, the optimal control problem of a general system may be handled by the stochastic dynamic programming or stochastic maximum principles. The practical application of these two principles, however, is confined to the low-dimensional or weakly nonlinear system due to the difficulty of solving the dynamic programming equation and forward–backward stochastic differential equations with high dimension or strong nonlinearity. To attenuate the solving difficulty, a nonlinear stochastic optimal control method in the Hamiltonian framework has been conceived by taking the low-dimensional averaged system as the controlled system. This method reduces the difficulty of solving equations to some extent, while not including the displacement feedback mechanism in the control force. In this manuscript, a new procedure is proposed to establish the control strategy for vibrating systems with relatively high dimension and strong nonlinearity. By directly separating the control force to conservative and dissipative components and combining the stochastic averaging technique, the functional extreme value problem associated with the original optimal control problem is converted to an extremum value problem of multivariable function. Numerical results on a single-degree-of-freedom Duffing oscillator, a single-degree-of-freedom Van der Pol oscillator, and a two-degree-of-freedom nonlinear system demonstrate the high control effectiveness and efficiency by being comparing with the linear quadratic Gaussian control and nonlinear stochastic optimal control. This direct method not only avoids the difficulty of solving complex differential equations, but also includes the whole information of system displacement and velocity.

A new and simple planar wavefront model is presented for synthesizing the Fourier spectra of the seismic rocking ground motion (i.e., seismic ground rotation about a horizontal axis) at a station near the epicenter by using the corresponding translational motion data. As in the conventional models, the ground motion was assumed to result primarily from the incidence of planar wavefronts of body waves emitted by a point source buried in a homogeneous, elastic half-space. In contrast to the conventional models, however, the spatial variations of both the amplitudes and the incidence angles of the waves were considered. The spatial variation of the amplitudes was formulated by considering the far-field radiation patterns of body waves due to a kinematic shear dislocation point source. The proposed model can therefore accommodate information on the underlying focal mechanism and give the estimates of both in-plane and out-of-plane rocking spectra. It is shown through a numerical study that the proposed model leads to more accurate estimates of rocking spectra than the conventional models over a large range of frequencies, even when the input source information is unavailable.

This study investigated the pore pressure responses of overconsolidated (OC) soils during a piezocone penetration test (PCPT). The influences of overconsolidation ratio (OCR) and hydraulic conductivity were accounted in investigating the generated pore pressures during the PCPT. The modified Cam-clay model and Darcy’s law were incorporated in the quasi-static Biot theory to study the fluid-mechanical interaction during PCPT. The study found that a substantial negative pore pressure could be developed at the ${\mathrm{u}}_2$ position (cone shoulder) for heavily OC soils with low hydraulic conductivity. Moreover, an increase in ${\mathrm{u}}_2$ pore pressure was observed for a hydraulic conductivity range from ${10}^{-10}$ to ${10}^{-8}\mathrm{m}/\mathrm{s}$. This was attributed to the instantaneous dissipation of shear generated negative pore pressure due to the diffusion of positive pore pressure from the ${\mathrm{u}}_1$ position (cone face), where the diffusion process is faster in high hydraulic conductivity condition. The findings of this study could explain a complicated multiphysics problem, and therefore may enhance the general understanding of PCPT results and the accuracy of specialized techniques such as on-the-fly estimation of the hydraulic conductivity of soils.

Bolts are often used to hold flat components together while transmitting a tensile (separating) load. When the components are relatively rigid and the transmitted load exceeds the combined bolt preloads, complete separation of the components can occur, resulting in the load simply being shared among the bolts. However when the components are flexible, the tensile load may cause elastic partial separation, in which case there is a concentrated contact force at the separation boundary. This prying force adds significantly to the load carried by the bolts. It therefore creates an unexpected risk of bolt yielding accompanied by a deleterious tension loss upon unloading. In the case of repeated loading it can cause bolt fatigue. In this paper, we perform a novel receding contact beam analysis of prying action in the bolted joint of a cantilever-loaded beam/plate. The flexural deformation of the plate induces prying forces that result in a substantial increase in the bolt force well above that which would be predicted by the simple beam reaction force. The design parameters are the joint dimensions, material properties, the bolt preload, and the applied force. It is modeled using two beam theories (Euler–Bernoulli and Timoshenko) to provide insight into the roles of the main parameters. A comparison with a finite-element analysis of the three-dimensional elasticity problem shows a reduction in the bolt force of 10%–26% compared with the beam theories, which are more conservative. This difference is consistent with the idea that a one-dimensional beam model is artificially stiffened compared to a full three-dimensional analysis.

This paper developed a nonlinear model for analysis of full-locked coil ropes under high external radial forces, in particular for prediction of deformations, stresses, and strains. This nonlinear model is based on homogenized layers and consists of the mathematical model in a generalized plane strain approach and the nonlinear model of orthotropic material properties. The material properties of each layer can be determined in the model in the radial and circumferential directions independently. The nonlinear characteristics of material properties have a significant effect on the mechanical behavior when multilayered wire strands are under high external pressure, e.g., as in the case of clenching. These nonlinearities considered in the model cover the contact mechanics of wires within and between layers, including geometrical and material nonlinearities for line and point contact as well as initial gaps between wires. The performance of the developed nonlinear model was presented and compared with experimental data and with a conventional linear approach. The predictions based on this nonlinear model matched the experimental data closely. The sensitivity of the results to geometrical tolerances was demonstrated. The results showed clearly that a linear approach is not appropriate for the investigated problem. The proposed nonlinear model is an accurate and effective method for calculation of the response of a rope under high external radial forces. It can be applied to any multilayered wire strand.

The aim of this work is to significantly accelerate the process of parameter optimization of cardiac mechanics problems. This is achieved by coupling a reduced-order method, called the proper orthogonal decomposition with interpolation (PODI), with the frequently used Levenberg-Marquardt method (LVM). The PODI method involves a database to generate solution fields of the problem at hand. This database consists of precomputed solution fields such as displacement, strain, and stress fields that are associated with a parametric domain. When coupling PODI with LVM, the parametric domain of the database coincides with the parametric bounds of LVM. For each optimization step, the solutions corresponding to the updated set of parameters and their perturbations can then be obtained by using these data sets for the purpose of interpolation in the low-dimensional space. Two cardiac problems are investigated to compare the PODI-LVM method with a conventional approach where LVM makes use of full-scale simulations to compute the update of the parameters. Here, this is the element-free Galerkin method. In the first example, the diastolic filling of a left-ventricle heart model is considered and in the second one, a biventricle model is studied. In both cases, optimized values of the parameters of the cardiac constitutive equation are found that match the given diastolic pressure-volume curve. The PODI-LVM optimization procedure results in a computation speed-up factor of 900 on a standard desktop computer at high levels of accuracy.

We explore the shape effect of microparticles (MPs) on their margination behaviors in blood flow through three-dimensional numerical simulations. Six different shapes of MPs were considered with identical volume, such as sphere, rod, cubic, disk, oblate, and prolate with different aspect ratios. These MPs were immersed in the blood plasma, which consisted of a suspension of red blood cells (RBCs). A simple shear flow was applied with moderate shear rate ($200{\mathrm{s}}^{-1}$). The fluid flow and immersed particles (RBCs and MPs) were solved by the lattice Boltzmann method (LBM) and lattice spring model, respectively. The fluid–structure interaction was coupled by the immersed boundary method. Additionally, we adopted a stochastic model to capture the adhesive behavior of MPs near the vessel wall for ligand–receptor binding. Without near-wall adhesion, the spherical particles demonstrated the strongest margination in the blood flow. It can be attributed to the large collision displacement with RBCs and small migration distance in the cross-stream direction under shear flow of spherical particles. Furthermore, under the influence of near-wall adhesion, the margination of differently shaped MPs was examined. Interestingly, the adhesion can either promote or impede the margination behavior depending on the shapes of MPs. When the major axes of MPs are smaller than or comparative to the thickness of the cell-free layer in the flow channel, the adhesion can promote margination of these MPs, while for MPs with large major axes, due to the near-wall adhesion effect, the reduced tumbling frequencies enable them to have enough time to interact with RBCs. In turn, the long interaction with RBCs can drag these MPs to the central stream of blood flow, impeding their margination. However, the prolate particles demonstrated distinct behaviors. Apart from tumbling, the transition to precession of prolate particles near the vessel wall results in the enhancement of margination. Overall, the spherical MPs outperform other nonspherical MPs for their high margination propensity under the influence of near-wall adhesion and moderate shear flow rate. This study might offer theoretical guidance to design MP-based drug carriers in blood flow with high efficacy.