Periodicity and multi-periodicity generated by impulses in delayed differential inclusions: application to discontinuous Nicholson’s blowflies model

Nonlinear Dynamics - Based on Krasnoselskii’s fixed point theorem of set-valued maps type, this paper studies the existence and multiplicity of periodic positive solutions for delayed...     

Strain gradient solution for a finite-domain Eshelby-type plane strain inclusion problem and Eshelby’s tensor for a cylindrical inclusion in a finite elastic matrix

A solution for the finite-domain Eshelby-type inclusion problem of a finite elastic body containing a plane strain inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). The formulation is facilitated by an extended Betti’s reciprocal theorem and an extended Somigliana’s identity based on the SSGET and suitable for plane strain problems. The disturbed displacement field is obtained in terms of the SSGET-based Green’s function for an infinite plane strain elastic body, which differs from that in earlier studies using the three-dimensional Green’s function. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is suppressed. The problem of a cylindrical inclusion embedded concentrically in a finite plane strain cylindrical elastic matrix of an enhanced continuum is analytically solved for the first time by applying the general solution, with the Eshelby tensor and its average over the circular cross section of the inclusion obtained in closed forms. This Eshelby tensor, being dependent on the position, inclusion size, matrix size, and a material length scale parameter, captures the inclusion size and boundary effects, unlike existing ones. It reduces to the classical elasticity-based Eshelby tensor for the cylindrical inclusion in an infinite matrix if both the strain gradient and boundary effects are not considered. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing with the increase of the inclusion size, and the boundary effect is vanishing as the inclusion volume fraction becomes sufficiently low.     

The self-stabilization effect of lattice’s historical flow in a new lattice hydrodynamic model

In order to reveal the self-stabilization effect of the lattice’s historical information on traffic flow, a new lattice hydrodynamic model with consideration of the considered lattice’s historical flow is proposed. The impact of the lattice’s historical flow on traffic stability is uncovered through theoretical analyses and numerical simulation. Through theoretical analyses, the linear stability condition of the new model is obtained, and the nonlinear mKdV equation is derived to describe traffic jamming transition of the new model near the critical point. From numerical simulation, the theoretical analyses are verified and it is shown that the traffic stability can be enhanced by considering the current lattice’s self-information of its historical flow.     

Measurement of Temperature-Dependent Young’s Modulus at a Strain Rate for a Molding Compound by Nanoindentation

The mechanical properties of a molding compound on a packaged integrated circuit (IC) were measured by spherical nanoindentation using a 50 μm radius diamond tip. The molding compound is a heterogeneous material, consisting of assorted diameters of glass beads embedded in an epoxy. Statistical analysis was conducted to determine the representative volume element (RVE) size for a nanoindentation grid. Nanoindentation was made on the RVE to determine the effective viscoelastic properties. The relaxation functions were converted to temperature-dependent Young’s modulus at a given strain rate at several elevated temperatures. The Young’s modulus values at a given strain rate from nanoindentation were found to be in a good agreement with the corresponding data obtained from tensile samples at or below 90 °C. However, the values from nanoindentation were significantly lower than the data obtained from tensile samples when the temperature was near or higher than 110 °C, which is near the glass transition. The spatial distribution of the Young’s modulus at a given strain rate was determined using nanoindentation with a Berkovich tip. The spatial variation of the Young’s modulus at a given strain rate is due to the difference in nanoindentation sites (glass beads, epoxy or the interphase region). A graphical map made from an optical micrograph agrees reasonably well with the nanoindentation results.     

Rabotnov’s two-layer model of a shell and critical time of shell buckling during creep

The main propositions of Rabotnov’s two-layer model of a shell are given. It is shown that the Rabotnov’s functional can be obtained from the mixed variational principle of creep theory. The notion of critical time is introduced and a procedure for obtaining an explicit formula for it using a variational equation is described.     

Refinement of a global model for the Earth’s gravitational field using airborne gravimetry data

An algorithm for combining airborne gravimetry data with the data supplied by a global model of the Earth’s gravitational field is considered. The global model is specified by a spherical wavelet decomposition. An optimal guaranteed estimation of the wavelet coefficients for the gravitational field is used.     

Dynamical behavior of a stochastic Nicholson’s blowflies model with distributed delay and degenerate diffusion

Nonlinear Dynamics - The mathematical model with time delay is often more practical because it is subject to current and past state. What remains unclear are the details, such as how time delay and...     

Bingham’s model in the oil and gas industry

Yield stress fluid flows occur in a great many operations and unit processes within the oil and gas industry. This paper reviews this usage within reservoir flows of heavy oil, drilling fluids and operations, wellbore cementing, hydraulic fracturing and some open-hole completions, sealing/remedial operations, e.g., squeeze cementing, lost circulation, and waxy crude oils and flow assurance, both wax deposition and restart issues. We outline both rheological aspects and relevant fluid mechanics issues, focusing primarily on yield stress fluids and related phenomena.     

Topology optimization of a flexible multibody system with variable-length bodies described by ALE–ANCF

Recent years have witnessed the application of topology optimization to flexible multibody systems (FMBS) so as to enhance their dynamic performances. In this study, an explicit topology optimization approach is proposed for an FMBS with variable-length bodies via the moving morphable components (MMC). Using the arbitrary Lagrangian–Eulerian (ALE) formulation, the thin plate elements of the absolute nodal coordinate formulation (ANCF) are used to describe the platelike bodies with variable length. For the thin plate element of ALE–ANCF, the elastic force and additional inertial force, as well as their Jacobians, are analytically deduced. In order to account for the variable design domain, the sets of equivalent static loads are reanalyzed by introducing the actual and virtual design domains so as to transform the topology optimization problem of dynamic response into a static one. Finally, the novel MMC-based topology optimization method is employed to solve the corresponding static topology optimization problem by explicitly evolving the shapes and orientations of a set of structural components. The effect of the minimum feature size on the optimization of an FMBS is studied. Three numerical examples are presented to validate the accuracy of the thin plate element of ALE–ANCF and the efficiency of the proposed topology optimization approach, respectively.     

A single helicopter’s flying model in the low airspace with a parallel electrical wire network

In this paper, we use car-following theory to propose a model with consideration of multi-telegraph poles and electrical wires to describe a single helicopter’s flying behavior in the low airspace with a parallel electrical wire network. The numerical results show that the proposed model can describe the qualitative effects of the parallel electrical wire network on the evolutions of a helicopter’s speed, safe distances for the telegraph poles and electrical wires and safe sphere. These results can help us to better understand the helicopter’s flying behavior in the low airspace with a parallel electrical wire network.     

Chaos in a tethered satellite system induced by atmospheric drag and Earth’s oblateness

Nonlinear Dynamics - This paper describes the chaos behavior of an in-plane tethered satellite system induced by atmospheric drag and the Earth’s oblateness. A commonly used model, the...     

Optimization of a pentagonal cross section of the truck crane boom using Lagrange’s multipliers and differential evolution algorithm

The cross sections of truck crane booms are complex box-like cross sections which should provide continuous stress distribution. It is difficult to analytically determine the optimal relations among geometric parameters of such cross sections. The paper deals with the method for determination of relations among geometric parameters in order to reach the optimal shape of the cross section. The method is based on Lagrange’s multipliers used for determination of extreme values. The optimization of geometric parameters has been also done by the algorithm of Differential Evolution (DE). The optimization of cross section is based on the strength criterion. The results of applied methods have been verified by means of numerical example for an existing solution. The comparative analysis of the results of both methods has been done, too.     

Conservation form of Helbing’s fluid dynamic traffic flow model

A standard conservation form is derived in this paper. The hyperbolicity of Helbing’s fluid dynamic traffic flow model is proved, which is essential to the general analytical and numerical study of this model. On the basis of this conservation form, a local discontinuous Galerkin scheme is designed to solve the resulting system efficiently. The evolution of an unstable equilibrium traffic state leading to a stable stop-and-go traveling wave is simulated. This simulation also verifies that the model is truly improved by the introduction of the modified diffusion coefficients, and thus helps to protect vehicles from collisions and avoide the appearance of the extremely large density.     

Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing

In this paper, we studied the effect of driver’s anticipation with passing in a new lattice model. The effect of driver’s anticipation is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. Using nonlinear stability analysis, we obtained the range of passing constant for which kink soliton solution of mKdV equation exist. For smaller values of passing constant, uniform flow and kink jam phase are present on the phase diagram and jamming transition occurs between them. When passing constant is greater than the critical value depending on the anticipation coefficient, jamming transitions occur from uniform traffic flow to kink-bando traffic wave through chaotic phase with decreasing sensitivity. The theoretical findings are verified using numerical simulation which confirm that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model.