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The boundary condition of a 3D continuum model for a quasi 2D plane strain condition
(2021-06-01)
Chaiyaput, Salisa Fern
;
Sugimoto, M.
The half-model has been used in the finite element analysis, based on the symmetric condition against the tunnel’s longitudinal, vertical plane, but this design concept cannot apply to a staggered lining. Therefore, the authors have proposed a multi-ring model to present the segmental lining behavior of a 3D continuum ground model in the case of staggered building, but the proposed 12-ring model shows the different axial force distributions in circumferential directions between the center of the model and the end of the model, especially in cases of soft soil. Accordingly, to make clear, the mechanism of the above difference and to establish the analysis condition of the proposed model for quasi 2D plane strain condition, this paper evaluates the influence of boundary condition on the transverse cross section at the end of the segmental lining on the segmental lining behavior, based on the analyzed axial force and bending moment in soft and stiff ground conditions using both the 2-ring model and a 12-ring model. As a result, it was confirmed that the proposed 2-ring model could simulate the segmental lining behavior under quasi 2D plane strain condition.
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Boundary conditions and behavior of the macroscopic fundamental diagram based network traffic dynamics: A control systems perspective
(2018-05-01)
Zhong, R. X.
;
Huang, Y. P.
;
Chen, C.
;
Lam, W. H.K.
;
Xu, D. B.
Macroscopic fundamental diagram (MFD), establishing a mapping from the network flow accumulation to the trip completion rate, has been widely used for aggregate modeling of urban traffic network dynamics. Based on the MFD framework, extensive research has been dedicated to devising perimeter control strategies to protect the network from gridlock. Recent research has revealed that the stochasticity and time-varying nature of travel demand can introduce significant scattering in the MFD, thus reducing the definition of the MFD dynamics. However, this type of demand effect on the behavior of the MFD dynamics has not been well studied. In this article, we investigate such effect and propose some appropriate boundary conditions to ensure that the MFD dynamics are well-defined. These boundary conditions can be regarded as travel demand adjustment in traffic rationing. For perimeter control design, a set of sufficient conditions that guarantee the controllability, an important but yet untouched issue, are derived for general multi-region MFD systems. The stability of the network equilibrium and convergence of the network dynamics are then analyzed in the sense of Lyapunov. Both theoretical and numerical results indicate that the network traffic converges to the desired uncongested equilibrium under proper boundary conditions in conjunction with proper control measures. The results are consistent with some existing studies and offer a control systems perspective regarding the demand-oriented behavior analysis of MFD-based network traffic dynamics. A surprising finding is that if the control purpose is to regulate the traffic to a desired level of service, the perimeter control gain can be simply chosen as its desired steady state, that is, the control gain is a constant and can be implemented as proportional control. This property sheds light on the road pricing design based on the MFD framework by minimizing the gap between the actual traffic state and the desired traffic state.
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Generalised approach for transient computation of start-up pressure-driven viscoelastic flow
(2008-05-16)
Keshtiban, I. J.
;
Puangkird, B.
;
Tamaddon-Jahromi, H.
;
Webster, M. F.
This article investigates a generalised solution approach for transient viscoelastic flows employing consistent dynamic boundary conditions. Such a procedure vaunts three key properties-independence of reference frame, problem dimension and constitutive equation type. Three different boundary condition protocols have been investigated, two transient and one steady, through a time-dependent incremental pressure-correction formulation with a hybrid finite element/finite volume scheme. These procedures are compared and contrasted through application to pressure-driven start-up flow in 4:1 planar rounded-corner contractions for two fluid models, Oldroyd and pom-pom. Some novel differences are highlighted in the dynamic evolution of flow structure and the impact upon stress generation, as a consequence of protocol, whether steady or transient, under flow-rate or force-driven control. Overshoot-undershoot kinematics observed under any particular flow protocol have been mutually linked to the precise boundary conditions imposed. Under flow-rate controlled protocols, large oscillations are stimulated in pressure, which may disturb computational tractability. Comparatively, the evolution of force-driven flow can provide considerably smoother development patterns in pressure, with largest attached vortices and strong oscillatory vortex structure features. Specifically under transient flow-rate control, some distinct complex flow features have emerged, including reversed flow, followed by vortex detachment and reattachment. For pom-pom SXPP-fluids and force-driven protocol, transient flow development is observed to be relatively smooth and non-oscillatory at a Weissenburg number of unity. At larger levels of Weissenburg number, transient overshoots have been detected in characteristic variables of stress and molecular backbone-stretch. In addition, Weissenburg number continuation to steady state, has been shown to disconnect the dynamics between velocity and stress, which prevents highly elastic localised regions from developing. © 2008 Elsevier B.V. All rights reserved.

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