On the modeling of pedestrian motion

A model for the simulation of pedestrian flows and crowd dynamics has been developed. The model is based on a series of forces, such as: will forces (the desire to reach a place at a certain time), pedestrian collision avoidance forces, obstacle/wall avoidance forces; pedestrian contact forces, and obstacle/wall contact forces. Except for the will force, it is assumed that for any given pedestrian these forces are the result of only local (nearest neighbour) situations. The near-neighbour search problem is solved by an efficient incremental Delaunay triangulation that is updated at every timestep. In order to allow for general geometries a so-called background triangulation is used to carry all geographic information. At any given time the location of any given pedestrian is updated on this mesh. The results obtained to date show that the model performs well for standard benchmarks, and allows for typical crowd dynamics, such as lane forming, overtaking, avoidance of obstacles and panic behaviour.     

The contact problem with the bulk application of intermolecular interaction forces (a refined formulation)

A refined formulation of the contact problem when there are intermolecular interaction forces between the contacting bodies is considered. Unlike the traditional formulation, it is assumed that these forces are applied to points within the body, rather than to the surface of the deformable body as a contact pressure, and that the body surface is load-free. Solutions of the contact problems for a thin elastic layer attached to an absolutely rigid substrate and for an elastic half-space are analysed. The refined and traditional formulations of the problem when there is intermolecular interaction are compared. ©2013     

An investigation of the impact and penetration of solids of revolution into soft earth

The numerical method proposed earlier in [1] is developed to solve problems of the impact and penetration of rigid and deformable bodies of revolution into soft soil, which are described by Grigoryan's model [2]. The effect of the surface Coulomb friction, the bulk compressibility and the shear strength of soft soil on the forces of resistance and contact pressures in the contact zone is analysed. The results of numerical solutions of problems in a coherent formulation are compared with analytical relations and experimental data on the determination of the forces and coefficients of resistance to the penetration of impactors of different shapes into soft soil.     

A reformulation of the nonsmooth approaches of M. Frémond and J.J. Moreau for rigid body dynamics

This paper deals with the nonsmooth dynamics of a rigid bodies system. The proposed theory is inspired by the formalism of J.J. Moreau and that of M. Frémond and relies on the notion of percussion which is the integral of the contact force during the duration of the collision. Contrary to classical discrete element models, it is here assumed that percussions can be expressed as a function of only the velocity before the impact. This assumption is checked for the usual mechanical constitutive laws for collisions derived from a pseudopotential of dissipation or the Coulomb friction law. Motion equations are then reformulated taking into account simultaneous collisions of solids. A mathematical study of the new model is presented: the existence and uniqueness of the solution are discussed according to the regularity of both the forces (Lebesgue‐density occurring during the regular evolution of the system) and the percussions (Dirac‐density describing the collision). In the light of the principles of thermodynamics, a condition on the internal percussion assuring that the collision is thermodynamically admissible, is established. Finally, an application of this new model to the motion of a system of rigid disks, including simultaneous collisions is presented.     

Analysis of a nonlinear beam in contact with a foundation

The paper investigates the contact between a nonlinear dynamic Gao beam and a rigid or reactive foundation. The contact is modeled with the normal compliance condition for the deformable foundation and with the Signorini condition for the rigid foundation. The existence and uniqueness of the weak solution for the problem with normal compliance are obtained. The solution of the Signorini condition for the rigid foundation is obtained by passing to the limit when the normal compliance approaches infinity.     

Hybrid simulation strategy for multiple planar collisions with changing topologies and local deformation

The development of a hybrid strategy for the simulation of multiple plastic-elastic collisions is presented. The strategy attempts to bridge the gap between finite element methods (FEM), which typically require excessively long computation times for multiple impact simulations, and lumped parameter approaches that cannot provide accurate local deformation information. The proposed strategy employs a finite element routine solely to simulate the impact phase, thereby obtaining detailed local deformation information. The simulation of the flight phase between impacts, however, proceeds under rigid body dynamics, resulting in significant reduction in computation time. The transfer of control between FEM and rigid body dynamics is automatic and the points of contact need not be known a priori. The progressive object internal plastic strain, determined from FEM, is retained from one impact to the next, thereby ensuring a certain degree of continuity of the physical properties of the body. An example is presented to demonstrate the efficacy of this approach.     

Modelling of unilateral constraints using power-based restriction functions within Lagrangian mechanics

The consideration of unilateral contacts within multi-body systems is a common but also difficult task. Established modelling approaches such as the rigid body theory or the Hertzian contact are suitable for single-body systems but show serious problems with increasing system complexity. Indeed, there are different approaches to extend the existing models to multi-body systems, but with a growing number of contacts and the consideration of tangential friction, those enhancements are hardly applicable, showing numeric problems or becoming unmanageable. Thus, to overcome these limitations, a new modelling approach for unilateral contacts defined by power-based restriction functions is proposed in this contribution. The proposed contact model is based on continuous functions, making it numerically robust as well as applicable within Lagrangian mechanics. The approach is easily applicable and even remains manageable for multiple contacts since each constraint can be independently adapted by four physical parameters. The simple applicability and generalizability of the approach is demonstrated by several examples.     

An atomic interaction-based continuum model for computational multiscale contact mechanics

A computational multiscale contact mechanics model is presented which describes the interaction between deformable solids based on the interaction of individual atoms or molecules. The contact model is formulated in the framework of large deformation continuum mechanics and combines the approaches of molecular modelling [1] and continuum contact mechanics [2]. In the following a brief overview of the contact model is given. Further details can be found in [3], [4] and [5]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Macroscopic modeling and simulations of room evacuation

We analyze numerically two macroscopic models of crowd dynamics: the classical Hughes model and the second order model being an extension to pedestrian motion of the Payne–Whitham vehicular traffic model. The desired direction of motion is determined by solving an eikonal equation with density dependent running cost, which results in minimization of the travel time and avoidance of congested areas. We apply a mixed finite volume-finite element method to solve the problems and present error analysis for the eikonal solver, gradient computation and the second order model yielding a first order convergence. We show that Hughes’ model is incapable of reproducing complex crowd dynamics such as stop-and-go waves and clogging at bottlenecks. Finally, using the second order model, we study numerically the evacuation of pedestrians from a room through a narrow exit.     

A solution method for the sub-surface stresses and local deflection of a semi-infinite inhomogeneous elastic medium

This paper proposes analytical Fourier series solutions (based on the Airy stress function) for the local deflection and subsurface stress field of a two-dimensional graded elastic solid loaded by a pre-determined pressure distribution. We present a selection of numerical results for a simple sinusoidal pressure which indicates how the inhomogeneity of the solid affects its behaviour. The model is then adapted and used to derive an iterative algorithm which may be used to solve for the contact half width and pressure induced from contact with a rigid punch. Finally, the contact of a rigid cylindrical stamp is studied and our results compared to those predicted by Hertzian theory. It is found that solids with a slowly varying elastic modulus produce results in good agreement with those of Hertz whilst more quickly varying elastic moduli which correspond to solids that become stiffer below the surface give rise to larger maximum pressures and stresses whilst the contact pressure is found to act over a smaller area.     

不同行为风格下路段行人与机动车行为博弈分析

针对路段过街行人与机动车的博弈决策行为,考虑不同交通行为风格下行人的过街特征和驾驶人的驾驶行为习惯等影响因素,开展路段行人交通行为风格调查,掌握不同交通行为风格下路段行人的过街特征,构建非合作动态人车博弈模型.通过分析不同策略下行人与驾驶人的收益,求解纳什均衡,得到不同策略下行人与驾驶人的最优策略.为解决路段行人与机动车冲突提供新的思路.     

Dynamic navigation field in the social force model for pedestrian evacuation

This paper presents a generalized walking cost distribution to determine a dynamic navigation field in the social force model for pedestrian evacuation. The local walking cost per unit distance of movement includes the cost associated with travel time and other additional costs incurred by pedestrians to avoid colliding with obstacles in a dynamic environment. In the dynamic navigation field, pedestrians expect to choose an optimal path with the lowest walking cost to reach their target destination reactively based on available instantaneous information. The social force model with the dynamic navigation field is validated by comparing the simulation results with empirical observations. The fundamental diagrams for observations and simulation data agree well, which indicates the effectiveness of the model. Numerical results show that the model with the dynamic navigation field can reproduce typical stages of the dynamics of pedestrian evacuation, such as self-organized arching and queuing phenomena, and can capture the route choice and exit choice behaviors of pedestrians during the evacuation process. Compared to the model with the static navigation field, the model with the dynamic navigation field can reduce the total evacuation time of the room and save the required CPU time for a large group of pedestrians. Furthermore, the strong tendency to avoid local high-density regions (i.e., minimizing collisions) can also reduce the total evacuation time under the same conditions.     

A mixed variational formulation for a class of contact problems in viscoelasticity

We consider a deformable body in frictionless unilateral contact with a moving rigid obstacle. The material is described by a viscoelastic law with short memory, and the contact is modeled by a Signorini condition with a time-dependent gap. The existence and uniqueness results for a weak formulation based on a Lagrange multipliers approach are provided. Furthermore, we discuss an efficient algorithm approximating the weak solution for the more general case of a two-body contact problem including friction. In order to illustrate the theory we present two numerical examples in 3D.     

A neural network model for enhanced operation of midblock signalled pedestrian crossings

UK transport policy has shifted dramatically in recent years. The new policy direction to promote walking as an alternative to car for short trips. Midblock signalled pedestrian crossings are a common method of resolving the conflict between pedestrians and vehicles. This paper considers alternative operating strategies for midblock signalled pedestrian crossings that are more responsive to the needs of pedestrians without increasing the delay to motorists and freight traffic. A succession of artificial neural network (ANN) models is developed and factors influencing the performance of pedestrian gap acceptance models both in terms of accuracy and processing requirements are considered in detail. The paper concludes that a feedforward ANN using backpropagation can deliver a gap acceptance model with a high degree of accuracy with acceptable constraints.     

Static frictional indentation of an elastic half-plane by a rigid unsymmetrical punch

Static rigid 2-D indentation of a linearly elastic half-plane in the presence of Coulomb friction which reverses its sign along the contact length is studied. The solution approach lies within the context of the mathematical theory of elastic contact mechanics. A rigid punch, having an unsymmetrical profile with respect to its apex and no concave regions, both slides over and indents slowly the surface of the deformable body. Both a normal and a tangential force may, therefore, be exerted on the punch. In such a situation, depending upon the punch profile and the relative magnitudes of the two external forces, a point in the contact zone may exist at which the surface friction changes direction. Moreover, this point of sign reversal may not coincide, in general, with the indentor's apex. This position and the positions of the contact zone edges can be determined only by first constructing a solution form containing the three problem's unspecified lengths, and then solving numerically a system of non-linear equations containing integrals not available in closed form.The mathematical procedure used to construct the solution deals with the Navier-Cauchy partial differential equations (plane-strain elastostatic field equations) supplied with boundary conditions of a mixed type. We succeed in formulating a second-kind Cauchy singular integral equation and solving it exactly by analytic-function theory methods.Representative numerical results are presented for two indentor profiles of practical interest—the parabola and the wedge.     

Harmonic decomposition analysis of contact mechanics of bonded layered elastic solids

The paper presents an iterative method for obtaining footprint, pressure distribution, local deformation and sub-surface stress field for the contact between a rigid cylindrical indenter and an elastic flat substrate. The methodology is applicable for semi-infinite, as well as for thin or thick bonded elastic layered solids with high or low elastic moduli. All findings are in accord with the observed behaviour of hard wear resistant and soft solid lubricating coatings. It is shown that the decomposed contact pressure distribution into a series of harmonic waves induces sub-surface stress fields that decay into the depth of the solid according to their wavelengths. Consequently, conditions vis-à-vis fatigue spalling and adhesion performance may be predicted for given thickness of layered bonded elastic solids.     

Non-local first-order modelling of crowd dynamics: A multidimensional framework with applications

In this work a physical modelling framework is presented, describing the intelligent, non-local, and anisotropic behaviour of pedestrians. Its phenomenological basics and constitutive elements are detailed, and a qualitative analysis is provided. Within this common framework, two first-order mathematical models, along with related numerical solution techniques, are derived. The models are oriented to specific real world applications: a one-dimensional model of crowd–structure interaction in footbridges and a two-dimensional model of pedestrian flow in an underground station with several obstacles and exits. The noticeable heterogeneity of the applications demonstrates the significance of the physical framework and its versatility in addressing different engineering problems. The results of the simulations point out the key role played by the physiological and psychological features of human perception on the overall crowd dynamics.     

无信号控制路口行人过街行为特征及博弈模型分析

过城市实地行人问卷调查及过街行为分析,描述了行人过街重要行为特征,在此基础上,引入了交通工程相关结果,针对无信号控制路口行人过街问题,构建了行人先行和车辆先行的扩展式行人过街冲突博弈模型。纳什均衡分析结果揭示了行人过街冲突的机理,并给出了各种冲突情况下相应参数临界分析。预期结果对行人过街设施的管理与建设也具有意义。