In this work, a modified surface-effect incorporated beam model based on Gurtin and Murdoch (GM) surface elasticity theory is established by satisfying the required balance equations on surfaces, which is often overlooked by researchers in this field. With the refinement, the proposed model is more rigorous in mathematics and mechanics compared with GM theory-based beam models in literature. To demonstrate the model, the problem for static bending of simply supported beam considering surface effects is solved by applying the general equations derived, and numerical results are obtained and discussed.
相似文献This paper addresses the problem of synchronization control for networked multi-mobile robot systems from the perspective of analytical mechanics. By reformulating the task requirement as a constrained motion problem, a unified synchronization algorithm for networked multi-mobile robot systems with or without leaders is proposed in combination with algebraic graph theory and the Udwadia–Kalaba approach. With the proposed algorithm, the networked mobile robot system can achieve synchronization from arbitrary initial conditions for the leaderless case and realize accurate trajectory tracking with explicitly given reference trajectories for the leader-following case. Numerical simulations of a networked wheeled mobile robot system are performed under different network structures and various trajectory requirements to show the performance of the proposed control algorithm.
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||u||a2=òW |x|-2a|?u|2dx.||u||_a^2=\int_\Omega |x|^{-2a}|\nabla u|^2{d}x. 相似文献
13.
Simon Bogner Jens Harting Ulrich Rüde 《International Journal of Computational Fluid Dynamics》2017,31(10):463-475
Direct numerical simulation of liquid–gas–solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary – in particular, if the bubble–particle aspect ratio is on the order of 10 or larger. Hence, it arises the question of both feasibility and reasonability. In this paper, we present a fully parallel, scalable method for direct numerical simulation of bubble–particle interaction at a size ratio of 1–2 orders of magnitude that makes simulations feasible on currently available super-computing resources. With the presented approach, simulations of bubbles in suspension columns consisting of more than 100,000 fully resolved particles become possible. Furthermore, we demonstrate the significance of particle-resolved simulations by comparison to previous unresolved solutions. The results indicate that fully resolved direct numerical simulation is indeed necessary to predict the flow structure of bubble–particle interaction problems correctly. 相似文献
14.
Wei Cao Changyu Shen Chunjie Zhang Lixia Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(5):363-377
A numerical approach is introduced to solve the viscoelastic flow problem of filling and post-filling in injection molding.
The governing equations are in terms of compressible, non-isothermal fluid, and the constitutive equation is based on the
Phan–Thien–Tanner model. By introducing some hypotheses according to the characteristics of injection molding, a quasi-Poisson
type equation about pressure is derived with part integration. Besides, an analytical form of flow-induced stress is also
generalized by using the undermined coefficient method. The conventional Galerkin approach is employed to solve the derived
pressure equation, and the ‘upwind’ difference scheme is used to discrete the energy equation. Coupling is achieved between
velocity and stress by super relax iteration method. The flow in the test mold is investigated by comparing the numerical
results and photoelastic photos for polystyrene, showing flow-induced stresses are closely related to melt temperatures. The
filling of a two-cavity box is also studied to investigate the viscoelastic effects on real injection molding. 相似文献
15.
In this note, we give constructive upper and lower bounds for the minimal speed of propagation of traveling waves for a nonlocal
delayed reaction–diffusion equation. 相似文献
16.
Zhenyu Xue Jonas Faleskog John W. Hutchinson 《International Journal of Solids and Structures》2013,50(25-26):4258-4269
An extension of the Gurson model that incorporates damage development in shear is used to simulate the tension–torsion test fracture data presented in Faleskog and Barsoum (2013) (Part I) for two steels, Weldox 420 and 960. Two parameters characterize damage in the constitutive model: the effective void volume fraction and a shear damage coefficient. For each of the steels, the initial effective void volume fraction is calibrated against data for fracture of notched round tensile bars and the shear damage coefficient is calibrated against fracture in shear. The calibrated constitutive model reproduces the full range of data in the tension–torsion tests thereby providing a convincing demonstration of the effectiveness of the extended Gurson model. The model reinforces the experiments by highlighting that for ductile alloys the effective plastic strain at fracture cannot be based solely on stress triaxiality. For nominally isotropic alloys, a ductile fracture criterion is proposed for engineering purposes that depends on stress triaxiality and a second stress invariant that discriminates between axisymmetric stressing and shear dominated stressing. 相似文献
17.
With the aim of exploring whether the (1+1)-dimensional coupled nonlinear evolution equations admit abundant soliton interactions, like the cases in the Kadomtsev–Petviashvili II equation, we in this paper study the double Wronskian solutions to the Whitham–Broer–Kaup (WBK) system. We give the parametric condition for two double Wronskians to generate the non-singular, non-trivial and irreducible soliton solutions. Via the asymptotic analysis of two double Wronskians, we show that the soliton solutions of the WBK system is in general linearly combined of fully resonant (M,N)- and (M?1,N+1)-soliton configurations. It turns out that the WBK system can exhibit various complex soliton structures which are different pairwise combinations of elastic, confluent and divergent interactions. From a combinatorial viewpoint, we also explain that the asymptotic solitons of a [(M,N),(M?1,N+1)]-soliton solution are identified by a pair of Grassmannian permutations. 相似文献
18.
Meccanica - The principle of virtual power is used derive a microforce balance for a second-gradient phase-field theory. In conjunction with constitutive relations consistent with a free-energy... 相似文献
19.
20.
A. I. Borodin 《Journal of Applied Mechanics and Technical Physics》2001,42(5):748-756
The problem of gliding descent of a smooth blunted body possessing a lifting force and a heatconducting surface in the Earth's atmosphere is solved. The descent trajectory is represented not only by the altitude and velocity as functions of the flight time but also by angles of attack and sideslip varying with time. Threedimensional equations of a parabolized viscous shock layer for a multispecies mixture of gases are solved jointly with a threedimensional equation of unsteady heat conduction in the solid phase. 相似文献
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