Virtual Force Method Research Articles

Three-dimensional liquid sloshing in a tank with baffles

A numerical model has been developed to study three-dimensional (3D) liquid sloshing in a tank with baffles. The numerical model solves the spatially averaged Navier–Stokes equations, which are constructed on a non-inertial reference frame having six degree-of-freedom (DOF) of motions. The large-eddy-simulation (LES) approach is employed to model turbulence by using the Smagorinsky sub-grid scale (SGS) closure model. The two-step projection method is employed in the numerical solutions, aided by the Bi-CGSTAB technique to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate volume-of-fluid (VOF) method is used to track the distorted and broken free surface. The baffles in the tank are modeled by the concept of virtual boundary force (VBF) method. The numerical model is first validated against the available analytical solution and experimental data for two-dimensional (2D) liquid sloshing in a tank without baffles. The 2D liquid sloshing in tanks with baffles is then investigated. The numerical results are compared with other results from available literatures. Good agreement is obtained. Finally, the model is used to study 3D liquid sloshing in a tank with vertical baffles. The effect of the baffle is investigated and discussed.

Dynamic Analysis and Distributed Control of the Tetrobot Modular Reconfigurable Robotic System

Reconfigurable robotic systems can be adapted to different tasks or environments by reorganizing their mechanical configurations. Such systems have many redundant degrees of freedom in order to meet the combined demands of strength, rigidity, workspace kinematics, reconfigurability, and fault tolerance. In order to implement these new generations of robotic system, new approaches must be considered for design, analysis, and control. This paper presents an efficient distributed computational scheme which computes the kinematics, dynamics, redundancy resolution, and control inputs for real-time application to the control of the Tetrobot modular reconfigurable robots. The entire system is decomposed into subsystems based on a modular approach and Newton's equations of motion are derived and implemented using a recursive propagation algorithm. Two different dynamic resolution of redundancy schemes, the centralized Jacobian method and the distributed virtual force method, are proposed to optimize the actuating forces. Finally, distributed dynamic control algorithms provide an efficient modular implementation of the control architecture for a large family of configurations.

Green's function for steady-state heat conduction in a bimaterial composite solid

The derivation of a Green's function for steady-state heat conduction in anisotropic bimaterials is presented. The Green's function is obtained through a Fourier representation to obtain both free-space, singular parts and region-dependent, regular parts. To obtain the region-dependent parts of the Green's function, the homogeneous solution is written using the virtual force method. Full details of the necessary inversion integrals are provided. The Green's function is shown to degenerate to the usual logarithmic potential for steady-state heat conduction in isotropic solids. The normal derivatives necessary for implementation of the Green's function in boundary integral equations are provided, and an example calculation of the Green's function in a quartz-copper material system is presented.

A classical virtual work force method for time-harmonic eddy-current analysis

The calculation of accurate and consistent forces is an essential part of the computational analysis and design of many time-harmonic eddy-current systems. While most of the magnetostatic force formulations have been extended to quasi-static applications, a viable equivalent to the multiple solution Classical Virtual Work method (CVW) has not been established. An effective and efficient CVW-type method for the calculation of time-averaged net forces and torques in time-harmonic eddy-current systems is derived. The computational performance of the method is tested and evaluated using finite element analysis.

Shakedown Analysis in Plastic Design of Steel Structures

In this paper, a virtual force method for solving shakedown limit λs is introduced. The elastic deformations of a structure are taken as the virtual displacements of the residual moment in the structure so that the virtual work equations of the residual moment can be expressed and solved by a mathematical programming method. It is mentioned that comprehensive combinations of failure mechanisms are not necessary for the solution and thus it is most suitable for computational analysis.