INTERPOLATION OF RIGID-BODY MOTION AND GALERKIN METHODS FOR FLEXIBLE MULTIBODY DYNAMICS

Traditionally, flexible multibody dynamics problems are formulated as initial value problems: initial states of the system are given and solving for the equations of motion yields the dynamic response. Many practical problems, however, are boundary rather than initial value problems; two-point and periodic boundary problems, in particular, are quite common. For instance, the trajectory optimization of robotic arms and spacecrafts is formulated as a two-point boundary value problem; determination of the periodic dynamic response of helicopter and wind turbine blades is formulated as a periodic boundary value problem; the analysis of the stability of these periodic solutions is another important of problem. The objective of this thesis is to develop a unified solution procedure for both initial and boundary value problems. Galerkin methods provide a suitable framework for the development of such solvers. Galerkin methods require interpolation schemes that approximate the unknown rigid-body motion fields. Novel interpolation schemes for rigid-body motions are proposed based on minimization of eighted distance measures of rigid-body motions. Based on the proposed interpolation schemes, a unified continuous/discontinuous Galerkin solver is developed for the formulation of geometrically exact beams, for the determination of solutions of initial and periodic boundary value problems, for the stability analysis of periodic solutions, and for the optimal control/optimization problems of flexible multibody systems

On singular values decomposition and patterns for human motion analysis and simulation

We are interested in human motion characterization and automatic motion simulation. The apparent redun- dancy of the humanoid w.r.t its explicit tasks lead to the problem of choosing a plausible movement in the framework of redun- dant kinematics. This work explores the intrinsic relationships between singular value decomposition at kinematic level and optimization principles at task level and joint level. Two task- based schemes devoted to simulation of human motion are then proposed and analyzed. These results are illustrated by motion captures, analyses and task-based simulations. Pattern of singular values serve as a basis for a discussion concerning the similarity of simulated and real motions

A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3,700 are used to verify the accuracy and physical fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational Physic

Liquid-gas-solid flows with lattice Boltzmann: Simulation of floating bodies

This paper presents a model for the simulation of liquid-gas-solid flows by means of the lattice Boltzmann method. The approach is built upon previous works for the simulation of liquid-solid particle suspensions on the one hand, and on a liquid-gas free surface model on the other. We show how the two approaches can be unified by a novel set of dynamic cell conversion rules. For evaluation, we concentrate on the rotational stability of non-spherical rigid bodies floating on a plane water surface - a classical hydrostatic problem known from naval architecture. We show the consistency of our method in this kind of flows and obtain convergence towards the ideal solution for the measured heeling stability of a floating box.Comment: 22 pages, Preprint submitted to Computers and Mathematics with Applications Special Issue ICMMES 2011, Proceedings of the Eighth International Conference for Mesoscopic Methods in Engineering and Scienc