Recursive dynamics for flexible multibody systems using spatial operators

Due to their structural flexibility, spacecraft and space manipulators are multibody systems with complex dynamics and possess a large number of degrees of freedom. Here the spatial operator algebra methodology is used to develop a new dynamics formulation and spatially recursive algorithms for such flexible multibody systems. A key feature of the formulation is that the operator description of the flexible system dynamics is identical in form to the corresponding operator description of the dynamics of rigid multibody systems. A significant advantage of this unifying approach is that it allows ideas and techniques for rigid multibody systems to be easily applied to flexible multibody systems. The algorithms use standard finite-element and assumed modes models for the individual body deformation. A Newton-Euler Operator Factorization of the mass matrix of the multibody system is first developed. It forms the basis for recursive algorithms such as for the inverse dynamics, the computation of the mass matrix, and the composite body forward dynamics for the system. Subsequently, an alternative Innovations Operator Factorization of the mass matrix, each of whose factors is invertible, is developed. It leads to an operator expression for the inverse of the mass matrix, and forms the basis for the recursive articulated body forward dynamics algorithm for the flexible multibody system. For simplicity, most of the development here focuses on serial chain multibody systems. However, extensions of the algorithms to general topology flexible multibody systems are described. While the computational cost of the algorithms depends on factors such as the topology and the amount of flexibility in the multibody system, in general, it appears that in contrast to the rigid multibody case, the articulated body forward dynamics algorithm is the more efficient algorithm for flexible multibody systems containing even a small number of flexible bodies. The variety of algorithms described here permits a user to choose the algorithm which is optimal for the multibody system at hand. The availability of a number of algorithms is even more important for real-time applications, where implementation on parallel processors or custom computing hardware is often necessary to maximize speed

Universality Class of Confining Strings

A recently proposed model of confining strings has a non-local world-sheet action induced by a space-time Kalb-Ramond tensor field. Here we show that, in the large-D approximation, an infinite set of ghost- and tachyon-free truncations of the derivative expansion of this action all lead to c=1 models. Their infrared limit describes smooth strings with world-sheets of Hausdorff dimension D_H=2 and long-range orientational order, as expected for QCD strings.Comment: 11 pages, harvma

Time-parallel iterative solvers for parabolic evolution equations

We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of parabolic problems, we show that the standard nonsymmetric time-global system can be equivalently reformulated as an original symmetric saddle-point system that remains inf-sup stable with respect to the same natural parabolic norms. We then propose and analyse an efficient and readily implementable parallel-in-time preconditioner to be used with an inexact Uzawa method. The proposed preconditioner is non-intrusive and easy to implement in practice, and also features the key theoretical advantages of robust spectral bounds, leading to convergence rates that are independent of the number of time-steps, final time, or spatial mesh sizes, and also a theoretical parallel complexity that grows only logarithmically with respect to the number of time-steps. Numerical experiments with large-scale parallel computations show the effectiveness of the method, along with its good weak and strong scaling properties

Microscopic Aspects of Stretched Exponential Relaxation (SER) in Homogeneous Molecular and Network Glasses and Polymers

Because the theory of SER is still a work in progress, the phenomenon itself can be said to be the oldest unsolved problem in science, as it started with Kohlrausch in 1847. Many electrical and optical phenomena exhibit SER with probe relaxation I(t) ~ exp[-(t/{\tau}){\beta}], with 0 < {\beta} < 1. Here {\tau} is a material-sensitive parameter, useful for discussing chemical trends. The "shape" parameter {\beta} is dimensionless and plays the role of a non-equilibrium scaling exponent; its value, especially in glasses, is both practically useful and theoretically significant. The mathematical complexity of SER is such that rigorous derivations of this peculiar function were not achieved until the 1970's. The focus of much of the 1970's pioneering work was spatial relaxation of electronic charge, but SER is a universal phenomenon, and today atomic and molecular relaxation of glasses and deeply supercooled liquids provide the most reliable data. As the data base grew, the need for a quantitative theory increased; this need was finally met by the diffusion-to-traps topological model, which yields a remarkably simple expression for the shape parameter {\beta}, given by d*/(d* + 2). At first sight this expression appears to be identical to d/(d + 2), where d is the actual spatial dimensionality, as originally derived. The original model, however, failed to explain much of the data base. Here the theme of earlier reviews, based on the observation that in the presence of short-range forces only d* = d = 3 is the actual spatial dimensionality, while for mixed short- and long-range forces, d* = fd = d/2, is applied to four new spectacular examples, where it turns out that SER is useful not only for purposes of quality control, but also for defining what is meant by a glass in novel contexts. (Please see full abstract in main text

Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic materials, geometric nonlinearity at finite strain, and a quasi-static response. The optimization problem is solved by a nonlinear programming method and the sensitivities computed via the adjoint method. Two-dimensional structures identified using this optimization method are additively manufactured and their uniaxial tensile strain response compared with the numerically predicted behavior. The optimization approach herein enables the design and development of lattice-like materials with prescribed nonlinear effective properties, for use in myriad potential applications, ranging from stress wave and vibration mitigation to soft robotics