Buckling and vibration of periodic lattice structures

Lattice booms and platforms composed of flexible members or large diameter rings which may be stiffened by cables in order to support membrane-like antennas or reflector surfaces are the main components of some large space structures. The nature of these structures, repetitive geometry with few different members, makes possible relatively simple solutions for buckling and vibration of a certain class of these structures. Each member is represented by a stiffness matrix derived from the exact solution of the beam column equation. This transcendental matrix gives the current member stiffness at any end load or frequency. Using conventional finite element techniques, equilibrium equations can be written involving displacements and rotations of a typical node and its neighbors. The assumptions of a simple trigonometric mode shape is found to satisfy these equations exactly; thus the entire problem is governed by just one 6 x 6 matrix equation involving the amplitude of the displacement and rotation mode shapes. The boundary conditions implied by this solution are simple supported ends for the column type configurations

New Symbolic Tools for Differential Geometry, Gravitation, and Field Theory

DifferentialGeometry is a Maple software package which symbolically performs fundamental operations of calculus on manifolds, differential geometry, tensor calculus, Lie algebras, Lie groups, transformation groups, jet spaces, and the variational calculus. These capabilities, combined with dramatic recent improvements in symbolic approaches to solving algebraic and differential equations, have allowed for development of powerful new tools for solving research problems in gravitation and field theory. The purpose of this paper is to describe some of these new tools and present some advanced applications involving: Killing vector fields and isometry groups, Killing tensors and other tensorial invariants, algebraic classification of curvature, and symmetry reduction of field equations.Comment: 42 page

The curatorial consequences of being moved, moveable or portable: the case of carved stones

It matters whether a carved stone is moved, moveable or portable. This influences perceptions of significance and of form and nature – is it a monument or an artefact? This duality may in turn affect understanding and appreciation of the resource. It has implications for how and if carved stones can be legally protected, who owns them, where and how they are administered, and by whom. The complexities of the legislation mean that all too often this is also a grey area. This paper explores these curatorial issues and their impact

PASCO: Structural panel analysis and sizing code, capability and analytical foundations

A computer code denoted PASCO which can be used for analyzing and sizing uniaxially-stiffened composite panels is described. Buckling and vibration analyses are carried out with a linked-plate analysis computer code denoted VIPASA, which is incorporated in PASCO. Sizing is based on nonlinear mathematical programming techniques and employs a computer code denoted CONMIN, also incorporated in PASCO. Design requirements considered are initial buckling, material strength, stiffness, and vibration frequency. The capability of the PASCO computer code and the approach used in the structural analysis and sizing are described

The Annular Suspension and Pointing (ASP) system for space experiments and predicted pointing accuracies

An annular suspension and pointing system consisting of pointing assemblies for coarse and vernier pointing is described. The first assembly is attached to a carrier spacecraft (e.g., the space shuttle) and consists of an azimuth gimbal and an elevation gimbal which provide 'coarse' pointing. The second or vernier pointing assembly is made up of magnetic actuators of suspension and fine pointing, roll motor segments, and an instrument or experiment mounting plate around which is attached a continuous annular rim similar to that used in the annular momentum control device. The rim provides appropriate magnetic circuits for the actuators and the roll motor segments for any instrument roll position. The results of a study to determine the pointing accuracy of the system in the presence of crew motion disturbances are presented. Typical 3 sigma worst-case errors are found to be of the order of 0.001 arc-second

Schema Independent Relational Learning

Learning novel concepts and relations from relational databases is an important problem with many applications in database systems and machine learning. Relational learning algorithms learn the definition of a new relation in terms of existing relations in the database. Nevertheless, the same data set may be represented under different schemas for various reasons, such as efficiency, data quality, and usability. Unfortunately, the output of current relational learning algorithms tends to vary quite substantially over the choice of schema, both in terms of learning accuracy and efficiency. This variation complicates their off-the-shelf application. In this paper, we introduce and formalize the property of schema independence of relational learning algorithms, and study both the theoretical and empirical dependence of existing algorithms on the common class of (de) composition schema transformations. We study both sample-based learning algorithms, which learn from sets of labeled examples, and query-based algorithms, which learn by asking queries to an oracle. We prove that current relational learning algorithms are generally not schema independent. For query-based learning algorithms we show that the (de) composition transformations influence their query complexity. We propose Castor, a sample-based relational learning algorithm that achieves schema independence by leveraging data dependencies. We support the theoretical results with an empirical study that demonstrates the schema dependence/independence of several algorithms on existing benchmark and real-world datasets under (de) compositions

Structural analyses for the modification and verification of the Viking aeroshell

The Viking aeroshell is an extremely lightweight flexible shell structure that has undergone thorough buckling analyses in the course of its development. The analytical tools and modeling technique required to reveal the structural behavior are presented. Significant results are given which illustrate the complex failure modes not usually observed in simple models and analyses. Both shell-of-revolution analysis for the pressure loads and thermal loads during entry and a general shell analysis for concentrated tank loads during launch were used. In many cases fixes or alterations to the structure were required, and the role of the analytical results in determining these modifications is indicated