Applications of combinatorics to statics—rigidity of grids

AbstractThe infinitesimal rigidity (or briefly rigidity) of a bar-and-joint framework (in any dimension) can be formulated as a rank condition of the so-called rigidity matrix. If there are n joints in the framework then the size of this matrix is O(n), so the time complexity of determining its rank is O(n3). But in special cases we can work with graph and matroid theoretical models from which very fast and effective algorithms can be obtained. At first the case of planar square grids will be presented where they can be made rigid with diagonal rods and cables in the squares, and with long rods and cables which may be placed between any two joints of the grid. Then we will consider the one- and multi-story buildings, and finally some other results and algorithms

Applications of combinatorics to statics—a second survey

AbstractSome recent results are presented, concerning the algorithmic aspects of 2-dimensional generic rigidity, and 1-story buildings as tensegrity frameworks. Most of these results were obtained after the completion of the first survey (Recski, 1984) for a ‘Winter School’ organized by the late Professor Z. Frolík. Results in Sections 3 and 4 of the first survey are used throughout

Adaptive control of large space structures using recursive lattice filters

The use of recursive lattice filters for identification and adaptive control of large space structures is studied. Lattice filters were used to identify the structural dynamics model of the flexible structures. This identification model is then used for adaptive control. Before the identified model and control laws are integrated, the identified model is passed through a series of validation procedures and only when the model passes these validation procedures is control engaged. This type of validation scheme prevents instability when the overall loop is closed. Another important area of research, namely that of robust controller synthesis, was investigated using frequency domain multivariable controller synthesis methods. The method uses the Linear Quadratic Guassian/Loop Transfer Recovery (LQG/LTR) approach to ensure stability against unmodeled higher frequency modes and achieves the desired performance

Definition of technology development missions for early space stations: Large space structures

The objectives studied are the definition of the tested role of an early Space Station for the construction of large space structures. This is accomplished by defining the LSS technology development missions (TDMs) identified in phase 1. Design and operations trade studies are used to identify the best structural concepts and procedures for each TDMs. Details of the TDM designs are then developed along with their operational requirements. Space Station resources required for each mission, both human and physical, are identified. The costs and development schedules for the TDMs provide an indication of the programs needed to develop these missions

Cargo transportation by airships: A systems study

A systems engineering study of a lighter than air airship transportation system was conducted. The feasibility of the use of airships in hauling cargo was demonstrated. Social, legal, environmental and political factors were considered as well as the technical factors necessary to design an effective airship transportation system. In order to accomplish an effective airship transportation program two phases of implementation were recommended. Phase I would involve a fleet of rigid airships of 3.5 million cubic feet displacement capable of carrying 25 tons of cargo internal to the helium-filled gas bag. The Phase I fleet would demonstrate the economic and technical feasibility of modern-day airships while providing a training capability for the construction and operation of larger airships. The Phase II portion would be a fleet of rigid airships of 12 million cubic feet displacement capable of carrying a cargo of 100 tons a distance of 2,000 miles at a cruising speed of 60 mph. An economic analysis is given for a variety of missions for both Phase I and Phase II airships

Elastic timber gridshells - structures with an integrated design

A timber gridshell is a special type of structure that establishes a new framework for lightweight construction. It is possible to create a wide variety of shapes and geometries, therefore guaranteeing an enormous architectural freedom. However, given the variety of forms and the difficulty they can present, it is necessary to use different tools and information to support this complex process.The present paper explores the interaction between the information and the different tools used by architects and engineers during the designing and construction process of an elastic timber gridshell, by presenting a real case study with 42m(2)(6,5mx6,5m) after being erected, built with the intent to explore the design and constructive process together with integrated form finding methods. In the paper, both the architect's and the engineer's optimization goals are performed on the same case study. The designing process will be presented and the construction of the elastic gridshell will be described.Una malla estructural de madera es un tipo especial de estructura que establece un nuevo marco para la construcción ligera. Es posible crear una amplia variedad de formas y geometrías, garantizando así una enorme libertad arqui-tectónica. Sin embargo, dada la variedad de formas y la complejidad que pueden presentar es necesario utilizar difer-entes herramientas e información para avalar este complejo proceso. El presente trabajo explora la interacción entre la información y las diferentes herramientas utilizadas por arquitectos e ingenieros durante el proceso de diseño y construcción de una malla elástica de madera, presentando un caso de estu-dio real con 42m2 (6,5mx6,5m), después de la elevación, construida con la intención de explorar el diseño y el proceso constructivo junto con métodos de integración de “form finding”. En el trabajo, los objetivos de optimización tanto del arquitecto como del ingeniero se realizan sobre el mismo caso de estudio. Se presentará el proceso de diseño y se descri-birá la construcción de la malla elástica.This work is financed by FEDER funds through the Competitively Factors Operational Programme - COMPETE and by national funds through FCT -Foundation for Science and Technology within the scope of the project POCI01-0145-FEDER-007633. The support of the Foundation for Science and Technology (FCT) through doctoral fellowship SFRH/BD/104677/2014 is grateful