Deformations of 2k-Einstein structures

It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional at compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the corresponding moduli space.Comment: 12 pages. Manuscript accepted for publication on Journal of Geometry and Physic

Unified control/structure design and modeling research

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed

On the groupoid of transformations of rigid structures on surfaces

We prove that the groupoid of transformations of rigid structures on surfaces has a finite presentation as a 2-groupoid establishing a result first conjectured by G.Moore and N.Seiberg. An alternative proof was given by B.Bakalov and A.Kirillov Jr. We present some applications to TQFTs. This is also related to recent work on the Grothendieck-Teichmuller groupoid by P.Lochak, A.Hatcher and L.Schneps.Comment: 38 pages, 35 eps figure

Recent research and development in semi-rigid composite joints with precast hollowcore slabs

Composite structure incorporating steel beams and precast hollowcore slabs is a recently developed composite floor system for building structures. This form of composite construction is so far limited to simple beam-column connections. Although the concept of semi-rigid composite joints has been widely research in the past, most of the researches have been carried out on composite joints with metal deck flooring and solid concrete slabs. Research on composite joints with precast hollowcore slabs is rather limited. As the construction industry demands for rapid construction with reduction in cost and environmental impacts, this form of composite floor system, which does not require major onsite concreting, has become very popular among the designers and engineers in the UK. In this paper, full-scale tests of beam-to-column semi-rigid composite joints with steel beam and precast hollowcore slabs are reported. Based on the tests data; the structural behaviour of these semi-rigid composite joints is discussed together with numerical and finite element modelling. Through parametric studies, an analytical model for the semirigid composite joints is proposed and is verified by both the experimental data and finite element model; and good agreement is obtained

Exact seismic response of smooth rigid retaining walls resting on stiff soil

The assessment of forces exerted on walls by the backfill is a recurrent problem in geotechnical engineering, owing to its relevance for both retaining systems and underground structures. In particular, the work by Arias and colleagues, and later also the one by Veletsos and Younan, among others, becomes pertinent when considering pressure increments on underground structures triggered by seismic events. As a first step, they studied the response of a rigid retaining wall resting on rigid bedrock subjected to SV waves, introducing some simplifying assumptions. This paper presents the exact solution to this reference problem. The solution is given in horizontal wavenumber domain; hence, it comes in terms of inverse Fourier transforms, which can be approximated numerically in Mathematica , which in turn are verified against finite‐element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed

Length spectra and degeneration of flat metrics

In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to "mixed structures" on the surface: part flat metric and part measured foliation.Comment: 36 page