The construction of self-dual normal polynomials over GF(2) and their applications to the Massey-Omura algorithm

Gaussian periods are used to locate a normal element of the finite field GF(2e) of odd degree e and an algorithm is presented for the construction of self-dual normal polynomials over GF(2) for any odd degree. This gives a new constructive proof of the existence of a self-dual basis for odd degree. The use of such polynomials in the Massey-Omura multiplier improves the efficiency and decreases the complexity of the multiplie

Experimental characterisation of rate-dependent compression behaviour of fibre reinforced composites

Fibre reinforced polymers (FRP) materials are being increasingly used for aerospace and automotive structural applications. One of the critical loading conditions for such applications is impact, consequently, understanding of the composite behavior under such loads becomes critical for structural design. The analysis and design process for achieving impact-resistant composite structures requires rate-dependent constitutive models, which, in turn, requires material properties of the composite over a range of strain rates. It is, therefore, the objective of the research to investigate the strain rate-dependent behavior of fiber reinforced composites under compressive loads for a wide range of fiber orientations. Quasi-static (≈ 1e-3 s-1) and high loading (≈ 200 s-1) rates are considered for the experimental study. Accordingly, two different test setups are utilized, a screw-driven universal testing machine for quasi-static tests and a Split Hopkinson Pressure Bar (SHPB) system for dynamic tests. The stress-strain response of the composite is reported for the different fiber orientations and the strain rates, revealing the rate-dependent characteristics of the carbon fiber reinforced composite. From the test results, it is observed that, the dependency of the fracture strength on the loading rate is significant. The results are summarised in terms of the failure envelope in the transverse compression-in-plane shear σ22-σ12 plane for the two strain rates

A Wedge-DCB Test Methodology to Characterise High Rate Mode-I Interlaminar Fracture Properties of Fibre Composites

A combined numerical-experimental methodology is presented to measure dynamic Mode-I fracture properties of fiber reinforced composites. A modified wedge-DCB test using a Split-Hopkinson Bar technique along with cohesive zone modelling is utilised for this purpose. Three different comparison metrics, namely, strain-displacement response, crack propagation history and crack opening history are employed in order to extract unique values for the cohesive fracture properties of the delaminating interface. More importantly, the complexity of dealing with the frictional effects between the wedge and the DCB specimen is effectively circumvented by utilising right acquisition techniques combined with an inverse numerical modelling procedure. The proposed methodology is applied to extract the high rate interlaminar fracture properties of carbon fiber reinforced epoxy composites and it is further shown that a high level of confidence in the calibrated data can be established by adopting the proposed methodology

On the Rate-dependent Plasticity Modelling of Unidirectional Fibre-reinforced Polymeric Matrix Composites

Three different approaches to plasticity are investigated to model the experimentally-observed non-linear behaviour of unidirectional fibre-reinforced polymeric matrix materials. The first and simplest approach consists on assuming independent one-dimensional rate-dependent plasticity on in-plane (12) and through-thickness longitudinal (13) shear components of the Cauchy stress tensor. The second, employs a 3D extension of the plane stress Hill'48 anisotropic plastic surface. The third and the last is formulated as a quadratic yield function inspired by Puck's fracture initiation criterion. It searches for a plastic localisation plane in which a certain combination of normal and shear stresses is maximum. Numerical simulations are conducted to analyse the off-axis compression behaviour of carbon fibre reinforced epoxy composite under varying loading rates. The afore-mentioned three different approaches are explored with an aim to predict the experimentally-observed non-linear response of such composites. The model parameters are determined using a deterministic inverse modelling strategy employing an iterative domain reduction optimisation technique. As far as the experiments are concerned, the quasi-static and medium rate tests were carried out in universal testing machines, while the experiments at high rate were conducted in a Split Hopkinson Pressure Bar system. The effectiveness in terms of accuracy and robustness of the three approaches are discussed

On generalized Lagrange–Hermite–Bernoulli and related polynomials

We introduce a new class of generalized polynomials, ascribed to the family of Hermite, Lagrange, Bernoulli, Miller–Lee, and Laguerre polynomials and of their associated forms. These polynomials can be expressed in the form of generating functions, which allow a high degree of exibility for the formulation of the relevant theory. We develop a point of view based on generating relations, exploited in the past, to study some aspects of the theory of special functions. We propose a fairly general analysis allowing a transparent link between different forms of special polynomials

Vigorous Module Based Data Management

Data is important in today’s life and it must be saved using less amount of memory. Data is important in day to day life for many purposes, like Government activities, any organization needs their own database, hospitals, schools etc. It is necessary to save data into database as per the user’s query generation with less memory conjunction. One of the novel techniques we have developed for saving data into database by using file similarity algorithm. This technique is used to split the text file into number of paragraphs and save these paragraphs using appropriate reference number. These reference numbers are stored in database, whenever same paragraph will appeared in another text file it will check database and then save the other references of that file which are new for that file. This technique requires less memory and data can be stored in appropriate manner

DL-Lite: Tractable Description Logics for Ontologies: A Survey

Description Logic, called DL-Lite, specially used to capture essential ontology languages, and keeping low difficulty of logic. Here logic means computing subsumption between concepts, and checking satisfiability of the whole knowledge base, as well as answer complex queries over the set of instances maintained in secondary storage. DL-Lite the usual DL logical tasks are polynomial in the amount of the TBox, and query answering is polynomial in the amount of the ABox (i.e., in data difficulty). To the best of knowledge, this is the first result of polynomial data difficulty for query answering over DL knowledge bases. A distinguished visage of logic is to allow for a partitions between TBox and ABox logic during query evaluation: the part of the process requiring TBox logic is self-determining of the ABox, and the some part of the process requiring access to the ABox which can be carried out by an SQL engine, thus taking benefit of the query optimization strategies provided by current DBMSs