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

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

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

Distribution and Attachment of Bryozoans in the Intertidal Region of South Andaman Island

Aiming to collate the distribution and the attachment preference of intertidal bryozoan of Andaman waters, a study was carried out in three intertidal sites (Burmanallah, Kodiyaghat, and Chidiytapu) of southeastern coasts of the Andaman Islands between June and August 2016. The present study is the first exclusive report on bryozoans from the Andaman Islands after a long research gap of nine decades. During our investigation, a total of twelve genera were identified from both calcareous and non-calcareous substratum. Out of the twelve genera, eight genera were new records from the island. The present study showed that the attachment affinity of the Bryozoans is more towards natural substratum particularly on the rocks. The Thalamoporella sp. reported the most abundant species with maximum average colony length of 3.5 cm from the rock substratum

HEPATOPROTECTIVE ACTIVITY OF MAYTENUS EMARGINATA AGAINST PARACETAMOL INDUCED LIVER INJURY IN MALE WISTAR RATS

Objective: To study the hepatoprotective activity of ethanol extract of Maytenus emarginata against Paracetamol induced toxicity in male Wistar rats. Methods: The liver injury was induced by Paracetamol @ 500 mg/kg B.W. orally for entire duration of study. The rats were divided in six groups. Rats of Group C1 served healthy control received no treatment, Group C2 served vehicle control received 1ml of Propylene glycol orally. C3 group rats acted as toxic control and received Paracetamol orally @ 500 mg/kg B.W. of rats. Group T1, T2 and T3 received Silymarin @ 100 mg/kg B.W., Maytenus emarginata extract @ 100 mg/kg B.W. and Maytenus emarginata extract @ 150 mg/kg B.W. orally of rats respectively along with Paracetamol @ 500 mg/kg B.W. of rats orally for 28 days. Results: Histopathological examination and elevation of biochemical marker enzymes ALP, ALT and AST along with decreased levels of serum total protein and serum albumin confirmed the liver injury produced by Paracetamol. Treatment of rats with Maytenus emarginata extract showed significant reduction in levels of serum ALP, ALT and AST with elevation of serum protein and albumin near to normal in a dose dependant manner. Dose of 150 mg/kg B.W. of Maytenus emarginata extract showed significant effects comparable to the effects showed by standard treatment drug Silymarin @ 100 mg/kg B.W. orally. Conclusion: Maytenus emarginata ethanol extract possess potent hepatoprotective effect

Predictions of the mechanical properties of unidirectional fibre composites by supervised machine learning

We present an application of data analytics and supervised machine learning to allow accurate predictions of the macroscopic stiffness and yield strength of a unidirectional composite loaded in the transverse plane. Predictions are obtained from the analysis of an image of the material microstructure, as well as knowledge of the constitutive models for fibres and matrix, without performing physically-based calculations. The computational framework is based on evaluating the 2-point correlation function of the images of 1800 microstructures, followed by dimensionality reduction via principal component analysis. Finite element (FE) simulations are performed on 1800 corresponding statistical volume elements (SVEs) representing cylindrical fibres in a continuous matrix, loaded in the transverse plane. A supervised machine learning (ML) exercise is performed, employing a gradient-boosted tree regression model with 10-fold cross-validation strategy. The model obtained is able to accurately predict the homogenized properties of arbitrary microstructures