Distributed Fibre Optic Sensor-Based Continuous Strain Measurement along Semicircular Paths Using Strain Transformation Approach

Distributed fibre optic sensors (DFOS) are popular for structural health monitoring applications in large engineering infrastructure because of their ability to provide spatial strain measurements continuously along their lengths. Curved paths, particularly semicircular paths, are quite common for optical fibre placement in large structures in addition to straight paths. Optical fibre sensors embedded in a curved path configuration typically measure a component of strain, which often cannot be validated using traditional approaches. Thus, for most applications, strain measured along curved paths is ignored as there is no proper validation tool to ensure the accuracy of the measured strains. To overcome this, an analytical strain transformation equation has been developed and is presented here. This equation transforms the horizontal and vertical strain components obtained along a curved semicircular path into a strain component, which acts tangentially as it travels along the curved fibre path. This approach is validated numerically and experimentally for a DFOS installed on a steel specimen with straight and curved paths. Under tensile and flexural loading scenarios, the horizontal and vertical strain components were obtained numerically using finite element analysis and experimentally using strain rosettes and then, substituted into the proposed strain transformation equation for deriving the transformed strain values. Subsequently, the derived strain values obtained from the proposed transformation equation were validated by comparing them with the experimentally measured DFOS strains in the curved region. Additionally, this study has also shown that a localised damage to the DFOS coating will not impact the functionality of the sensor at the remaining locations along its length. In summary, this paper presents a valid strain transformation equation, which can be used for transforming the numerical simulation results into the DFOS measurements along a semicircular path. This would allow for a larger scope of spatial strains measurements, which would otherwise be ignored in practice.

Investigation of the shapes of cuts in a plate in contact with a rigid stamp

A mathematical model of a contact interaction between a plate and rigid stamp is derived taking into account physical and design details. The plate is considered to have a crack, that changes its form. The problem of the contact is evaluated based on the theory of variational inequalities. The shape of the stamp is assumed to be perpendicular to the plate surface and the Poisson’s ratio is between 0 and 0.5. Analytical formulation of the study consists of transformation equation, boundary conditions and integral equation. The result is used in maximization and minimization problems for choosing extremal shape of the vertical break in the plate.

KAJIAN KOMPUTASI POLA GELOMBANG RESONANSI MAGNET INTI (NMR) DENGAN TRANSFORMASI FOURIER

Research on nuclear magnetic resonance (NMR) modeling has been done with computational approach. This study aims to determine the shape of signals and spectra of some of the combined nuclear spins. The physical parameters were determined using Fourier transformation equation modeled with the wolfram mathematical software 9.0. The relaxation time of the 1/2 nuclear spin was varied according to the nuclear state of cancer tissue.This produces a cosine wave pattern for the signal at T2 = 0.11 ms. Variations of this in chemical shift (Δ) and J-coupling (J) for modeling were performed in 9 times. The spectrum of one spin is generated at the value of Δ = 0.001 Hz and J = 0 Hz, the spectrum of two spins at Δ = 849,001 Hz and J = 24 Hz. These results can be applied to research interests for the medical world and as reference data for research standards.

MATCHING OF IMAGES BASED ON THEIR DIFFEOMORPHIC MAPPING

We discuss a problem of comparison of two diffeomorphic images, namely, the source and target images of a diffeomorphism, which are given by two sets of points. The problem is solved on the basis of a method of constructing a minimized functional characterizing the evolution of the diffeomorphic source-to-target image transformation and a penalty for the image path deviation from the required trajectory. An algorithm for solving the diffeomorphic transformation equation is developed on the basis of the gradient descent method. The considered problem of comparison of two images can be used for constructing an optimal metamorphism of images, when there is no exact correspondence between the source and target images of the diffeomorphism.