Semi-analytical Simulation Method Research Articles

A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads

This paper presents a novel semi-analytical simulation approach for analysing the behaviour of bi-directional functionally graded cantilever beams subjected to arbitrary static loads, such as concentrated moments, concentrated forces, distributed force and their combinations applied at any location along the beam. The fundamental equations governing the cantilever beam’s response are derived, on the basis of which the proposed semi-analytical method is implemented using MATLAB programming language. The simulation results include field variables as well as stress contours, providing a compressive understanding of the beam’s behaviour. To validate the accuracy and reliability of the proposed method, a convergence study is conducted in comparison with the graded finite element method (GFEM) and analytical solutions. In the end, the developed method is applied to simulate the bending behaviour of bi-directional functionally graded cantilever beams under various loads individually and their combinations. The stress contours and deflection curves obtained from the simulation are compared with the solutions obtained using GFEM, revealing that the developed method possesses excellent capability in accurately simulating the bending behaviour of cantilever beams.

Development of a semi-analytical method to calculate depth-dependent temperature and stress changes: investigation of micro-seismicity at Unterhaching Uha GT-2 geothermal well

Since October 2007 when the hydrothermal production of geothermal energy from the deep underground started at Unterhaching, near Munich (Germany), several micro-seismic events have been observed. Three of the five strongest events, with local magnitudes (ML) ranging from 2.0 to 2.4, occurred in 2008 and were partially felt by the residents. The reasons for these events are not clear. These micro-seismic events could have been induced by a variety of factors. The strongest micro-seismic event was observed soon after the injection of cold water, pointing to an intrinsic relationship between micro-seismic event and cold water injection. One of the possible reasons for the observed micro-seismic events could be the reinjection of cooled thermal water into the hotter underground inducing stress redistribution and shear failures in the reservoir formations around the injection wellbore Uha GT-2. To justify this reason, further investigation will be carried out in another simulation study to verify whether the shear failures induced by cold water injection were the major cause for the occurrence of these micro-seismic events. Nevertheless, before the simulation of shear failures, temperature profiles in both the wellbore and surrounding rocks as well as their corresponding thermal stresses during cold water injection should be established in this study. In this paper, a new semi-analytical simulation method has been developed to calculate simultaneously the temperature profiles in the wellbore and the surrounding rock formations and also determine the corresponding thermal stresses in the surroundings near wellbore field and subsequently verified by analytical solution. Results show that great tensile thermal stresses in the reservoir were initiated by the injection of the cooled thermal water in the injection wellbore Uha GT-2. The results of the simulated thermal stresses indicate a great potential for the ensuing shear failures to affect an extensive area and could be used as input data for the planned shear failure simulations in the future.

High-Performance LSPR Fiber Sensor Based on Nanometal Rings

A novel localized surface plasmon resonance (LSPR) fiber sensor was proposed. This LSPR fiber sensor was primarily constructed by conducting etching of the cladding layer and core layer on a single-mode fiber, followed by plating of 1444 nanometal rings. Sensor design and relevant calculations were conducted using a semi-analytical simulation method, which integrated the exact mode solver for the cylindrical coordinate and eigenmode expansion method. It was examined that the current metallic patterns in the fiber sensor can trigger the LSPR by the electric field Er of the core mode HE11, and this is the main reason why this novel fiber sensor can obtain high performance. After performing algorithms, images showed evident excitation of the LSPR. The LSPR fiber sensor designed in this paper possesses excellent attributes of short length (185.173 μm), high resolution (approximately - 70 dB), and high sensitivity (approximately 34 257 nm/RIU).

Application of the distributed point source method to rough surface scattering and ultrasonic wall thickness measurement

The distributed point source method is commonly used to predict the complex acoustic field emitted by ultrasonic transducers. In this paper, it is presented as an alternative to conventional approaches often used when solving rough surface scattering problems. Surface shadowing and multiple scattering effects are inherently included in the mesh-free semi-analytical simulation method through matrix manipulation making it very efficient and simple to implement. Results are presented which illustrate the improvement in accuracy gained over the Kirchhoff approximation and the decrease in computational load over the finite element method, culminating in greater than an order of magnitude decrease in required simulation time. The method is applied to the practical problem of online wall thickness monitoring within corrosive environments, illustrating the variability in reflected pulse shape that could be expected from rough surfaces with similar statistics. Three commonly implemented time-of-flight algorithms are used to analyze a large number of simulated signals from which it is concluded that those based on first arrival time are more stable under increasing roughness conditions than those which are based on reflected pulse shape.

SNR approach for performance evaluation of time-stretching photonic analogue to digital converter system

A semi-analytical simulation method (SASM) is proposed to evaluate the signal-to-noise ratio (SNR) of time stretched signals at the output of photonic analogue-to-digital converter (Ph-ADC) system. Analytical expressions of the signal at Ph-ADC output considering generic electrical signals applied to the electro-optic modulators of the Ph-ADC are derived. The contribution to the total variance of the received signal from the noise introduced by the electrical transmitter and receiver, and by the optical amplifier are derived analytically taking into account the pulsed nature of the optical signal. The proposed SASM shows excellent agreement of SNR estimates with the estimates provided by Monte Carlo simulation. This result is confirmed for variance dominantly imposed by the noise introduced by the electrical transmitter, by the optical amplifier and by the electrical receiver. A simplified approach is also proposed and compared with previous work. It is shown that mean power estimates obtained from this simplified approach are valid while the modulator is operating in the linear region and the signal is not affected by the frequency response of the electrical receiver filter. Additionally, it is concluded that the estimates of the noise variance due to the electrical transmitter are acceptable when a small signal analysis of noise along the Ph-ADC is valid.

Optical DQPSK System Performance Evaluation Using Equivalent Differential Phase in Presence of Receiver Imperfections

The performance evaluation of optical differential quadrature phase-shift keying (DQPSK) systems through numerical simulation using a Gaussian approach (GA) for the equivalent differential phase (EDP) statistics is analyzed. It is shown that the GA describes quite accurately the probability density function (PDF) of EDP for a large range of DQPSK receiver (RX) imperfections. A semi-analytical simulation method (SASM) for bit error probability (BEP) evaluation based on the GA for the EDP is derived, proving to be quite accurate in presence of RX imperfections. The SASM takes into account the signal-noise beat variance dependence on signal waveform distortion and arbitrary optical and electrical filtering frequency responses. Closed-form expressions for the mean and standard deviation of EDP are derived which allows evaluating the DQPSK system performance in a quite time-efficient manner. Discrepancies not exceeding 0.1 dB on the optical SNR penalty estimated by the SASM for a BEP of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> when compared with Monte Carlo simulation are observed for the majority of the acceptable RX imperfections. Only the time-misalignment of the signals at the balanced detector input leads to higher discrepancies but not exceeding 0.3 dB even for considerable time-misalignment.

Reliability-based integrated design of steel portal frames with tapered members

Integrated structural designs, with consideration of system reliability for steel portal frames comprising tapered members, are studied in this paper. The reliability-based integrated design (RID) directly checks the structural system limit states and the corresponding system reliability, based on structural nonlinear analysis. The nonlinear integrated analysis model, the semi-analytical simulation method employed for system reliability assessment, the development processes of RID format and the design application of RID formula and curves are presented in this paper. Design examples and comparisons among three different design formats demonstrate that RID proposed in this paper is of certain and consistent system reliability levels, and provides a feasible way for structural engineers to improve the design quality and flexibility of steel frame structures.

A semi-analytical simulation method for reliability assessments of structural systems

Abstract A semi-analytical simulation method is proposed in this paper to assess system reliability of structures. Monte Carlo simulation with variance-reduction techniques, systematic and antithetic sampling, is employed to obtain the samples of the structural resistance in this method. Variance-reduction techniques make it possible to sufficiently simulate the structural resistance with less runs of structural analysis. When resistance samples and its moments determined, exponential polynomial method (EPM) is used to fit the probability density function of the structural resistance. EPM can provide the approximate distribution and statistical characteristic of the structural resistance and then the first-order second-moment method can be carried out to calculate the structural failure probability. Numerical examples are provided for a structural component and two ductile frames, which illustrate the method proposed facilitates the evaluation of system reliability in assessments of structural safety.

Simulations of growing ordered arrays of islands on substrate steps

The spacing of islands in systems where the diffusion of adatoms is restricted to one dimension is studied. We initially consider a point-island model on a one-dimensional lattice before moving on to a more realistic system in which two- or three-dimensional islands grow exclusively at steps on a two-dimensional substrate. Monte Carlo simulations of both of these systems have been performed, and an analytical expression giving the distribution of gaps between adjacent islands is formulated which is general with respect to the critical island size. This expression indicates that higher critical island sizes should yield more evenly spaced arrays of islands and a narrowly distributed range of island sizes, both of which are technologically desirable. These effects are studied via a simple simulation of nucleation behaviour and a new semi-analytical simulation method and the results show a distinct improvement in the evenness of size and spacing of the islands.