Semi-analytical Method Research Articles

A Road Map to the Structural Optimization of a Type-C Composite UAV

The present paper investigates the design process and the dimensioning of a tailless type-C composite sandwich unmanned aerial vehicle (UAV). The objective is to investigate an innovative aircraft configuration which exceeds the standard approach of ribs and spars and replaces them with a sandwich structure for future unmanned aerial systems. The necessity of carbon fiber-reinforced materials arose due to the weight constraint of a Class C UAV, i.e., the whole vehicle must be under 25 kg, which limits the mass of the structure to 9 kg. The structural design of composite structures differs from the one of traditional isotropic structures. The number of holes should be limited, as drilling down the composite aerostructure would conclude to the generation of delaminations. In addition, the joints between sections with different thicknesses could lead to stress concentrations and disbands. Therefore, the present report is crucial for the continuance of the present project as it has contributed both to the structural design and assessment of the UAV. This work focusses on the computation of loads, the process of structural sizing through a multi-disciplinary optimization approach, and the simulation-based structural proof. Particular attention is paid to the specifically developed semi-analytical method for predicting the aero-elastic load. Based on the detailed finite element model of the global structure, the applicability of the minimum number of bolts as a major structural joining variant is proven. The design process from single components to the assembly of the overall aircraft results in the realization of the demonstrator structure.

A semi-analytical procedure to determine the ion recombination correction factor in high dose-per-pulse beams.

The conventional theories and methods of determining the ion recombination correction factor, such as Boag theory and the related two voltage method and Jaffé plot extrapolation, do not seem to yield accurate results in FLASH /high dose per pulse (DPP) beams ( 10 mGy DPP). This is due to the presence of a large free electron fraction that distorts the electric field inside the chamber sensitive volume. To understand the influence of these effects on the ion recombination correction factor and to develop new expressions for it, it is necessary to re-visit the underlyingphysics. To present a mathematical procedure to develop an analytical expression for the ion recombination correction factor. The expression is the basis for an extrapolation method so the correction factor can be determined in a clinical setting. A semi-analytical solution method, the homotopy perturbation method (HPM), is used to solve the partial differential equations(PDEs) describing the charge carrier physics, including space charge and free electrons. The electron velocity and attachment rate are modeled as functions of the electric field strength. An expression for the charge collection efficiency and ion recombination correction factor are developed. A fit procedure based on this expression is used to compare it to measured data from previously published articles. Another fit procedure using a general equationis also proposed and compared to the data. The series obtained for the charge collection efficiency and the ion recombination correction factor are determined to be asymptotic series and the optimal truncation established. The ion recombination correction factor exhibits a dependency due to the free electron presence. The fit using this expression agrees well with measured data as long as (1) the DPP is below 1 Gy for chambers with a 1 mm plate separation and (2) when the DPP is below 3 Gy for chambers with a 0.5 mm plate separation. In these DPP ranges, the deviation between measured and fit value did not exceed 6%. In both chamber cases the voltage range where the fit applies decreases as DPP increases. The general equationyielded comparable results. The HPM was shown to be applicable to a complex system of PDEs and generate meaningful and novel solutions, as they include both space charge and free electrons. The HPM also lends itself to other chamber geometries. The fit procedure was also shown to yield accurate results for the ion recombination correction up to the 1 Gy DPPlevel.

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, in particular beam-coupling impedance, can significantly affect Schottky spectra when large bunch charges are involved. In such conditions, the available interpretation methods are difficult to apply directly to the measured spectra, thus preventing the extraction of beam and machine parameters, which is possible for lower bunch charges. To study the impact of impedance on such spectra, we introduce a method for building Schottky spectra from macro-particle simulations performed with the PyHEADTAIL code, applied to LHC beam conditions. In this case, the use of a standard Fast Fourier Transform (FFT) algorithm to recover the spectral content of the beam becomes computationally intractable memory-wise, because of the relatively short bunch length compared to the large revolution period. To circumvent this difficulty, a semi-analytical method was developed to efficiently compute the Fourier transform. The simulated Schottky spectrum is then compared against theoretical formulas and measurements of Schottky signals previously obtained with lead ion beams in the LHC where impedance effects are expected to be limited. Furthermore, this study provides preliminary interpretations of the impact of beam-coupling impedance on proton Schottky spectra by incorporating longitudinal and transverse resonator-like impedance models into the simulations. A theoretical framework is also introduced for the case of the longitudinal impedance, allowing the extension of the existing theoretical formalism.

Hydrodynamic forces in higher modes of a thin cantilever beam resonator

The hydrodynamic force in a thin uniform beam cantilever is essential quantity for designing a resonator. We obtained the hydrodynamic drag forces in a uniform cantilever vibrating at the first four transverse modes using a semi-analytical boundary element method (BEM) and finite element method (FEM) in ANSYS. The present three-dimensional (3D) BEM inertial and damping forces are compared with FEM over a frequency range with less than 9.5% deviation until frequency parameter of 100; thereafter, it deviates numerically due to neglecting the non-linear convective forces. Considering the hydrodynamic damping force, the quality factor is estimated for the first four transverse modes of a uniform cantilever beam. As a result, the present 3D BEM model behaves well at the first bending mode compared to FEM. We also study the effect of the aspect ratio (ratio of width to length) of the beam for all four modes. However, the first mode quality factor sufficiently correlates with the numerical value for all aspect ratios. For uniform beams operating with higher modes, the influence of nonlinear and resonance frequency by the numerical model is more pronounced at smaller lengths. Hence, the 3D BEM approach can estimate the hydrodynamic forces on cantilever-based resonators, for example, atomic force microscopy and biosensors.

A Semi-Analytical Method for Obtaining the Flux-Linkage Characteristics of Mutually-Coupled Switched Reluctance Machine

A Semi-Analytical Method for Obtaining the Flux-Linkage Characteristics of Mutually-Coupled Switched Reluctance Machine

Theoretical optimization of micropillar arrays for structurally stable bioinspired dry adhesives

Inspired by the excellent adhesion performances of setae structure from organisms, micro/nano-pillar array has become one of the paradigms for adhesive surfaces. The micropillar arrays are composed of the resin pillars for adhesion and the substrate with different elastic modulus for supporting. The stress singularity at the bi-material corner between the pillars and the substrate can induce the failure of the micropillar-substrate corner and further hinder the fabrication and application of micropillar arrays, yet the design for the stability of the micropillar array lacks systematical and quantitative guides. In this work, we develop a semi-analytical method to provide the full expressions for the stress distribution within the bi-material corner combining analytical derivations and numerical calculations. The predictions for the stress within the singularity field can be obtained based on the full expressions of the stress. The good agreement between the predictions and the FEM results demonstrates the high reliability of our method. By adopting the strain energy density factor approach, the stability of the pillar-substrate corner is assessed by predicting the failure at the corner. For the elastic mismatch between the pillar and substrate given in this paper, the stability can be improved by increasing the ratio of the shear modulus of the substrate to that of the micropillar. Our study provides accurate predictions for the stress distribution at the bi-material corner and can guide the optimization of material combinations of the pillars and the substrate for more stable bioinspired dry adhesives.

A Computationally Efficient Semi-Analytical Method for Circulating Current Loss of High Speed Permanent Magnet Machines

A Computationally Efficient Semi-Analytical Method for Circulating Current Loss of High Speed Permanent Magnet Machines

Solving Linear Volterra-Fredholm Integro-Differential Equations using Chebyshev-Galerkin with Error Estimation

The semi-analytic method based on the Galerkin technique with Chebyshev basis is presented in this paper to solve the linear integro-differential equations in the Volterra-Fredholm type. To facilitate, the use of the Chebyshev-Galerkin technique, new theorems and lemmas are established. Different numerical examples are introduced to demonstrate how the proposed method has efficacy and is easier to apply for this problem type. Some issues’ domains don’t match the Chebyshev’s domain. So, how to adequate the solution domain is presented. The error estimate is computed to prove the method's applicability and accuracy of the proposed method for any problem, especially in the case of the exact solution is not easy to determine.

Parametric optimisation for heat transfer through nanofluid impinging upon a Riga plate: the Taguchi method

The article presents a comprehensive analysis of the flow and heat transfer characteristics of the stagnation point flow of Casson nanofluid towards a Riga plate. The mathematical modelling of the problem is carried out by using Buongiorno's two-phase model for convective heat transport within nanofluids. The solution methodology includes the process of transforming the system of Partial Differential Equations (PDEs) into a set of Ordinary Differential Equations (ODEs) which then solved using a semi-analytical Optimal Homotopy Analysis Method (OHAM). The influence of various flow parameters on the skin friction coefficient ( C f x ) and Nusselt number is presented and analysed graphically. Furthermore, a parametric study for the optimisation of skin friction coefficient and Nusselt number ( N u x ) is performed using the Taguchi analysis along with ANOVA and the multivariate regression analysis. The parametric optimisation reveals that for skin friction coefficient, EMHD parameter is most significant term, whereas Prandtl number is found to be the parameter with the highest influence on the Nusselt number. The findings of the study may have bearings in engineering and industrial applications such as the thermal design of industrial equipment dealing with molten plastics and polymeric liquids.

A semi-analytical method for stress-strain analysis of tunnels under dip-slip faulting based on an elastic-plastic foundation beam model

Tunnels under faulting will be seriously damaged, and an accurate analytical method is an effective tool for tunnel response assessment in preliminary design. A series of mechanical analytical methods have been developed for tunnels under faulting. However, some unrealistic assumptions are still employed in the analytical method for tunnels under dip-slip faulting, including tunnel segmentation, constant stratum stress, and axial force in governing equations of tunnel displacement, which increases the solution complexity and decreases the accuracy. In this paper, a tunnel crossing an active fault is simplified as a large deformed continuous beam acting on an elastic-plastic foundation, and the tunnel-stratum interaction is treated as a series of axial and vertical elastic-plastic springs; the elastic-plastic tunnel-stratum interaction stresses and axial force are considered in the governing equations by using the finite difference method and a novel iterative method. In this way, the three assumptions employed in the existing analytical methods are removed. Later, the proposed method is verified by comparing it with the results from the model test, numerical simulation, and existing method. The comparisons show that the results of the proposed method agree excellently with those from the model test and numerical model, and the accuracy is higher than that of the existing analytical method. Finally, the failure scope and stress distribution of tunnels under the action of normal and reverse faulting are analyzed in detail.

Efficient semi-analytic method for single tooth contact analysis of loaded spiral bevel gears

Accurately and fast calculation of single tooth load contact state of a gear pair is the basis for accurate calculation of multi-tooth load contact analysis. Therefore, this study proposed a semi-analytical quick single tooth load tooth contact analysis (Q-SLTCA) method. First, the ease-off tooth contact analysis (ease-off TCA) method was established, and a numerically stable initial contact stress distribution and contact ellipse analytical model was derived. Then, considering the influence of edge contact, the real-time division method of gear tooth slice was derived. Based on this, the equivalent principle of contact elliptical node and the load correction strategy were innovatively proposed. Then, the calculation method of the meshing characteristics of the tooth slice was established by coupling the boundary element method (BEM) with the equivalent cylindrical Hertz contact theory. The bending deformation, tooth root stress distribution, contact stress, contact deformation and meshing stiffness of the tooth slice were analyzed and calculated, and the instantaneous meshing stiffness of the single tooth was determined by combining the parallel method of the gear tooth stiffness. Finally, a single-tooth finite element method (FEM) meshing model was created for comparison with the method in this study, which verified the calculation accuracy and efficiency of the proposed method. This method can be easily developed into a quick multi-tooth load contact analysis algorithm, which can provide a new method for gear tooth crack and failure analysis.

Active vibration control of fluid-conveying pipelines: Theoretical and experimental studies

For the fluid-conveying pipeline with macro-fiber composites (MFC), relevant dynamic modeling and experimental testing studies are rarely found in previous papers. Therefore, this paper has carried out related research work. Firstly, considering the fluid-structure interaction and piezoelectric effects, a semi-analytical modeling method for the fluid-conveying pipeline with MFC attaching to any position is proposed. A new Runge-Kutta-Gear (RKG) time-domain solution method is presented for solving state-space equations with the characteristics of rigid equations, and the design methods of Linear-Quadratic Regulator (LQR) controller and Proportional-Integral-Derivative (PID) controller are introduced, respectively. Secondly, an experimental system for active control and vibration test is built, and the dynamic model and control method are verified by experiments and simulations. Finally, the influence of relevant control parameters in the controller on the active control effect is discussed, and the influence law of fluid parameters such as fluid velocity and fluid pressure on the active control is also clarified. The novelty of this work is that the active vibration control and solution methods for the fluid-conveying pipeline with MFC are proposed, and the feasibility of MFC for pipeline vibration suppression is verified by experiments, which provides a new technical idea for the vibration reduction design of the fluid-conveying pipeline.

A fast convergent solution of wave propagation for multilayer inhomogeneous cylindrical dielectric waveguides using a semianalytical method

Abstract This paper presents an accurate and efficient semianalytical method based on the Galerkin procedure for solving electromagnetic wave propagation problems in multilayer inhomogeneous cylindrical dielectric waveguides. The method represents the field in each inhomogeneous layer by a linear combination of eigenfunctions with unknown coefficients, which are expressed using the inner products of a series of basis functions, following the Galerkin procedure. The continuity of the field and its radial derivative is enforced at the interface between adjacent layers. By applying this procedure to all inhomogeneous layers, the Helmholtz equations are transformed into linear algebraic equations with expanded coefficients in matrix form, allowing the complicated wave propagation problem in a multilayer inhomogeneous waveguide to be solved as a matrix eigenvalue problem. The method is validated by providing detailed propagation characteristics for various multilayer inhomogeneous cylinders with different permittivity profiles. The accuracy and efficiency of the proposed method are demonstrated through comparisons with results obtained using other numerical techniques.

Determination of Young’s Modulus of PET Sheets from Lamb Wave Velocity Measurement

BackgroundThe elastic modulus of polyethylene terephthalate (PET) sheets is typically measured through destructive tests that require specific sample preparation and time-consuming testing procedures.ObjectiveTo improve the efficiency of measuring the elastic modulus of PET sheets, research on a non-destructive measurement approach using guided Lamb waves was conducted.MethodsIn this approach, the group velocity of the zero-order symmetric Lamb wave mode (S0 mode) at a single frequency is first measured from PET sheets. The semi-analytical finite element method (SAFEM) is used as the forward model to calculate the corresponding numerical group velocity. Particle swarm optimisation (PSO) is used to update the elastic modulus in the SAFEM model until the numerical group velocity from the model matches the experimental results.ResultsThe results show that measuring the group velocity data at a single frequency is sufficient for elastic modulus measurement while the material thickness can be assumed as a constant, which improves the efficiency of the measurement. The identified modulus differs from the tensile modulus of the material due to the frequency dependence of the elastic modulus. However, this discrepancy could be eliminated by using a linear regression model.ConclusionsThe method mentioned above can achieve non-destructive and efficient measurement of the elastic modulus of PET sheets, which can potentially be applied for in-line quality inspection in PET bottle production processes.

Experimental Methods for Measuring the Efficiency of a Molten Salt Central Receiver

In this work, two different methods for measuring the efficiency of central receivers are analyzed by the case of the High Performance Molten Salt II Project (HPMS-II): the continuous power-on method, and the semi-analytical method. The main difference between the two methods is the procedure to calculate the thermal losses of the receiver: on the one hand, the continuous power-on method calculates the thermal losses from the measurement of the absorbed power by the molten salt for different measured incident powers on the receiver. Here, it is assumed that the thermal losses are independent of the incident power if the molten salt temperature is kept constant. On the other hand, the semi-analytical method calculates the thermal losses as the sum of convective and radiative losses, calculated directly from the Newton and Stefan-Boltzmann equations by measuring the temperature of the tube surface, the ambient temperature, and the wind speed. Therefore, the calculation of the thermal losses is independent from one method to another. The procedure of applying these methods during the experimental test campaign of the HPMS-II receiver is detailed in this paper. Additionally, an uncertainty analysis of both methods is conducted to determine the uncertainty expected for the receiver efficiency measurements.

Rapid and accurate semi-analytical method for the fatigue assessment with critical plane methods under non-proportional loading and material plasticity

Despite the substantial progress made over recent decades, fatigue assessment of structural components remains a challenge for designers, often culminating in unforeseen failures. Among the well established methods for evaluating fatigue, critical plane models have the capability of identifying the critical location and the direction of early crack propagation within a component. However, the use of the critical plane concept with the standard plane scanning method results extremely demanding when dealing with real-world scenarios, since, due to complex geometries, loading conditions and constraints, a comprehensive analysis of the part is required. In such situations, a more efficient computational method can be the discriminant to finalize a fatigue assessment. This study introduces a novel semi-analytical algorithm, which efficiently calculates critical plane factors. The algorithm was designed to be implemented alongside finite element analysis which may include elastic–plastic material behavior and non-proportional loading conditions. The method was tested on a notched component subjected to proportional and non-proportional loading conditions. As compared to the plane scanning method, the proposed method offers a time-efficient tool for evaluating critical plane factors and their associated plane orientations, with almost identical results.

A semi-analytical thermal model for craters with application to the crater-induced YORP effect

Context. The YORP effect is the thermal torque generated by radiation from the surface of an asteroid. The effect is sensitive to surface topology, including small-scale roughness, boulders, and craters. Aims. The aim of this paper is to develop a computationally efficient semi-analytical model for the crater-induced YORP (CYORP) effect that can be used to investigate the functional dependence of this effect. Methods. This study linearizes the thermal radiation term as a function of the temperature in the boundary condition of the heat conductivity, and obtains the temperature field in a crater over a rotational period in the form of a Fourier series, accounting for the effects of self-sheltering, self-radiation, and self-scattering. By comparison with a numerical model, we find that this semi-analytical model for the CYORP effect works well for K > 0.1 Wm−1 K−1. This semi-analytical model is computationally three-orders-of-magnitude more efficient than the numerical approach. Results. We obtain the temperature field of a crater, accounting for the thermal inertia, crater shape, and crater location. We then find that the CYORP effect is negligible when the depth-to-diameter ratio is smaller than 0.05. In this case, it is reasonable to assume a convex shape for YORP calculations. Varying the thermal conductivity yields a consistent value of approximately 0.01 for the spin component of the CYORP coefficient, while the obliquity component is inversely related to thermal inertia, declining from 0.004 in basalt to 0.001 in metal. The CYORP spin component peaks at an obliquity of 0°, 90°, or 180°, while the obliquity component peaks at an obliquity of around 45° or 135°. For a z-axis symmetric shape, the CYORP spin component vanishes, while the obliquity component persists. Our model confirms that the total YORP torque is damped by a few tens of percent by uniformly distributed small-scale surface roughness. Furthermore, for the first time, we calculate the change in the YORP torque at each impact on the surface of an asteroid explicitly and compute the resulting stochastic spin evolution more precisely. Conclusions. This study shows that the CYORP effect due to small-scale surface roughness and impact craters is significant during the history of asteroids. The semi-analytical method that we developed, which benefits from fast computation, offers new perspectives for future investigations of the YORP modeling of real asteroids and for the complete rotational and orbital evolution of asteroids accounting for collisions. Future research employing our CYORP model may explore the implications of space-varying roughness distribution, roughness in binary systems, and the development of a comprehensive rotational evolution model for asteroid groups.

On solving system of differential-algebraic equations using adomian decomposition method.

In this paper, we focus on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. The approximate solutions are computed rapidly and efficiently with the help of a semi-analytical method known as Adomian decomposition method (ADM). The logic of this method is simple and straightforward to understand. To demonstrate the proposed method, we presented several examples and the computations are compared with the exact solutions to show the efficient. One can employ this logic to different mathematical software tools such as Maple, SCILab, Mathematica, NCAlgebra, Matlab etc. for the problems in real life applications. In this paper, we offered a method for solving the given system of secondorder nonlinear DAEs with aid of the ADM. We shown that the proposed method is simple and efficient, also one can obtain the approximate solutions quickly using this method. A couple of examples are discussed for illustrating this method and graphical and mathematical assessments are discussed with the analytical solutions of the given problems.

Elastic Local Buckling and Width-to-Thickness Limits of I-Beams Incorporating Flange–Web Interactions

The local buckling of I-section beams is investigated with the flange–web interactions taken into account. Using numerical results employing the finite element method and a semi-analytical method, the flange–web interactions of I-sections and their effects on the buckling stresses are explored and discussed. Simple approximate solutions for the buckling coefficients of the web and compressive flange are developed using the energy method, and they are refined using the numerical results. Using the simple solutions for buckling coefficients, the limits for the width-to-thickness ratio of the compressive flange and web of I-section beams are then proposed. Comparisons with the results of existing solutions and provisions in design codes imply that the proposed solutions are superior in predicting the limits for width-to-thickness ratios, and they are capable of accounting for the flange–web interactions at the local buckling of I-section beams.

Triangular intuitionistic fuzzy linear system of equations with applications: an analytical approach

This study extended an existing semi-analytical technique, the Homotopy Perturbation Method, to the Block Homotopy Modified Perturbation Method by solving two n × n crisp triangular intuitionistic fuzzy (TIF) systems of linear equations. In the original system, the coefficient matrix is considered as real crisp, while the unknown variable vector and right hand side vector are regarded as triangular intuitionistic fuzzy numbers. The Block Homotopy Modified Perturbation Method is found to be efficient and practical to solve n × n TIF linear systems as it only requires the non-singularity of the n × n TIF linear system's coefficient matrix, whereas the point Homotopy Perturbation Method and other classical numerical iterative methods typically require non-zero diagonal entries in the coefficient matrix. A set of theorems relevant to this study are presented and demonstrated. We solve an engineering application, i.e. a current flow circuit problem that is represented in terms of a triangular intuitionistic fuzzy environment, using the suggested method. The unknown current is then obtained as a triangle intuitionistic fuzzy number. The proposed semi-analytic method is used to solve some numerical test problems in order to validate their performance and efficiency in comparison to other existing techniques. The numerical results of the example are displayed on graphs with different degrees of uncertainty. The efficiency and accuracy of the proposed method are further demonstrated by comparisons to block Jacobi, Adomain Decomposition method, Successive Over-Relaxation method and the classical Gauss-Seidel numerical method.