Search results

Showing both theoretically and experimentally that the Newton‐Raphson algorithm is a very efficient tool for computing the transfer factor characteristic of AM detectors.

An equation which describes the diode and transistor AM detectors has been investigated. Using elementary techniques of mathematical analysis, some theoretical properties of the equation have been formulated and convergence of the Newton‐Raphson algorithm has been proved.

It is shown that the Newton‐Raphson algorithm is an efficient tool for tracing the transfer factor characteristics of both diode and transistor AM detector. The convergence of this algorithm is proved and a comparison with SPICE simulation is made. Furthermore, the diode and transistor AM detectors have been built up and validating measurements have been carried out. The comparison shows that the algorithm proposed in the paper computes the characteristics fast achieving good accuracy.

The results obtained are limited to those described in the paper diode and transistor AM detectors.

Some properties of the nonlinear equation describing the AM detectors are formulated and convergence of the Newton‐Raphson algorithm to a unique solution is proved.

This study aims to present the experimental results for neural network (NN) based harmonic elimination technique for single-phase inverters.

Switching angles applied to power switches are determined using the NN technique based on the harmonics to be suppressed. Thus, besides controlling the output voltage, NN controller provides elimination of predetermined harmonics from output signal of single-phase inverter. Simulation and experimental results for the elimination of 15 and 20 low-order harmonics are presented. The switching angle values calculated by a NN , fuzzy logic and Newton–Raphson are compared for elimination of first 10 harmonics.

This paper provides the harmonic spectra showing that first 15 and 20 harmonics are suppressed from output signal. The NN is proved to give closest results to angle values calculated by Newton–Raphson’s numerical solution method.

The value of this paper is to verify the simulation results with the experimental result for the elimination of 15 and 20 low-order harmonics. Both the simulation and the experimental results demonstrate the success of the NN based selected harmonic elimination.

This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection.

For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods.

The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points.

The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.

The initial stiffness method has been extensively adopted for elasto‐plastic finite element analysis. The main problem associated with the initial stiffness method, however, is its slow convergence, even when it is used in conjunction with acceleration techniques. The Newton‐Raphson method has a rapid convergence rate, but its implementation resorts to non‐symmetric linear solvers, and hence the memory requirement may be high. The purpose of this paper is to develop more advanced solution techniques which may overcome the above problems associated with the initial stiffness method and the Newton‐Raphson method.

In this work, the accelerated symmetric stiffness matrix methods, which cover the accelerated initial stiffness methods as special cases, are proposed for non‐associated plasticity. Within the computational framework for the accelerated symmetric stiffness matrix techniques, some symmetric stiffness matrix candidates are investigated and evaluated.

Numerical results indicate that for the accelerated symmetric stiffness methods, the elasto‐plastic constitutive matrix, which is constructed by mapping the yield surface of the equivalent material to the plastic potential surface, appears to be appealing. Even when combined with the Krylov iterative solver using a loose convergence criterion, they may still provide good nonlinear convergence rates.

Compared to the work by Sloan et al., the novelty of this study is that a symmetric stiffness matrix is proposed to be used in conjunction with acceleration schemes and it is shown to be more appealing; it is assembled from the elasto‐plastic constitutive matrix by mapping the yield surface of the equivalent material to the plastic potential surface. The advantage of combining the proposed accelerated symmetric stiffness techniques with the Krylov subspace iterative methods for large‐scale applications is also emphasized.

The purpose of this paper is to propose an efficient computational technique, which uses Haar wavelets collocation approach coupled with the Newton-Raphson method and solves the following class of system of Lane–Emden equations:

To deal with singularity, Haar wavelets are used, and to deal with the nonlinear system of equations that arise during computation, the Newton-Raphson method is used. The convergence of these methods is also established and the results are compared with existing techniques.

The authors propose three methods based on uniform Haar wavelets approximation coupled with the Newton-Raphson method. The authors obtain quadratic convergence for the Haar wavelets collocation method. Test problems are solved to validate various computational aspects of the Haar wavelets approach. The authors observe that with only a few spatial divisions the authors can obtain highly accurate solutions for both initial value problems and boundary value problems.

The results presented in this paper do not exist in the literature. The system of nonlinear singular differential equations is not easy to handle as they are singular, as well as nonlinear. To the best of the knowledge, these are the first results for a system of nonlinear singular differential equations, by using the Haar wavelets collocation approach coupled with the Newton-Raphson method. The results developed in this paper can be used to solve problems arising in different branches of science and engineering.

The purpose of this paper is to propose the speed-up of the fixed-point method by updating the reluctivity at each iteration (this is called a modified fixed-point method).

A modified fixed-point method, which updates the derivative of reluctivity at each iteration, is proposed. It is shown that the formulation of the fixed-point method using the derivative of reluctivity is almost the same as that of the Newton-Raphson method. The convergence characteristic of the newly proposed fixed-point method is compared with those of the Newton-Raphson method.

The modified fixed-point method has an advantage that the programming is easy and it has a similar convergence property to the Newton-Raphson method for an isotropic nonlinear problem.

This paper presents the formulation and convergence characteristic of the modified fixed-point method are almost the same as those of the Newton-Raphson method.

This study aims to develop an adaptive finite element method for structural eigenproblems of cracked Euler–Bernoulli beams via the superconvergent patch recovery displacement technique. This research comprises the numerical algorithm and experimental results for free vibration problems (forward eigenproblems) and damage detection problems (inverse eigenproblems).

The weakened properties analogy is used to describe cracks in this model. The adaptive strategy proposed in this paper provides accurate, efficient and reliable eigensolutions of frequency and mode (i.e. eigenpairs as eigenvalue and eigenfunction) for Euler–Bernoulli beams with multiple cracks. Based on the frequency measurement method for damage detection, using the difference between the actual and computed frequencies of cracked beams, the inverse eigenproblems are solved iteratively for identifying the residuals of locations and sizes of the cracks by the Newton–Raphson iteration technique. In the crack detection, the estimated residuals are added to obtain reliable results, which is an iteration process that will be expedited by more accurate frequency solutions based on the proposed method for free vibration problems.

Numerical results are presented for free vibration problems and damage detection problems of representative non-uniform and geometrically stepped Euler–Bernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method.

The proposed combination of methodologies described in the paper leads to a very powerful approach for free vibration and damage detection of beams with cracks, introducing the mesh refinement, that can be extended to deal with the damage detection of frame structures.

The purpose of this paper is to apply a new systematic simulation approach to an existing liquid propellant engine.

The simulation approach is based on following the liquids (oxidizer and fuel) in their respective paths. The nonlinear dynamic model of the engine is composed of implicit nonlinear algebraic equations coupled with a set of differential equations. The model is solved by placing the implicit nonlinear algebraic equations in a set of nested Newton‐Raphson loops followed by numerical integration of the differential equations using a first‐order Euler technique.

It is found that the simulation algorithm may successfully be applied to an operating point model to predict the steady‐state values with errors under 10 percent. These results indicate that such engine models may be used to design reiable robust engine control systems because a robust control system design would allow for about 20 percent discrepancy between the model and the actual case.

At present, the research is limited to liquid propellant engines that are modeled by a set of implicit nonlinear algebraic equations coupled with a set of differential equations; engine models that are entirely modeled by differential equations are subject of future research.

The major outcome of this research is that verifies liquid engines may be simulated by the novel idea of following the engine liquids in their respective paths.

This is the first paper that adapts an existing simulation algorithm for simulation of the specific liquid engine under study with experimental verification.

This work addresses the computational aspects of a model for elastoplastic damage at finite strains. The model is a modification of a previously established model for large strain elastoplasticity described by Perić et al. which is here extended to include isotropic damage and kinematic hardening. Within the computational scheme, the constitutive equations are numerically integrated by an algorithm based on operator split methodology (elastic predictor—plastic corrector). The Newton—Raphson method is used to solve the discretized evolution equations in the plastic corrector stage. A numerical assessment of accuracy and stability of the integration algorithm is carried out based on iso‐error maps. To improve the stability of the local N—R scheme, the standard elastic predictor is replaced by improvedinitial estimates ensuring convergence for large increments. Several possibilities are explored and their effect on the stability of the N—R scheme is investigated. The finite element method is used in the approximation of the incremental equilibrium problem and the resulting equations are solved by the standard Newton—Raphson procedure. Two numerical examples are presented. The results are compared with those obtained by the original elastoplastic model.

This paper discusses the use of a complex‐valued reluctivity tensor for modelling non‐linear, anisotropic and hysteretic materials in a time‐harmonic finite element context. It is shown how these problems can be solved by the Newton‐Raphson method. The method is applied for the simulation of the magnetic field distribution in a three‐phase transformer.