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Article
Publication date: 31 July 2020

Jingyu Pei, Xiaoping Wang, Leen Zhang, Yu Zhou and Jinyuan Qian

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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

Details

Engineering Computations, vol. 38 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 15 November 2011

Xi Chen and Yong‐Gang Cheng

The initial stiffness method has been extensively adopted for elasto‐plastic finite element analysis. The main problem associated with the initial stiffness method

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Article
Publication date: 9 September 2013

Norio Takahashi, Kousuke Shimomura, Daisuke Miyagi and Hiroyuki Kaimori

– 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).

Abstract

Purpose

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).

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 32 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 7 September 2015

Yoshifumi Okamoto, Akihisa Kameari, Koji Fujiwara, Tomonori Tsuburaya and Shuji Sato

– The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA).

Abstract

Purpose

The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA).

Design/methodology/approach

Nonlinear magnetic field analysis is achieved by using Newton-Raphson method implemented by relaxed convergence criterion of Krylov subspace method.

Findings

This paper mathematically analyzes the reason why nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed.

Research limitations/implications

The proposed method is essential to reduce the elapsed time in nonlinear magnetic field analysis of quasi-stationary field.

Practical implications

The proposed method is able to be extended to not only static field but also time domain FEA strongly coupled with circuit equation.

Social implications

Because the speedup of performance evaluation of electrical machines would be achieved using proposed method, the work efficiency in manufacturing would be accelerated.

Originality/value

It can be seen that the nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed. The verification of proposed method is demonstrated using practical nonlinear magnetic field problem.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 34 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 3 June 2020

Ehsan Zia, Ebrahim Farshidi and Abdolnabi Kosarian

Pipelined analog-to-digital converters (ADCs) are widely used in electronic circuits. The purpose of this paper is to propose a new digital background calibration method

Abstract

Purpose

Pipelined analog-to-digital converters (ADCs) are widely used in electronic circuits. The purpose of this paper is to propose a new digital background calibration method to correct the capacitor mismatch, finite direct current (DC) gain and nonlinearity of residue amplifiers in pipelined ADCs.

Design/methodology/approach

The errors are corrected by defining new functions based on generalized Newton–Raphson algorithm. Although the functions have analytical solutions, an iterative procedure is used for calibration. To accelerate the calibration process, proper initialization for the errors is identified by using evaluation estimation block and solving inverse matrix.

Findings

Several behavioral simulations of a 12-bit 100MS/s pipelined ADC in MATLAB indicate that signal-to-(noise + distortion) ratio (SNDR) and spurious free dynamic range (SFDR) are improved from 30dB/33dB to 70dB/79dB after calibration. Calibration is achieved in approximately 2,000 clock cycles.

Practical implications

The digital part of the proposed method is implemented on field-programmable gate array to validate the performance of the pipelined ADC. The experimental result shows that the degradation of SNDR, SFDR, integral nonlinearity, differential nonlinearity and effective number of bits is negligible according to fixed-point operation vs floating-point in simulation results.

Originality/value

The novelty of this study is to use Newton–Raphson algorithm combined with appropriate initialization to reduce the number of divisions as well as calibration time, which is suitable in the recent nano-meter complementary metal oxide semiconductor technologies.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 39 no. 4
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 August 2016

Pawel Stapór

The purpose of this paper is to carry out a finite element simulation of a physically non-linear phase change problem in a two-dimensional space without adaptive remeshing…

Abstract

Purpose

The purpose of this paper is to carry out a finite element simulation of a physically non-linear phase change problem in a two-dimensional space without adaptive remeshing or moving-mesh algorithms. The extended finite element method (XFEM) and the level set method (LSM) were used to capture the transient solution and motion of phase boundaries. It was crucial to consider the effects of unequal densities of the solid and liquid phases and the flow in the liquid region.

Design/methodology/approach

The XFEM and the LSM are applied to solve non-linear transient problems with a phase change in a two-dimensional space. The model assumes thermo-dependent properties of the material and unequal densities of the phases; it also allows for convection in the liquid phase. A non-linear system of equations is derived and a numerical solution is proposed. The Newton-Raphson method is used to solve the problem and the LSM is applied to track the interface.

Findings

The robustness and utility of the method are demonstrated on several two-dimensional benchmark problems.

Originality/value

The novel procedure based on the XFEM and the LSM was developed to solve physically non-linear phase change problems with unequal densities of phases in a two-dimensional space.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 August 1997

Wenhua Ling and Henryk K. Stolarski

Some frictional contact problems are characterized by significant variations in the location and size of the contact area occurring in the process of deformation. When…

Abstract

Some frictional contact problems are characterized by significant variations in the location and size of the contact area occurring in the process of deformation. When this feature is combined with strongly non‐linear, path‐dependent material behaviour, difficulties with convergence of the typically used iterative processes can be encountered. Demonstrates this by analysis of press‐fit connection, a typical problem in which both of those characteristics can be present. Offers an explanation as to the possible source of those difficulties. Suggests in support of this explanation, two simple modifications of the usual iterative schemes. In spite of their simplicity, they are found to be more robust than those usual schemes which are normally used in numerical analysis of similar problems.

Details

Engineering Computations, vol. 14 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 August 2001

M.H. Onsa, S.M. Sapuan, S. Basri, M.M.H. Megat Ahmad and M.A. Maleque

Presents a study on the application of boundary element method (BEM) to the solution of elastohydrodynamic lubricated hard rolling contacts in comparison with a solution…

Abstract

Presents a study on the application of boundary element method (BEM) to the solution of elastohydrodynamic lubricated hard rolling contacts in comparison with a solution using finite difference method (FDM). The developed program for the solution of Reynolds equation and the elasticity equation give results of pressure distribution and the lubricant film thickness for steady state, isothermal Newtonian lubricant behavior. Compares the BEM results and the computer effort with the solution using FDM. Uses an iterative Newton‐Raphson method to solve the non‐linearity of the problem. Discusses the effects of Hertzian pressure and rolling speeds on film thickness and pressure distribution. The numerical scheme of BEM has proved to have the advantage of being very effective and optimum in terms of accuracy, less computational effort and good constancy compared to other applied numerical techniques.

Details

Industrial Lubrication and Tribology, vol. 53 no. 4
Type: Research Article
ISSN: 0036-8792

Keywords

Article
Publication date: 4 July 2016

Nasrin Jafari and Mojtaba Azhari

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of…

Abstract

Purpose

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates.

Design/methodology/approach

Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function.

Findings

The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered.

Originality/value

This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

Details

Engineering Computations, vol. 33 no. 5
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 April 1988

E. Ramm and A. Matzenmiller

The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is…

Abstract

The present paper is directed towards elasto‐plastic large deformation analysis of thin shells based on the concept of degenerated solids. The main aspect of the paper is the derivation of an efficient computational strategy placing emphasis on consistent elasto‐plastic tangent moduli and stress integration with the radial return method under the restriction of ‘zero normal stress condition’ in thickness direction. The advantageous performance of the standard Newton iteration using a consistent tangent stiffness matrix is compared to the classical scheme with an iteration matrix based on the infinitesimal elasto‐plastic constitutive tensor. Several numerical examples also demonstrate the effectiveness of the standard Newton iteration with respect to modified and quasi‐Newton methods like BFGS and others.

Details

Engineering Computations, vol. 5 no. 4
Type: Research Article
ISSN: 0264-4401

1 – 10 of 938