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Article
Publication date: 29 June 2022

Fan Lin, Jianshe Peng, Shifeng Xue and Jie Yang

In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear

Abstract

Purpose

In this paper, the authors aim to propose an effective method to indirectly determine nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials, and then study the nonlinear free torsional vibration of Al–1%Si shaft.

Design/methodology/approach

In this study the authors use BoxLucas1 model to fit the determined-experimentally nonlinear elastic normal stress–strain constitutive relationship curve of Al–1%Si, a typical case of isotropic nonlinear elasticity materials, and then derive its nonlinear shear stress-strain constitutive relationships based on the fitting constitutive relationships and general equations of plane-stress and plane-strain transformation. Hamilton’s principle is utilized to gain nonlinear governing equation and boundary conditions for free torsional vibration of Al–1%Si shaft. Differential quadrature method and an iterative algorithm are employed to numerically solve the gained equations of motion.

Findings

The effect of four variables, namely dimensionless fundamental vibration amplitude ϑmax, radius α and length β, and nonlinear-elasticity intensity factor δ, on frequencies and mode shapes of the shafts is obtained. Numerical results are in good agreement with reference solutions, and show that compared with linearly elastic shear stress-strain constitutive relationships of the shafts made of the nonlinear elasticity materials, its actual nonlinearly elastic shear stress-strain constitutive relationships have smaller torsion frequencies. In addition, but β having opposite hardening effect, the rest of the four variables have softening effect on nonlinearly elastic torsion frequencies. Eventually, taking into account nonlinearly elastic shear stress-strain constitutive relationships, changes of the four factors, i.e. ϑmax, α, β and δ, cause inflation and deflation behaviors of mode shapes in nonlinear free torsional vibration.

Originality/value

The study could provide a reference for indirectly determining nonlinear elastic shear stress-strain constitutive relationships for nonlinear elasticity materials and for structure design of torsional shaft made of nonlinear elasticity materials.

Details

Multidiscipline Modeling in Materials and Structures, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 10 June 2022

Hong-Sen Yan, Zhong-Tian Bi, Bo Zhou, Xiao-Qin Wan, Jiao-Jun Zhang and Guo-Biao Wang

The present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).

Abstract

Purpose

The present study is intended to develop an effective approach to the real-time modeling of general dynamic nonlinear systems based on the multidimensional Taylor network (MTN).

Design/methodology/approach

The authors present a detailed explanation for modeling the general discrete nonlinear dynamic system by the MTN. The weight coefficients of the network can be obtained by sampling data learning. Specifically, the least square (LS) method is adopted herein due to its desirable real-time performance and robustness.

Findings

Compared with the existing mainstream nonlinear time series analysis methods, the least square method-based multidimensional Taylor network (LSMTN) features its more desirable prediction accuracy and real-time performance. Model metric results confirm the satisfaction of modeling and identification for the generalized nonlinear system. In addition, the MTN is of simpler structure and lower computational complexity than neural networks.

Research limitations/implications

Once models of general nonlinear dynamical systems are formulated based on MTNs and their weight coefficients are identified using the data from the systems of ecosystems, society, organizations, businesses or human behavior, the forecasting, optimizing and controlling of the systems can be further studied by means of the MTN analytical models.

Practical implications

MTNs can be used as controllers, identifiers, filters, predictors, compensators and equation solvers (solving nonlinear differential equations or approximating nonlinear functions) of the systems of ecosystems, society, organizations, businesses or human behavior.

Social implications

The operating efficiency and benefits of social systems can be prominently enhanced, and their operating costs can be significantly reduced.

Originality/value

Nonlinear systems are typically impacted by a variety of factors, which makes it a challenge to build correct mathematical models for various tasks. As a result, existing modeling approaches necessitate a large number of limitations as preconditions, severely limiting their applicability. The proposed MTN methodology is believed to contribute much to the data-based modeling and identification of the general nonlinear dynamical system with no need for its prior knowledge.

Details

Kybernetes, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 7 April 2022

Hongwei Yang, Yingying Wang, Meng Zhang and Lianchun Long

This paper aims to provide a symplectic conservation numerical analysis method for the study of nonlinear LC circuit.

Abstract

Purpose

This paper aims to provide a symplectic conservation numerical analysis method for the study of nonlinear LC circuit.

Design/methodology/approach

The flux linkage control type nonlinear inductance model is adopted, and the LC circuit can be converted into the Hamiltonian system by introducing the electric charge as the state variable of the flux linkage. The nonlinear Hamiltonian matrix equation can be solved by perturbation method, which can be written as the sum of linear and nonlinear terms. Firstly, the linear part can be solved exactly. On this basis, the nonlinear part is analyzed by the canonical transformation. Then, the coefficient matrix of the obtained equation is still a Hamiltonian matrix, so symplectic conservation is achieved.

Findings

Numerical results reveal that the method proposed has strong stability, high precision and efficiency, and it has great advantages in long-term simulations.

Originality/value

This method provides a novel and effective way in studying the nonlinear LC circuit.

Details

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

Keywords

Article
Publication date: 16 December 2021

Le Dian Zheng, Yi Yang, Guang Lin Qiang and Zhengqi Gu

This paper aims to propose a precise turbulence model for automobile aerodynamics simulation, which can predict flow separation and reattachment phenomena more accurately.

Abstract

Purpose

This paper aims to propose a precise turbulence model for automobile aerodynamics simulation, which can predict flow separation and reattachment phenomena more accurately.

Design/methodology/approach

As the results of wake flow simulation with commonly used turbulence models are unsatisfactory, by introducing a nonlinear Reynolds stress term and combining the detached Eddy simulation (DES) model, this paper proposes a nonlinear-low-Reynolds number (LRN)/DES turbulence model. The turbulence model is verified in a backward-facing step case and applied in the flow field analysis of the Ahmed model. Several widely applied turbulence models are compared with the nonlinear-LRN/DES model and the experimental data of the above cases.

Findings

Compared with the experimental data and several turbulence models, the nonlinear-LRN/DES model gives better agreement with the experiment and can predict the automobile wake flow structures and aerodynamic characteristics more accurately.

Research limitations/implications

The nonlinear-LRN/DES model proposed in this paper suffers from separation delays when simulating the separation flows above the rear slant of the Ahmed body. Therefore, more factors need to be considered to further improve the accuracy of the model.

Practical implications

This paper proposes a turbulence model that can more accurately simulate the wake flow field structure of automobiles, which is valuable for improving the calculation accuracy of the aerodynamic characteristics of automobiles.

Originality/value

Based on the nonlinear eddy viscosity method and the scale resolved simulation, a nonlinear-LRN/DES turbulence model including the nonlinear Reynolds stress terms for separation and reattachment prediction, as well as the wake vortex structure prediction is first proposed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 July 2021

Zhi Li, Song Cen and Chenfeng Li

The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical…

Abstract

Purpose

The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis.

Design/methodology/approach

Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions.

Findings

Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements.

Originality/value

The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

Article
Publication date: 1 December 2020

Swen Koerner, Mario S. Staller and André Kecke

The study compares the impact of two different pedagogical approaches in police training by assessing the knife defense performance of German police recruits against…

Abstract

Purpose

The study compares the impact of two different pedagogical approaches in police training by assessing the knife defense performance of German police recruits against different types of knife attacks. Linear or nonlinear – which pedagogical approach leads to more efficient knife defense performance?

Design/methodology/approach

A total of 20 German state police recruits (w = 5, m = 15) were assigned to linear and nonlinear groups. The linear and nonlinear groups' performance on knife defense was assessed in a pretest, after a three-week training intervention in a posttest and eight weeks thereafter in a retention test, utilizing a mixed-method design (Sendall et al., 2018).

Findings

Quantitative data on knife defense performance suggest a lastingly better performance of the nonlinear group: in the retention test, participants of the nonlinear group were hit less (p = 0.029), solved the attack faster (p = 0.044) and more often (81.8%) than participants of the linear group (55.6%). In contrast, qualitative data reveal that, despite of evidence for a high level of perceived competence, the nonlinear teaching of knife defense skills has been accompanied by considerable uncertainties, affected by the lack of techniques and the focus on principles and operational parameters only.

Originality/value

It is the first study assessing the impact of different pedagogical approaches in police training. For the practice of police trainers, the results provide empirical orientations for an evidence-based planning of and reflection on pedagogical demands within their training (Mitchell and Lewis, 2017).

Details

Policing: An International Journal, vol. 44 no. 3
Type: Research Article
ISSN: 1363-951X

Keywords

Article
Publication date: 5 June 2019

Gang Li, Shuo Jia and Hong-Nan Li

The purpose of this paper is to make a theoretical comprehensive efficiency evaluation of a nonlinear analysis method based on the Woodbury formula from the efficiency of…

Abstract

Purpose

The purpose of this paper is to make a theoretical comprehensive efficiency evaluation of a nonlinear analysis method based on the Woodbury formula from the efficiency of the solution of linear equations in each incremental step and the selected iterative algorithms.

Design/methodology/approach

First, this study employs the time complexity theory to quantitatively compare the efficiency of the Woodbury formula and the LDLT factorization method which is a commonly used method to solve linear equations. Moreover, the performance of iterative algorithms also significantly effects the efficiency of the analysis. Thus, the three-point method with a convergence order of eight is employed to solve the equilibrium equations of the nonlinear analysis method based on the Woodbury formula, aiming to improve the iterative performance of the Newton–Raphson (N–R) method.

Findings

First, the result shows that the asymptotic time complexity of the Woodbury formula is much lower than that of the LDLT factorization method when the number of inelastic degrees of freedom (IDOFs) is much less than that of DOFs, indicating that the Woodbury formula is more efficient for local nonlinear problems. Moreover, the time complexity comparison of the N–R method and the three-point method indicates that the three-point method is more efficient than the N–R method for local nonlinear problems with large-scale structures or a larger ratio of IDOFs number to the DOFs number.

Originality/value

This study theoretically evaluates the efficiency of nonlinear analysis method based on the Woodbury formula, and quantitatively shows the application condition of the comparative methods. The comparison result provides a theoretical basis for the selection of algorithms for different nonlinear problems.

Details

Engineering Computations, vol. 36 no. 4
Type: Research Article
ISSN: 0264-4401

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: 7 March 2016

Fei Zhong, Chunlei Zhang, Wensheng Li, Jingpin Jiao and Liqiang Zhong

Super304H steel is a new fine-grained austenitic heat-resistant stainless steel developed in recent years, and it is widely used in high temperature section superheater…

Abstract

Purpose

Super304H steel is a new fine-grained austenitic heat-resistant stainless steel developed in recent years, and it is widely used in high temperature section superheater and reheater tubes of ultra-supercritical thermal power units’ boiler. Currently intergranular corrosion (IGC) has occurred in a few austenitic stainless steel tubes in ultra-supercritical units and led to boiler leakage. The purpose of this paper is to find a nondestructive method to quickly and easily detect IGC of austenitic stainless steel tube.

Design/methodology/approach

This paper uses the nonlinear characteristics of ultrasonic propagation in steel tube to detect the IGC of Super304H tube.

Findings

The experimental results show that the nonlinear coefficient generally increases sensitively with the degree of IGC; hence, the nonlinear coefficient can be used to assess IGC degree of tubes, and the nonlinear coefficient measurement method is repeatable for the same tube.

Research limitations/implications

A theory of how IGC would affect the ultrasonic signals and lead to a nonlinear response needs further research.

Practical implications

A nondestructive method to quickly and easily detect IGC is provided.

Social implications

Using ultrasonic nonlinear coefficient to assess IGC degree of tubes is a new try.

Originality/value

This paper provides a new way to test IGC.

Details

Anti-Corrosion Methods and Materials, vol. 63 no. 2
Type: Research Article
ISSN: 0003-5599

Keywords

Article
Publication date: 3 May 2016

Peyman Rafiee, Golta Khatibi and Francesco Solazzi

The purpose of this study is to address the nonlinear oscillations of single-crystal silicon micro-electromechanical systems (MEMS) accelerometers subjected to mechanical…

Abstract

Purpose

The purpose of this study is to address the nonlinear oscillations of single-crystal silicon micro-electromechanical systems (MEMS) accelerometers subjected to mechanical excitation.

Methodology/approach

The nonlinear behavior was detected and analyzed by using experimental, analytical and numerical approaches. Piezoelectric shaker as a source of mechanical excitation and differential laser Doppler vibrometer in combination with a micro system analyzer were used in the experimental effort. Two types of devices considered included nonencapsulated samples and samples encapsulated in nitrogen gas compressed between two glasses. Numerical and analytical investigations were conducted to analyze the nonlinear response. A novel method has been suggested to calculate the nonlinear parameters. The obtained experimental, numerical and analytical results are in good agreement.

Findings

It has been found that the nonlinearity leads to a shift in frequencies and generates higher harmonics, but, most importantly, reveals new phenomena, such as the jump and instability of the vibration amplitudes and phases.

Originality/value

It has been shown that under the constant excitation force, the MEMS device can work in both linear and nonlinear regions. The role of the beat phenomenon has been also addressed and discussed. It has been found that the attributes of the nonlinear response are strongly dependent on the level and duration of the excitation. It is concluded that the nonlinear response of the systems is strongly dependent on the level of the excitation energy. It has been also concluded that larger quality factors are able to enhance dramatically the nonlinear effects and vice versa.

Details

Microelectronics International, vol. 33 no. 2
Type: Research Article
ISSN: 1356-5362

Keywords

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