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Article
Publication date: 1 May 1998

G. Chiandussi, R. Fontana and F. Urbinati

A method to solve shape and size optimisation problems with linear and non‐linear responses has been studied taking advantage of statistical methodologies. A nested…

Abstract

A method to solve shape and size optimisation problems with linear and non‐linear responses has been studied taking advantage of statistical methodologies. A nested optimisation procedure has been fixed. The global optimisation problem is decomposed in several subproblems where each non‐linear response is locally approximated with a first degree polynomial function identified by the definition and execution of an experimental plan. The approximating functions so obtained are used to evaluate the design sensitivity coefficients required by the optimisation procedure. The numerical results obtained during the optimisation process to verify exactly the value of the non‐linear responses are used to verify and to improve the approximating function accuracy. The non‐linear design sensitivity analysis method so defined has been used to solve a multidisciplinary shape optimisation problem involving a real 3D automotive structure.

Details

Engineering Computations, vol. 15 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 April 1991

S. RAKHEJA and A.K.W. AHMED

A local equivalent linearization methodology is proposed to simulate non‐linear shock absorbers and dual‐phase dampers in the convenient frequency domain. The methodology…

Abstract

A local equivalent linearization methodology is proposed to simulate non‐linear shock absorbers and dual‐phase dampers in the convenient frequency domain. The methodology based on principle of energy similarity, characterizes the non‐linear dual‐phase dampers via an array of local damping constants as function of local excitation frequency and amplitude, response, and type of non‐linearity. The non‐linear behaviour of the dual‐phase dampers can thus be predicted quite accurately in the entire frequency range. The frequency response characteristics of a vehicle model employing non‐linear dual‐phase dampers, evaluated using local linearization algorithm, are compared to those of the non‐linear system, established via numerical integration, to demonstrate the effectiveness of the algorithm. An error analysis is performed to quantify the maximum error between the damping forces generated by non‐linear and locally linear simulations. The influence of damper parameters on the ride improvement potentials of dual‐phase dampers is further evaluated using the proposed methodology and discussed.

Details

Engineering Computations, vol. 8 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 11 September 2007

Vedat Dogan

The transverse shear deformation and rotary inertia effects need to be included for an accurate analysis in the response of the relatively thick plates. This paper seeks…

Abstract

Purpose

The transverse shear deformation and rotary inertia effects need to be included for an accurate analysis in the response of the relatively thick plates. This paper seeks to use, one of the refined theories which takes into account those effects, The First Order Shear Deformation Theory, to obtain linear and non‐linear responses for anti‐symmetric angle‐ply composite plates under random excitation.

Design/methodology/approach

The random excitation is assumed to be stationary, ergodic and Gaussian with zero‐mean. A Monte Carlo Simulation of stationary random process is used. A multi‐mode Galerkin approach and numerical integration procedure are employed to find linear and non‐linear response solutions. Laminated composite plate is taken to be simply‐supported along four edges.

Findings

The vibration of composite plates at elevated temperatures is also investigated. The linear and non‐linear deflections root‐mean‐square (RMS) are obtained for various input levels, the different lamination angles and the number of layers.

Practical implications

Further, case studies might lead to a lighter design of thick panels used in high‐performance systems such as aerospace structures.

Originality/value

The paper provides information on the linear and more realistic non‐linear vibrations of thick composite plates in time domain so that it would be possible to obtain key statistical information directly from time‐response history.

Details

Aircraft Engineering and Aerospace Technology, vol. 79 no. 5
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 1 October 2005

Alessio Bonelli and Oreste S. Bursi

To propose novel predictor‐corrector time‐integration algorithms for pseudo‐dynamic testing.

Abstract

Purpose

To propose novel predictor‐corrector time‐integration algorithms for pseudo‐dynamic testing.

Design/methodology/approach

The novel predictor‐corrector time‐integration algorithms are based on both the implicit and the explicit version of the generalized‐α method. In the non‐linear unforced case second‐order accuracy, stability in energy, energy decay in the high‐frequency range as well as asymptotic annihilation are distinctive properties of the generalized‐α scheme; while in the non‐linear forced case they are the limited error near the resonance in terms of frequency location and intensity of the resonant peak. The implicit generalized‐α algorithm has been implemented in a predictor‐one corrector form giving rise to the implicit IPC‐ρ method, able to avoid iterative corrections which are expensive from an experimental standpoint and load oscillations of numerical origin. Moreover, the scheme embodies a secant stiffness formula able to approximate closely the actual stiffness of a structure. Also an explicit algorithm has been implemented, the EPC‐ρb method, endowed with user‐controlled dissipation properties. The resulting schemes have been tested experimentally both on a two‐ and on a six‐degrees‐of‐freedom system, exploiting substructuring techniques.

Findings

The analytical findings and the tests have indicated that the proposed numerical strategies enhance the performance of the pseudo‐dynamic test (PDT) method even in an environment characterized by considerable experimental errors. Moreover, the schemes have been tested numerically on strongly non‐linear multiple‐degrees‐of‐freedom systems reproduced with the Bouc‐Wen hysteretic model, showing that the proposed algorithms reap the benefits of the parent generalized‐α methods.

Research limitations/implications

Further developments envisaged for this study are the application of the IPC‐ρ method and of EPC‐ρb scheme to partitioned procedures for high‐speed pseudo‐dynamic testing with substructuring.

Practical implications

The implicit IPC‐ρ and the explicit EPC‐ρb methods allow a user to have defined dissipation which reduces the effects of experimental error in the PDT without needing onerous iterations.

Originality/value

The paper proposes novel time‐integration algorithms for pseudo‐dynamic testing. Thanks to a predictor‐corrector form of the generalized‐α method, the proposed schemes maintain a high computational efficiency and accuracy.

Details

Engineering Computations, vol. 22 no. 7
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 June 2000

C.A.N. Dias and J.R.D. Petreche

In marine structures, the long‐term non‐stationary response of flexible lines, due to random environmental loads, may be regarded as successive short‐term stationary…

Abstract

In marine structures, the long‐term non‐stationary response of flexible lines, due to random environmental loads, may be regarded as successive short‐term stationary processes in which current, wind and ocean wave conditions remain constant. The power spectrum of each stationary process can be characterized by its linear and non‐linear energy components: the linear energy defines a Gaussian process, and the additional nonlinear energy characterizes a non‐Gaussian process. Within this scope, digital bispectral analysis has enabled one to describe non‐linear stationary response of flexible lines in the frequency domain, so that the complex coefficients of a quadratic model, in the frequency domain, can be estimated. The real and symmetrical matrix constructed from these coefficients has eigenvalues and eigenvectors useful to describe the characteristic function of the response from where the probability density function can be obtained by using a fast Fourier transform algorithm. The bases of the method presented here have already been treated, in a similar but pure algebraic method, to obtain the asymptotic probability function applicable to the response of non‐linear systems in closed form.

Details

Engineering Computations, vol. 17 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 May 2001

Stefan Schwarz and Ekkehard Ramm

The present contribution deals with the sensitivity analysis and optimization of structures for path‐dependent structural response. Geometrically as well as materially…

Abstract

The present contribution deals with the sensitivity analysis and optimization of structures for path‐dependent structural response. Geometrically as well as materially non‐linear behavior with hardening and softening is taken into account. Prandtl‐Reuss‐plasticity is adopted so that not only the state variables but also their sensitivities are path‐dependent. Because of this the variational direct approach is preferred for the sensitivity analysis. For accuracy reasons the sensitivity analysis has to be consistent with the analysis method evaluating the structural response. The proposed sensitivity analysis as well as its application in structural optimization is demonstrated by several examples.

Details

Engineering Computations, vol. 18 no. 3/4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 January 1986

V.P. Iu and Y.K. Cheung

The theoretical development of the incremental finite element for non‐linear vibration of multilayer sandwich plates was presented in Part 1 and the equation of motion was…

Abstract

The theoretical development of the incremental finite element for non‐linear vibration of multilayer sandwich plates was presented in Part 1 and the equation of motion was established. In the second part of the paper, the solution techniques are described and a number of examples are given.

Details

Engineering Computations, vol. 3 no. 1
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 March 1996

A.A. Polynkine, F. Van Keulen and V.V. Toropov

Presents an approach for optimal design of geometrically non‐linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the…

Abstract

Presents an approach for optimal design of geometrically non‐linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the multi‐point approximation method. The finite element method is used for the structural analysis. Reformulation of the optimal design problem is applied to circumvent complications caused by the non‐linear behaviour of the structure. The latter may lead to bifurcations, limit points and/or significant reduction of the structural stiffness for individual intermediate designs generated by an optimization algorithm. Discretization errors are controlled using AMR. To reduce computational costs, the requested global and local discretization errors are not taken as fixed values but are specified on the basis of the current status of the optimization process. In the beginning relatively large errors are accepted, while as the process progresses discretization errors are reduced. The method is applied to thin‐walled structures with geometrically non‐linear behaviour.

Details

Engineering Computations, vol. 13 no. 2/3/4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 June 2003

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view…

Abstract

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Details

Engineering Computations, vol. 20 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 27 March 2020

Yan Xia, Yi Wan, Hongwei Wang and Zhanqiang Liu

As the transmission component of a locomotive, the traction gear pair system has a direct effect on the stability and reliability of the whole machine. This paper aims to…

Abstract

Purpose

As the transmission component of a locomotive, the traction gear pair system has a direct effect on the stability and reliability of the whole machine. This paper aims to provide a detailed dynamic analysis for the traction system under internal and external excitations by numerical simulation.

Design/methodology/approach

A non-linear dynamic model of locomotive traction gear pair system is proposed, where the comprehensive time-varying meshing stiffness is obtained through the Ishikawa formula method and verified by the energy method, and then the sliding friction excitation is analyzed based on the location of the contact line. Meantime, the adhesion torque is constructed as a function of the adhesion-slip feature between wheelset and rail. Through Runge–Kutta numerical method, the system responses are studied with varying bifurcation parameters consisting of exciting frequency, load fluctuation, gear backlash, error fluctuation and friction coefficient. The dynamic behaviors of the system are analyzed and discussed from bifurcation diagram, time history, spectrum plot, phase portrait, Poincaré map and three-dimensional frequency spectrum.

Findings

The analysis results reveal that as control parameters vary the system experiences complex transition among a diverse range of motion states such as one-periodic, multi-periodic and chaotic motions. Specifically, the significant difference in system bifurcation characteristics can be observed under different adhesion conditions. The suitable gear backlash and error fluctuation can avoid the chaotic motion, and thus, reduce the vibration amplitude of the system. Similarly, the increasing friction coefficient can also suppress the unstable state and improve the stability of the system.

Originality/value

The numerical results may provide a systemic understanding of dynamic characteristics and present some available information to design and optimize the transmission performance of the locomotive traction system.

Details

Engineering Computations, vol. 37 no. 8
Type: Research Article
ISSN: 0264-4401

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