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Article
Publication date: 12 June 2017

Hongliang Tian and Yuan Yu

This study considers a Lagrange direct way of modal assurance criterion (MAC) values of an undamped system. The mentioned method for the sensitivity analysis of the MAC of a…

Abstract

Purpose

This study considers a Lagrange direct way of modal assurance criterion (MAC) values of an undamped system. The mentioned method for the sensitivity analysis of the MAC of a sliding machine working table is more close to the exact solution and time efficient. The paper aims to discuss these issues.

Design/methodology/approach

Using the Lagrange multipliers to compute the first and second-order sensitivity analysis of MAC values.

Findings

Because of the Lagrange multiplier without considering the number of design parameters, one only needs to perform the calculation once. Compared with the indirect way, the direct way is more effective when the number of design parameters is greater than one. This calculation procedure is simple and accurate, which can be popularized and used.

Originality/value

Engineering structure often requires only some structure design, and most of the sub-structure design variables are not related to each other. In this case, this way is better and more efficient. The direct way can be applied to the dynamic optimization design of large structures, the frequency and the mode sensitivity analysis in the process of model modification.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 1
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 7 August 2019

Marie Tirvaudey, Robin Bouclier, Jean-Charles Passieux and Ludovic Chamoin

The purpose of this paper is to further simplify the use of NURBS in industrial environnements. Although isogeometric analysis (IGA) has been the object of intensive studies over…

Abstract

Purpose

The purpose of this paper is to further simplify the use of NURBS in industrial environnements. Although isogeometric analysis (IGA) has been the object of intensive studies over the past decade, its massive deployment in industrial analysis still appears quite marginal. This is partly due to its implementation, which is not straightforward with respect to the elementary structure of finite element (FE) codes. This often discourages industrial engineers from adopting isogeometric capabilities in their well-established simulation environment.

Design/methodology/approach

Based on the concept of Bézier and Lagrange extractions, a novel method is proposed to implement IGA from an existing industrial FE code with the aim of bringing human implementation effort to the minimal possible level (only using standard input-output of finite element analysis (FEA) codes, avoid code-dependent subroutines implementation). An approximate global link to go from Lagrange polynomials to non-uniform-rational-B-splines functions is formulated, which enables the whole FE routines to be untouched during the implementation.

Findings

As a result, only the linear system resolution step is bypassed: the resolution is performed in an external script after projecting the FE system onto the reduced, more regular and isogeometric basis. The novel procedure is successfully validated through different numerical experiments involving linear and nonlinear isogeometric analyses using the standard input/output of the industrial FE software Code_Aster.

Originality/value

A non-invasive implementation of IGA into FEA software is proposed. The whole FE routines are untouched during the novel implementation procedure; a focus is made on the IGA solution of nonlinear problems from existing FEA software; technical details on the approach are provided by means of illustrative examples and step-by-step implementation; the methodology is evaluated on a range of two- and three-dimensional elasticity and elastoplasticity benchmarks solved using the commercial software Code_Aster.

Details

Engineering Computations, vol. 37 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 30 September 2014

Zixiang Hu, Shi Zhang, Yun Zhang, Huamin Zhou and Dequn Li

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with…

Abstract

Purpose

The purpose of this paper is to propose an efficient iterative method for large-scale finite element equations of bad numerical stability arising from deformation analysis with multi-point constraint using Lagrange multiplier method.

Design/methodology/approach

In this paper, taking warpage analysis of polymer injection molding based on surface model as an example, the performance of several popular Krylov subspace methods, including conjugate gradient, BiCGSTAB and generalized minimal residual (GMRES), with diffident Incomplete LU (ILU)-type preconditions is investigated and compared. For controlling memory usage, GMRES(m) is also considered. And the ordering technique, commonly used in the direct method, is introduced into the presented iterative method to improve the preconditioner.

Findings

It is found that the proposed preconditioned GMRES method is robust and effective for solving problems considered in this paper, and approximate minimum degree (AMD) ordering is most beneficial for the reduction of fill-ins in the ILU preconditioner and acceleration of the convergence, especially for relatively accurate ILU-type preconditioning. And because of concerns about memory usage, GMRES(m) is a good choice if necessary.

Originality/value

In this paper, for overcoming difficulties of bad numerical stability resulting from Lagrange multiplier method, together with increasing scale of problems in engineering applications and limited hardware conditions of computer, a stable and efficient preconditioned iterative method is proposed for practical purpose. Before the preconditioning, AMD reordering, commonly used in the direct method, is introduced to improve the preconditioner. The numerical experiments show the good performance of the proposed iterative method for practical cases, which is implemented in in-house and commercial codes on PC.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 7 August 2019

Zhihua Niu, Zhimin Li, Sun Jin and Tao Liu

This paper aims to carry out assembly variation analysis for mechanisms with compliant joints by considering deformations induced by manufactured deviations. Such an analysis…

Abstract

Purpose

This paper aims to carry out assembly variation analysis for mechanisms with compliant joints by considering deformations induced by manufactured deviations. Such an analysis procedure extends the application area of direct linearization method (DLM) to compliant mechanisms and also illustrates the dimensional interaction within multi-loop compliant structures.

Design/methodology/approach

By applying DLM to both geometrical equations and Lagrange’s equations of the second kind, an analytical deviation modeling method for mechanisms with compliant joints are proposed and further used for statistical assembly variation analysis. The precision of this method is verified by comparing it with finite element simulation and traditional DLM.

Findings

A new modeling method is proposed to represent kinematic relationships between joint deformations and parts/components deviations. Based on a case evaluation, the computational efficiency is improved greatly while the modeling accuracy is maintained at more than 94% rate comparing with the benchmark finite element simulation.

Originality/value

The Equilibrium Equations of Incremental Forces derived from Lagrange’s equations are proposed to quantitatively represent the relationships between manufactured deviations and assembly deformations. The present method extends the application area of DLM to compliant structures, such as automobile suspension systems and some Micro-Electro-Mechanical-Systems.

Details

Assembly Automation, vol. 39 no. 4
Type: Research Article
ISSN: 0144-5154

Keywords

Article
Publication date: 1 December 1998

M.A. Gutierrez, Y.M. Ojanguren and J.J. Anza

The numerical simulation of metal forming processes approximated by means of finite element techniques, require large computational effort, which contradicts the need of…

Abstract

The numerical simulation of metal forming processes approximated by means of finite element techniques, require large computational effort, which contradicts the need of interactivity for industrial applications. This work analyses the computational efficiency of algorithms combining elastoplasticity with finite deformation and contact mechanics, and in particular, the optimum solution of the linear systems to be solved through the incremental‐iterative schemes associated with non linear implicit analysis. A method based on domain decomposition techniques especially adapted to contact problems is presented, as well as the improved performance obtained in the application to hot rolling simulation, as a consequence of bandwidth reduction and the differentiated treatment of subdomains along the non linear analysis.

Details

Engineering Computations, vol. 15 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 3 October 2023

Ning Zhang, Hong Zheng, Chi Yuan and Wenan Wu

This article aims to present a direct solution to handle linear constraints in finite element (FE) analysis without penalties or the Lagrange multipliers introduced.

Abstract

Purpose

This article aims to present a direct solution to handle linear constraints in finite element (FE) analysis without penalties or the Lagrange multipliers introduced.

Design/methodology/approach

First, the system of linear equations corresponding to the linear constraints is solved for the leading variables in terms of the free variables and the constants. Then, the reduced system of equilibrium equations with respect to the free variables is derived from the finite-dimensional virtual work equation. Finally, the algorithm is designed.

Findings

The proposed procedure is promising in three typical cases: (1) to enforce displacement constraints in any direction; (2) to implement local refinements by allowing hanging nodes from element subdivision and (3) to treat non-matching grids of distinct parts of the problem domain. The procedure is general and suitable for 3D non-linear analyses.

Research limitations/implications

The algorithm is fitted only to the Galerkin-based numerical methods.

Originality/value

The proposed procedure does not need Lagrange multipliers or penalties. The tangential stiffness matrix of the reduced system of equilibrium equations reserves positive definiteness and symmetry. Besides, many contemporary Galerkin-based numerical methods need to tackle the enforcement of the essential conditions, whose weak forms reduce to linear constraints. As a result, the proposed procedure is quite promising.

Details

Engineering Computations, vol. 40 no. 9/10
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 March 1989

E.A.W. Maunder

This paper offers a simple valid alternative approach to the formulation of finite element models. Using two‐dimensional steady state heat conduction as a representative problem…

Abstract

This paper offers a simple valid alternative approach to the formulation of finite element models. Using two‐dimensional steady state heat conduction as a representative problem, the paper formalizes and extends a direct approach, normally restricted to constant strain triangular (CST) elements, to the construction of general finite element models. The approach is illustrated with the conventional 4, 8, and 9 noded quadrilateral elements. The sufficient conditions for convergence are explained in straightforward physical terms. The direct approach is based on the dual roles of shape functions, and does not require the use of variational methods or functional analysis. The formulation is shown to be equivalent to a weak form of Galerkin which makes explicit use of three forms of residual. This approach is intended to enable engineering students to gain a sound understanding of basic finite element methods with a minimum of mathematics.

Details

Engineering Computations, vol. 6 no. 3
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 30 September 2014

Zixiang Hu, Zhenmin Wang, Shi Zhang, Yun Zhang and Huamin Zhou

The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to…

191

Abstract

Purpose

The purpose of this paper is to propose a combined reordering scheme with a wide range of application, called Reversed Cuthill-McKee-approximate minimum degree (RCM-AMD), to improve a preconditioned general minimal residual method for solving equations using Lagrange multiplier method, and facilitates the choice of the reordering for the iterative method.

Design/methodology/approach

To reordering the coefficient matrix before a preconditioned iterative method will greatly impact its convergence behavior, but the effect is very problem-dependent, even performs very differently when different preconditionings applied for an identical problem or the scale of the problem varies. The proposed reordering scheme is designed based on the features of two popular ordering schemes, RCM and AMD, and benefits from each of them.

Findings

Via numerical experiments for the cases of various scales and difficulties, the effects of RCM-AMD on the preconditioner and the convergence are investigated and the comparisons of RCM, AMD and RCM-AMD are presented. The results show that the proposed reordering scheme RCM-AMD is appropriate for large-scale and difficult problems and can be used more generally and conveniently. The reason of the reordering effects is further analyzed as well.

Originality/value

The proposed RCM-AMD reordering scheme preferable for solving equations using Lagrange multiplier method, especially considering that the large-scale and difficult problems are very common in practical application. This combined reordering scheme is more wide-ranging and facilitates the choice of the reordering for the iterative method, and the proposed iterative method has good performance for practical cases in in-house and commercial codes on PC.

Details

Engineering Computations, vol. 31 no. 7
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 April 1990

Christine Barbier, Philip J. Clark, Peter Bettess and Jacqueline A. Bettess

The use of algebraic languages such as REDUCE makes possible the automatic generation, from fairly concise data, of the main families of two and three dimensional C0 continuous…

Abstract

The use of algebraic languages such as REDUCE makes possible the automatic generation, from fairly concise data, of the main families of two and three dimensional C0 continuous finite element shape functions, with a high confidence in their correctness. This paper gives a tutorial introduction to the REDUCE language and describes how it was used to generate shape function routines.

Details

Engineering Computations, vol. 7 no. 4
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 21 September 2020

Jacobus D. Brandsen, Axelle Viré, Sergio R. Turteltaub and Gerard J.W. Van Bussel

When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims…

Abstract

Purpose

When simulating fluid-structure interaction (FSI), it is often essential that the no-slip condition is accurately enforced at the wetted boundary of the structure. This paper aims to evaluate the relative strengths and limitations of the penalty and Lagrange multiplier methods, within the context of modelling FSI, through a comparative analysis.

Design/methodology/approach

In the immersed boundary method, the no-slip condition is typically imposed by augmenting the governing equations of the fluid with an artificial body force. The relative accuracy and computational time of the penalty and Lagrange multiplier formulations of this body force are evaluated by using each to solve three test problems, namely, flow through a channel, the harmonic motion of a cylinder through a stationary fluid and the vortex-induced vibration (VIV) of a cylinder.

Findings

The Lagrange multiplier formulation provided an accurate solution, especially when enforcing the no-slip condition, and was robust as it did not require “tuning” of problem specific parameters. However, these benefits came at a higher computational cost relative to the penalty formulation. The penalty formulation achieved similar levels of accuracy to the Lagrange multiplier formulation, but only if the appropriate penalty factor was selected, which was difficult to determine a priori.

Originality/value

Both the Lagrange multiplier and penalty formulations of the immersed boundary method are prominent in the literature. A systematic quantitative comparison of these two methods is presented within the same computational environment. A novel application of the Lagrange multiplier method to the modelling of VIV is also provided.

Details

Engineering Computations, vol. 38 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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