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1 – 10 of 11Yiyi Dong, Si Yuan and Qinyan Xing
This study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element energy…
Abstract
Purpose
This study aims to propose a general and efficient adaptive strategy with local mesh refinement for two-dimensional (2D) finite element (FE) analysis based on the element energy projection (EEP) technique.
Design/methodology/approach
In view of the inflexibility of the existing global dimension-by-dimension (D-by-D) recovery method via EEP technique, in which displacements are recovered through element strips, an improved element D-by-D recovery strategy was proposed, which enables the EEP recovery of super-convergent displacements to be implemented mostly on a single element. Accordingly, a posteriori error estimate in maximum norm was established and an EEP-based adaptive FE strategy of h-version with local mesh refinement was developed.
Findings
Representative numerical examples, including stress concentration and singularity problems, were analyzed; the results of which show that the adaptively generated meshes reasonably reflect the local difficulties inherent in the physical problems and the proposed adaptive analysis can produce FE displacement solutions satisfying the user-specified tolerances in maximum norm with an almost optimal adaptive convergence rate.
Originality/value
The proposed element D-by-D recovery method is a more efficient and flexible displacement recovery method, which is implemented mostly on a single element. The EEP-based adaptive FE analysis can produce displacement solutions satisfying the specified tolerances in maximum norm with an almost optimal convergence rate and thus can be expected to apply to other 2D problems.
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Kaifeng Jiang, Si Yuan and Qinyan Xing
This paper aims to propose a new adaptive strategy for two-dimensional (2D) nonlinear finite element (FE) analysis of the minimal surface problem (MSP) based on the element energy…
Abstract
Purpose
This paper aims to propose a new adaptive strategy for two-dimensional (2D) nonlinear finite element (FE) analysis of the minimal surface problem (MSP) based on the element energy projection (EEP) technique.
Design/methodology/approach
By linearizing nonlinear problems into a series of linear problems via the Newton method, the EEP technique, which is an effective and reliable point-wise super-convergent displacement recovery strategy for linear FE analysis, can be directly incorporated into the solution procedure. Accordingly, a posteriori error estimate in maximum norm was established and an adaptive 2D nonlinear FE strategy of h-version mesh refinement was developed.
Findings
Three classical known surfaces, including a singularity problem, were analysed. Moreover, an example whose analytic solution is unavailable was considered and a comparison was made between present results and those computed by the MATLAB PDE toolbox. The results show that the adaptively-generated meshes reflect the difficulties inherent in the problems and the proposed adaptive analysis can produce FE solutions satisfying the user-preset error tolerance in maximum norm with a fair adaptive convergence rate.
Originality/value
The EEP technique for linear FE analysis was extended to the nonlinear procedure of MSP and can be expected to apply to other 2D nonlinear problems. The employment of the maximum norm makes point-wisely error control on the sought surfaces possible and makes the proposed method distinguished from other adaptive FE analyses.
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Haohan Sun and Si Yuan
A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique.
Abstract
Purpose
A general strategy is developed for adaptive finite element (FE) analysis of free vibration of elastic membranes based on the element energy projection (EEP) technique.
Design/methodology/approach
By linearizing the free vibration problem of elastic membranes into a series of linear equivalent problems, reliable a posteriori point-wise error estimator is constructed via EEP super-convergent technique. Hierarchical local mesh refinement is incorporated to better deal with tough problems.
Findings
Several classical examples were analyzed, confirming the effectiveness of the EEP-based error estimation and overall adaptive procedure equipped with a local mesh refinement scheme. The computational results show that the adaptively-generated meshes reasonably catch the difficulties inherent in the problems and the procedure yields both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm.
Originality/value
By reasonable linearization, the linear-problem-based EEP technique is successfully transferred to two-dimensional eigenproblems with local mesh refinement incorporated to effectively and flexibly deal with singularity problems. The corresponding adaptive strategy can produce both eigenvalues with required accuracy and mode functions satisfying user-preset error tolerance in maximum norm and thus can be expected to apply to other types of eigenproblems.
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Haohan Sun and Si Yuan
An improved adaptive finite element analysis based on local error estimate is proposed via the element energy projection (EEP) technique. This paper aims to discuss the…
Abstract
Purpose
An improved adaptive finite element analysis based on local error estimate is proposed via the element energy projection (EEP) technique. This paper aims to discuss the aforementioned idea.
Design/methodology/approach
The computational region for a posteriori error estimation based on EEP method is further confined to a critical set of local elements generated in the previous adaptive step, enhancing efficiency while maintaining accuracy. The adaptive procedure incorporated with hierarchical mesh refinement is then developed.
Findings
The effectiveness of the improved error estimation of the overall adaptive analysis is confirmed by several benchmark examples. The results show that the shrinkage of the local computational region has little negative influence on the accuracy of a posteriori error estimation, thus yielding an improved adaptive procedure with simplified logic and reduced cost.
Originality/value
By localizing the computational region for error estimation, two crucial but cumbersome tricks, i.e. treatments of virtual elements and hanging nodes, are removed, giving the proposed approach full clarity and flexibility. The improved adaptive procedure characterizes simpler and faster computational algorithm and can produce results with required accuracy measured in maximum norm.
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Si Yuan, Kangsheng Ye, Yongliang Wang, David Kennedy and Frederic W. Williams
The purpose of this paper is to present a numerically adaptive finite element (FE) method for accurate, efficient and reliable eigensolutions of regular second- and fourth-order…
Abstract
Purpose
The purpose of this paper is to present a numerically adaptive finite element (FE) method for accurate, efficient and reliable eigensolutions of regular second- and fourth-order Sturm–Liouville (SL) problems with variable coefficients.
Design/methodology/approach
After the conventional FE solution for an eigenpair (i.e. eigenvalue and eigenfunction) of a particular order has been obtained on a given mesh, a novel strategy is introduced, in which the FE solution of the eigenproblem is equivalently viewed as the FE solution of an associated linear problem. This strategy allows the element energy projection (EEP) technique for linear problems to calculate the super-convergent FE solutions for eigenfunctions anywhere on any element. These EEP super-convergent solutions are used to estimate the FE solution errors and to guide mesh refinements, until the accuracy matches user-preset error tolerance on both eigenvalues and eigenfunctions.
Findings
Numerical results for a number of representative and challenging SL problems are presented to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method.
Research limitations/implications
The method is limited to regular SL problems, but it can also solve some singular SL problems in an indirect way.
Originality/value
Comprehensive utilization of the EEP technique yields a simple, efficient and reliable adaptive FE procedure that finds sufficiently fine meshes for preset error tolerances on eigenvalues and eigenfunctions to be achieved, even on problems which proved troublesome to competing methods. The method can readily be extended to vector SL problems.
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Sadia Samar Ali, Rajbir Kaur and Jose Antonio Marmolejo Saucedo
Ceramic materials and glasses have become important in modern industry as well as in the consumer environment. Heat resistant ceramics are used in the metal forming processes or…
Abstract
Purpose
Ceramic materials and glasses have become important in modern industry as well as in the consumer environment. Heat resistant ceramics are used in the metal forming processes or as welding and brazing fixtures, etc. Ceramic materials are frequently used in industries where a wear and chemical resistance are required criteria (seals, liners, grinding wheels, machining tools, etc.). Electrical, magnetic and optical properties of ceramic materials are important in electrical and electronic industries where these materials are used as sensors and actuators, integrated circuits, piezoelectric transducers, ultrasonic devices, microwave devices, magnetic tapes, and in other applications. A significant amount of literature is available on the finite element modelling (FEM) of ceramics and glass. This paper gives a listing of these published papers and is a continuation of the author's bibliography entitled “Finite element modelling of ceramics and glass” and published in Engineering Computations, Vol. 16, 1999, pp. 510‐71 for the period 1977‐1998.
Design/methodology/approach
The form of the paper is a bibliography. Listed references have been retrieved from the author's database, MAKEBASE. Also Compendex has been checked. The period is 1998‐2004.
Findings
Provides a listing of 1,432 references. The following topics are included: ceramics – material and mechanical properties in general, ceramic coatings and joining problems, ceramic composites, piezoceramics, ceramic tools and machining, material processing simulations, fracture mechanics and damage, applications of ceramic/composites in engineering; glass – material and mechanical properties in general, glass fiber composites, material processing simulations, fracture mechanics and damage, and applications of glasses in engineering.
Originality/value
This paper makes it easy for professionals working with the numerical methods with applications to ceramics and glasses to be up‐to‐date in an effective way.
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Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the…
Abstract
Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.
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Mark Williams, Natasha Pauli and Bryan Boruff
Climate change, deforestation and hydropower dams are contributing to environmental change in the Lower Mekong River region, the combined effects of which are felt by many rural…
Abstract
Climate change, deforestation and hydropower dams are contributing to environmental change in the Lower Mekong River region, the combined effects of which are felt by many rural Cambodians. How people perceive and manage the effects of environmental change will influence future adaptation strategies. The objective of this research was to investigate whether the use of a low-cost, explicitly spatial method (participatory mapping) can help identify locally relevant opportunities and challenges to climate change adaptation in small, flood-prone communities. Four villages along the banks of the Mekong River in Kratie Province, Cambodia, were the subject of this research. To identify perceived environmental hazards and adaptive responses, eight workshops were conducted using focus-group interviews and participatory mapping. The communities’ responses highlight the evolving nature of environmental hazards, as droughts increase in perceived importance while the patterns of wet season flooding were also perceived to be changing. The attribution of the drivers of these hazards was strongly skewed towards local factors such as deforestation and less towards regional or global drivers affecting the hydrology of the Mekong and climate patterns. Combining participatory mapping with focus-group interviews allowed a greater depth of understanding of the vulnerabilities and opportunities available to communities than reliance on a single qualitative method. The study highlights the potential for a bottom-up transfer of information to strengthen existing climate change policies and tailor adaptation plans to local conditions.
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The purpose of this paper is to demonstrate the trends toward work being more suitable for machines than people, which promotes more addictive lifecycles. This paper suggests ways…
Abstract
Purpose
The purpose of this paper is to demonstrate the trends toward work being more suitable for machines than people, which promotes more addictive lifecycles. This paper suggests ways people can reverse this trend to cut them off from their humanity and create ways of working that are more natural, uplifting, life‐affirming and healthier for people.
Design/methodology/approach
The approach is to cite evidence of growing dysfunction, including facts and studies that support the trends; to explain how this has occurred; to describe how systems behave and misbehave; and to call for transformation.
Findings
This paper finds that people are suffering more stress, experiencing a reduced quality of life, getting sick more often and are less happy. And most of them don't realize why they are less happy because they seem to have so much (material wealth) to be grateful for. The findings include a way to reverse these trends and return to a life more suitable to human beings.
Practical implications
The practical implications are that people will start working in ways that are consistent with these new values and consciousness, finding newfound excitement and enthusiasm for their work, and reawakening their passions for living and working. This will produce happier people, more effective organizations and a healthier society.
Originality/value
The value of this paper is to provide a “wake‐up call” to those who find themselves entranced by convention and numbed by pressures from the systems they live and work in, so they start thinking less obsessively, working less mechanically and demanding more people‐friendly work and ways of living.
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