An adaptive nonlinear finite element analysis of minimal surface problem based on element energy projection technique

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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Adaptive finite element analysis of free vibration of elastic membranes via element energy projection technique

Engineering Computations ◽

10.1108/ec-09-2020-0511 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Haohan Sun ◽

Si Yuan

Keyword(s):

Finite Element ◽

Free Vibration ◽

Mesh Refinement ◽

Error Tolerance ◽

Maximum Norm ◽

Adaptive Finite Element ◽

Content Type ◽

Local Mesh Refinement ◽

Elastic Membranes ◽

Element Energy Projection

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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Damage mechanics based model for low-rise infilled RC frames incorporating neural networks

Engineering Computations ◽

10.1108/ec-05-2015-0140 ◽

2016 ◽

Vol 33 (4) ◽

pp. 1114-1140 ◽

Cited By ~ 2

Author(s):

Khalid Abou El-Ftooh ◽

Ahmed Atta ◽

Ayman Ahmed Seleemah ◽

Salah El-Din Fahmy Taher

Keyword(s):

Neural Networks ◽

Finite Element ◽

Damage Mechanics ◽

Nonlinear Finite Element ◽

School Buildings ◽

Element Analysis ◽

Content Type ◽

Capacity Curves ◽

Rc Frames ◽

Infilled Rc Frames

Purpose – Separately, nonlinear finite element analysis, artificial neural networks (ANNs) and continuous damage mechanics (CDM) attracted many investigators to model masonry infilled frames. The purpose of this paper is to pursue four phases to develop a versatile model for partially and fully low-rise infilled RC frames using these tools. Design/methodology/approach – The first phase included the study of the behavior of 1,620 low-rise infilled reinforced concrete frames using macro-scale nonlinear pushover finite element analysis. The approach helped to explore the effects of imposing different masonry infill distributions for one of the typical models of school buildings in Egypt. The outputs of this phase were used in the second phase for the development of an ANN model where input neurons included number of stories, continuity conditions, frame geometry, infill distribution and properties of RC sections. The third phase included the employment of the notions of CDM on the structural scale. Monitoring frames’ stiffness degradation allowed for damage variables identification. In the fourth phase, the simpler equivalent static lateral load (ESLL) for elastic analysis was employed in conjunction with ANN and CDM to obtain the capacity curves for partially and fully low-rise infilled RC frames. Findings – The obtained capacity curves were compared with the nonlinear finite element results. The close agreement of all curves indicated how rigorous, yet simple, the suggested solution procedure is. Social implications – The study is concerned with an important type of service buildings. These are the school buildings of Egypt. Originality/value – The paper presents a combination of four phases that include FE analysis, ANNs, ESLL, and CDM to obtain the capacity curves for partially and fully low-rise infilled RC frames. Such a combination of approaches in tackling a practical problem related to service buildings is innovative and deserves research interest.

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Non-invasive implementation of nonlinear isogeometric analysis in an industrial FE software

Engineering Computations ◽

10.1108/ec-03-2019-0108 ◽

2019 ◽

Vol 37 (1) ◽

pp. 237-261 ◽

Cited By ~ 1

Author(s):

Marie Tirvaudey ◽

Robin Bouclier ◽

Jean-Charles Passieux ◽

Ludovic Chamoin

Keyword(s):

Finite Element ◽

Isogeometric Analysis ◽

Three Dimensional ◽

Nonlinear Problems ◽

The Novel ◽

Input Output ◽

Element Analysis ◽

Content Type ◽

Lagrange Polynomials ◽

Non Invasive

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.

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Seismic Vulnerability Assessment of a Historical Church: Limit Analysis and Nonlinear Finite Element Analysis

Advances in Civil Engineering ◽

10.1155/2013/517454 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 24

Author(s):

G. Castellazzi ◽

C. Gentilini ◽

L. Nobile

Keyword(s):

Finite Element ◽

Limit Analysis ◽

Seismic Vulnerability ◽

Failure Mechanisms ◽

Fe Analysis ◽

Nonlinear Finite Element ◽

Element Analysis ◽

Seismic Vulnerability Assessment ◽

The Church ◽

Selection Of

The seismic vulnerability of a historical Basilica church located in Italy is studied by means of limit analysis and nonlinear finite element (FE) analysis. Attention is posed to the failure mechanisms involving the façade of the church and its interaction with the lateral walls. In particular, the limit analysis and the nonlinear FE analysis provide an estimate of the load collapse multiplier of the failure mechanisms. Results obtained from both approaches are in agreement and can support the selection of possible retrofitting measures to decrease the vulnerability of the church under seismic loads.

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