Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

Yuan, Songmei; Du, Yan; Xing, Qinyan; Ye, Kangsheng

doi:10.1007/s10483-014-1869-9

Cited by 10 publications

(4 citation statements)

References 2 publications

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“…He was promoted to be a professor of civil engineering in 1991 and was an honoured professor of Changjiang Scholars in 2000and Chinese Renowned Teacher in 2003. From 2008to 2014, he served as the Vice President and Provost of Tsinghua University. He also holds several important positions for some major associations and journals in civil engineering and computational mechanics.…”

Section: About the Authorsmentioning

confidence: 99%

“…Based on EEP method, a series of adaptive FE analyses have been developed and have successfully applied to various 1D FE (Yuan et al, 2014 and 2D linear FE adaptive analyses (Yuan et al, 2019;Dong et al, 2019). However, for 2D nonlinear problems, especially the MSP studied in this paper, the corresponding adaptive FE analysis has been absent.…”

Section: Introductionmentioning

confidence: 99%

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

Jiang

Yuan

Qiu

2020

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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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Section: About the Authorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Jiang

Yuan

Qiu

2020

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“…In the framework of the EEP method, not only super-convergent derivatives but also displacements can be recovered. The method has been successfully applied to a series of linear (Yuan et al , 2017; Yuan et al , 2018; Yuan and He, 2006; Dong et al , 2019) and nonlinear problems (Yuan et al , 2017; Yuan et al , 2014; Jiang et al , 2020). All the numerical results in the above-mentioned applications show that the EEP solutions can achieve super-convergence at least one order higher than the corresponding FE solutions, which has been mathematically proved in one-dimensional (1D) cases (Yuan and Xing, 2014).…”

Section: Introductionmentioning

confidence: 99%

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

Sun

Yuan

2021

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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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“…A number of research studies have been conducted on this subject [32,33]. In recent years, a super-convergence technique named Element Energy Projection (EEP) method was proposed by Yuan et al [34][35][36]. Its core assumption is to assume the energy projection theorem in the FEM mathematical theory [37] to be almost true for a single element.…”

Section: Introductionmentioning

confidence: 99%

Application of Finite Layer Method in Pavement Structural Analysis

et al. 2017

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Abstract:The finite element (FE) method has been widely used in predicting the structural responses of asphalt pavements. However, the three-dimensional (3D) modeling in general-purpose FE software systems such as ABAQUS requires extensive computations and is relatively time-consuming. To address this issue, a specific computational code EasyFEM was developed based on the finite layer method (FLM) for analyzing structural responses of asphalt pavements under a static load. Basically, it is a 3D FE code that requires only a one-dimensional (1D) mesh by incorporating analytical methods and using Fourier series in the other two dimensions, which can significantly reduce the computational time and required resources due to the easy implementation of parallel computing technology. Moreover, a newly-developed Element Energy Projection (EEP) method for super-convergent calculations was implemented in EasyFEM to improve the accuracy of solutions for strains and stresses over the whole pavement model. The accuracy of the program is verified by comparing it with results from BISAR and ABAQUS for a typical asphalt pavement structure. The results show that the predicted responses from ABAQUS and EasyFEM are in good agreement with each other. The EasyFEM with the EEP post-processing technique converges faster compared with the results derived from ordinary EasyFEM applications, which proves that the EEP technique can improve the accuracy of strains and stresses from EasyFEM. In summary, the EasyFEM has a potential to provide a flexible and robust platform for the numerical simulation of asphalt pavements and can easily be post-processed with the EEP technique to enhance its advantages.

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Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

Cited by 10 publications

References 2 publications

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

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

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

Application of Finite Layer Method in Pavement Structural Analysis

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