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

Sun, Haohan; Yuan, Songmei

doi:10.1108/ec-09-2020-0511

Cited by 4 publications

(4 citation statements)

References 54 publications

(56 reference statements)

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“…Sun and Yuan [7] proposed a finite element analysis (FEA) model to analyze the free vibration problem of elastic free membranes. This model linearized the free vibration problem of elastic membranes into a linear equivalent problem and introduced local mesh refinement.…”

Section: Related Workmentioning

confidence: 99%

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Research on estimation and control methods of natural frequency of irregular building structure vibration

Song

2024

J. vibroeng.

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With the continuous increase in the number of irregular buildings, ensuring the safety of building structures has become the primary concern. The study used finite element analysis to estimate the natural frequency of vibration of irregular building structures, and further designed a fuzzy control algorithm combined with magnetorheological dampers to improve their seismic performance. The research results showed that the longitudinal and transverse natural frequencies of Model 1 were 10.44 Hz and 10.51 Hz, respectively, while those of Model 2 were 10.31 Hz and 9.89 Hz, respectively. Using the fuzzy control method, the peak displacement of the building structure was reduced to 11.64 cm, and the peak acceleration was 7.9 m/s2. Comparing the open-plus-closed-loop control with open-loop control methods, it was found that although the fluctuation amplitude of the open-loop control method was relatively large, its control effect was poor, while the open-plus-closed-loop control methods had good overall control effect, with the peak acceleration of 8.26 m/s2 in the open-loop control. The study provides an accurate method for estimating the natural vibration frequency of irregular building structures and demonstrates the effectiveness of the designed fuzzy control algorithm in controlling building vibration.

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Section: Related Workmentioning

confidence: 99%

“…Among these five parts, the first part is the core of the FC system, and the structure of the FC system and fuzzy controller is shown in Fig. 2 [7,16]. In a FC system, the result of fuzzy inference is a membership function.…”

Section: Vnf Control Of Irregular Building Structure Based On Fc Systemmentioning

confidence: 99%

Research on estimation and control methods of natural frequency of irregular building structure vibration

Song

2024

J. vibroeng.

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“…, 2017, 2014; Jiang et al. , 2020; Sun and Yuan, 2021). The original EEP method in multi-dimensional problems (2D or 3D) poses strict restrictions on the mesh patterns, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, a novel recovery-based technique named element energy projection (EEP) method was proposed by Yuan and Wang (2004), Yuan and Lin (2007). The method has been successfully applied to a series of linear (Yuan et al, 2018;Yuan and He, 2006;Dong et al, 2019) and nonlinear problems (Yuan et al, 2017Jiang et al, 2020;Sun and Yuan, 2021). The original EEP method in multi-dimensional problems (2D or 3D) poses strict restrictions on the mesh patterns, i.e.…”

Section: Introductionmentioning

confidence: 99%

An improved local error estimate in adaptive finite element analysis based on element energy projection technique

Sun

Yuan

2023

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PurposeAn 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/approachThe 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.FindingsThe 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/valueBy 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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Condensed Galerkin Time-Element for Structural Dynamics with Adaptive Time-Stepping in Maximum Norm

Yuan,

Yuan

2024

Int. J. Comput. Methods

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In this paper, the newly-developed condensed Galerkin element of polynomial degree [Formula: see text] for first-order initial-value problems is reformulated for and extended to the structural dynamic equations, yielding a high-performance dynamic element of one-step, unconditionally stable type with the conventional finite element (FE) convergence [Formula: see text] within the element and the extra-superconvergence [Formula: see text] at the element end-nodes. Further, based on the element energy projection (EEP) technique, a superconvergence EEP formula for the condensed element is proposed in the paper and mathematical analysis is presented to prove that the derived EEP solution gains a superconvergence [Formula: see text], which is an order higher than the FE solution of [Formula: see text] for all element degree [Formula: see text] and is hence qualified to serve as a point-wise error estimator. As a result, a simple, efficient, and reliable algorithm with adaptive time-stepping controlled by the maximum norm is proposed. Representative numerical examples are presented to verify the validity of the proposed theorems and to demonstrate the high performance of the proposed element and the associated adaptivity algorithm.

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

Cited by 4 publications

References 54 publications

Research on estimation and control methods of natural frequency of irregular building structure vibration

Research on estimation and control methods of natural frequency of irregular building structure vibration

An improved local error estimate in adaptive finite element analysis based on element energy projection technique

Condensed Galerkin Time-Element for Structural Dynamics with Adaptive Time-Stepping in Maximum Norm

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