Comments on ‘4‐node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh‐distortion’ by Yan Shang and Wengen Ouyang, International Journal for Numerical Methods in Engineering 2018; 113: 1589‐1606

2021 ◽  
Author(s):  
Ying‐qing Huang
Keyword(s):  
Numerical Methods ◽  
Membrane Element ◽  
Mesh Distortion

A Generalized Conforming Quadrilateral Membrane Element Less Sensitive to Geometric Distortion

1998 ◽  
Vol 1 (3) ◽  
pp. 185-191 ◽  
Author(s):  
Yin Xu ◽  
Zhifei Long ◽  
Yuqiu Long
Keyword(s):  
Finite Element ◽  
High Precision ◽  
Degrees Of Freedom ◽  
Geometric Distortion ◽  
Finite Element Models ◽  
Membrane Element ◽  
Mesh Distortion ◽  
Long Period ◽  
Rotational Degrees Of Freedom ◽  
General Method

Many finite element models have very acceptable performance when the computing meshes are regular. However, as the level of mesh distortion is increasing, the accuracy of the solutions deteriorates rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion is an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element proposed by Long Yuqiu (1989). The new element exhibits excellent feature, that is, less sensitive to geometric distortion. A general method to formulate high precision finite element less sensitive to geometric distortion is provided in this paper.

scholarly journals Numerical Investigation of Progressive Slope Failure Induced by Sublevel Caving Mining Using the Finite Difference Method and Adaptive Local Remeshing

2021 ◽  
Vol 11 (9) ◽  
pp. 3812
Author(s):  
Jingzhi Tu ◽  
Yanlin Zhang ◽  
Gang Mei ◽  
Nengxiong Xu
Keyword(s):  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Computational Model ◽  
Difference Method ◽  
Large Scale ◽  
Slope Failure ◽  
Mesh Distortion ◽  
Sublevel Caving ◽  
The Finite Difference Method

Slope failure induced by sublevel caving mining is a progressive process, resulting in the large deformation and displacement of rock masses in the slope. Numerical methods are widely used to investigate the above phenomenon. However, conventional numerical methods have difficulties when simulating the process of progressive slope failure. For example, the discrete element method (DEM) for block systems is computationally expensive and possibly fails for large-scale and complex slope models, while the finite difference method (FDM) has a mesh distortion problem when simulating progressive slope failure. To address the above problems, this paper presents a finite difference modeling method using the adaptive local remeshing technique (LREM) to investigate the progressive slope failure induced by sublevel caving mining. In the proposed LREM, (1) the zone of the distorted mesh is adaptively identified, and the landslide body is removed; (2) the updated mesh is regenerated by the local remeshing, and the physical field variables of the original computational model are transferred to the regenerated computational model. The novelty of the proposed method is that (1) compared with the DEM for block systems, the proposed LREM is capable of modeling the progressive slope failure in large-scale rock slopes; (2) the proposed method is able to address the problem of mesh distortion in conventional FDM modeling; and (3) compared with the errors induced by the frequent updating of the mesh of the entire model, the adaptive local remeshing technique effectively reduces calculation errors. To evaluate the effectiveness of the proposed LREM, it is first used to investigate the failure of a simplified slope induced by sublevel caving mining. Moreover, the proposed LREM is applied in a real case, i.e., to investigate the progressive slope failure induced by sublevel caving mining in Yanqianshan Iron Mine.

Numerical Methods

2019 ◽  
Author(s):  
Rajesh Kumar Gupta
Keyword(s):  
Numerical Methods

THE METHODS OF DEVELOPING COMPUTATIONAL THINKING OF STUDENTS WHILE STUDYING THE COURSE "NUMERICAL METHODS" BASED ON BLENDED LEARNING

2019 ◽  
pp. 34-41
Author(s):  
M. M. Klunnikova
Keyword(s):  
Numerical Methods ◽  
Blended Learning ◽  
Computational Thinking ◽  
Individual Characteristics ◽  
Diagnostic Model ◽  
Mathematics Students ◽  
Professional Activities ◽  
Cognitive Component ◽  
Professional Field ◽  
The Individual

The work is devoted to the consideration of improving the quality of teaching students the discipline “Numerical methods” through the development of the cognitive component of computational thinking based on blended learning. The article presents a methodology for the formation of computational thinking of mathematics students, based on the visualization of algorithmic design schemes and the activation of the cognitive independence of students. The characteristic of computational thinking is given, the content and structure of computational thinking are shown. It is argued that a student with such a mind is able to manifest himself in his professional field in the best possible way. The results of the application of the technique are described. To determine the level of development of the cognitive component of computational thinking, a diagnostic model has been developed based on measuring the content, operational and motivational components. It is shown that the proposed method of developing computational thinking of students, taking into account the individual characteristics of students’ thinking, meaningfully based on the theoretical and practical aspects of studying the discipline, increases the effectiveness of learning the course “Numerical methods”. The materials of the article are of practical value for teachers of mathematical disciplines who use information and telecommunication technologies in their professional activities.

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