scholarly journals Constructing Steklov-type cubature formulas for a finite element in the shape of a bipyramid

2021 ◽  
Vol 4 (4(112)) ◽  
pp. 40-46
Author(s):  
Anzhelika Motailo ◽  
Galina Tuluchenko
Keyword(s):  
Finite Element ◽  
The Finite Element Method ◽  
Order Of Accuracy ◽  
Cubature Formulas ◽  
Compression Parameter ◽  
Algebraic Order ◽  
The Stability ◽  
Local Stiffness ◽  
Approximate Integration ◽  
Interpolation Nodes

This paper reports the construction of cubature formulas for a finite element in the form of a bipyramid, which have a second algebraic order of accuracy. The proposed formulas explicitly take into consideration the parameter of bipyramid deformation, which is important when using irregular grids. The cubature formulas were constructed by applying two schemes for the location of interpolation nodes along the polyhedron axes: symmetrical and asymmetrical. The intervals of change in the elongation (compression) parameter of a bipyramid semi-axis have been determined, within which interpolation nodes of the constructed formulas belong to the integration region, while the weight coefficients are positive, which warrants the stability of calculations based on these cubature formulas. If the deformation parameter of the bipyramid is equal to unity, then both cubature formulas hold for the octahedron and have a third algebraic order of accuracy. The resulting formulas make it possible to find elements of the local stiffness matrix on a finite element in the form of a bipyramid. When calculating with a finite number of digits, a rounding error occurs, which has the same order for each of the two cubature formulas. The intervals of change in the elongation (compression) parameter of the bipyramid semi-axis have been determined, which meet the requirements, which are employed in the ANSYS software package, for deviations in the volume of the bipyramid from the volume of the octahedron. Among the constructed cubature formulas for a bipyramid, the optimal formula in terms of the accuracy of calculations has been chosen, derived from applying a symmetrical scheme of the arrangement of nodes relative to the center of the bipyramid. This formula is invariant in relation to any affinity transformations of the local bipyramid coordinate system. The constructed cubature formulas could be included in libraries of methods for approximate integration used by those software suites that implement the finite element method.

scholarly journals Stability charts based on the finite element method for underground cavities in soft carbonate rocks: validation through case-study applications

2019 ◽  
Vol 19 (10) ◽  
pp. 2079-2095 ◽  
Author(s):  
Michele Perrotti ◽  
Piernicola Lollino ◽  
Nunzio Luciano Fazio ◽  
Mario Parise
Keyword(s):  
Finite Element ◽  
Safety Margin ◽  
Structural Elements ◽  
The Finite Element Method ◽  
Geometrical Features ◽  
Overall Stability ◽  
Underground Cavities ◽  
The Stability ◽  
Rock Mechanical Properties

Abstract. The stability of man-made underground cavities in soft rocks interacting with overlying structures and infrastructures represents a challenging problem to be faced. Based upon the results of a large number of parametric two-dimensional (2-D) finite-element analyses of ideal cases of underground cavities, accounting for the variability both cave geometrical features and rock mechanical properties, specific charts have been recently proposed in the literature to assess at a preliminary stage the stability of the cavities. The purpose of the present paper is to validate the efficacy of the stability charts through the application to several case studies of underground cavities, considering both quarries collapsed in the past and quarries still stable. The stability graphs proposed by Perrotti et al. (2018) can be useful to evaluate, in a preliminary way, a safety margin for cavities that have not reached failure and to detect indications of predisposition to local or general instability phenomena. Alternatively, for sinkholes that already occurred, the graphs may be useful in identifying the conditions that led to the collapse, highlighting the importance of some structural elements (as pillars and internal walls) on the overall stability of the quarry system.

scholarly journals Factor of Safety Reduction Factors for Accounting for Progressive Failure for Earthen Levees with Underlying Thin Layers of Sensitive Soils

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Adam J. Lobbestael ◽  
Adda Athanasopoulos-Zekkos ◽  
Josh Colley
Keyword(s):  
Finite Element ◽  
Strain Softening ◽  
Progressive Failure ◽  
Limit Equilibrium ◽  
Thin Layers ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Limit Equilibrium Methods ◽  
The Stability ◽  
Reduction Factors

The effects of progressive failure on flood embankments with underlying thin layers of soft, sensitive soils are investigated. Finite element analysis allows for investigation of strain-softening effects and progressive failure in soft and sensitive soils. However, limit equilibrium methods for slope stability analysis, widely used in industry, cannot capture these effects and may result in unconservative factors of safety. A parametric analysis was conducted to investigate the effect of thin layers of soft sensitive soils on the stability of flood embankments. A flood embankment was modeled using both the limit equilibrium method and the finite element method. The foundation profile was altered to determine the extent to which varying soft and sensitive soils affected the stability of the embankment, with respect to progressive failure. The results from the two methods were compared to determine reduction factors that can be applied towards factors of safety computed using limit equilibrium methods, in order to capture progressive failure.

Mechanics Analysis of Grade V Surrounding Rock Primary Support in Maanziliang Tunnel

2012 ◽  
Vol 164 ◽  
pp. 414-417
Author(s):  
Jia Ming Han
Keyword(s):  
Finite Element ◽  
Safety Factor ◽  
Surrounding Rock ◽  
Qinling Mountains ◽  
The Finite Element Method ◽  
Highway Tunnel ◽  
Geological Conditions ◽  
The Stability ◽  
Primary Support ◽  
Rock Section

Commonly used finite element strength reduction to calculate the safety factor of slope，to analyze the stability of the slope[1～3]. Recently it also proposed the methods to evaluate the safety factor for the stability of surrounding rock of underground chambers and supporting structural mechanics[4～6]. For Qinling Mountains of the complex geological conditions in the Maanziliang highway tunnel, this article use the finite element method from the bolt resist tension, bolt length, the force of sprayed layer of concrete to computing gradeⅤsurrounding rock section of primary support safety factor, to give evaluation to support mechanics of the Maanziliang tunnel.

A Generalized Approach to the Dynamics of Cracked Shafts

1989 ◽  
Vol 111 (3) ◽  
pp. 257-263 ◽  
Author(s):  
Changhe Li ◽  
O. Bernasconi ◽  
N. Xenophontidis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Experimental Method ◽  
The Finite Element Method ◽  
Nonlinear Formulation ◽  
Local Stiffness ◽  
Advanced Model ◽  
Cracked Shafts ◽  
Element Method

A new analytic-experimental method for describing crack breathing and obtaining shaft local stiffness change is presented. A generalized nonlinear formulation using the finite element method, which can be widely used for both horizontal and vertical cracked shafts, is derived. Some results previously explicited in other studies are confirmed and clarified. This advanced model can serve as a solid basis for further studies.

The Influence of Tangential Roller Pressure on the Stability of Circular Saw Blade

2014 ◽  
Vol 614 ◽  
pp. 32-35 ◽  
Author(s):  
Ming Song Zhang ◽  
Yi Zhang ◽  
Jian Jun Ke ◽  
Xiao Wei Li ◽  
Lian Bing Cheng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Symmetric Model ◽  
The Finite Element Method ◽  
Circular Saw ◽  
The Face ◽  
Circular Saw Blade ◽  
Cyclic Symmetric ◽  
The Stability ◽  
Saw Blade

The finite element method was used to study tangential roller method impact on the stability of circular saw blade. Using 30 ° cyclic symmetric model is analyzed. The results show that the tension of the saw blade is not the same, and tensioning effect is different, when the tangential roller pressure is not same. At the same time, after tangential roller, the face run out of saw blade is small, which show that the smoothness of tangential roller is better.

A Study on the Stability of a Mast Structure for Erecting a Large Crane

2011 ◽  
Vol 110-116 ◽  
pp. 1483-1490
Author(s):  
Hoon Hyung Jung ◽  
Chae Sil Kim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Analytical Model ◽  
Gantry Crane ◽  
The Finite Element Method ◽  
Analysis Model ◽  
The Stability ◽  
The One ◽  
Two Stages

This paper describes a finite element structural analysis model and determines analysis methods appropriate for determining the stability of the mast of a crane. This analysis model allows various analysis approaches to be applied to the conditions affecting the construction of a large gantry crane in order to ensure the stability of the mast of the crane. The finite element method is used as a way to construct an analytical model that can help ensure the stability of the mast in two stages. The model is used in a two-stage analytical process that takes into account the conditions of the model. In this way, the model can be used to judge the stability of the mast. By allowing variation in the analysis approach used for the crane mast, the analysis model may be changed if the conditions of the one-girder gantry crane require. Designers may apply this method for the active analysis of the stability of a crane mast.

Finite Element Analysis of Quench Propagation Velocity in Bi-2223/Ag Superconducting Multifilamentary Tape

2007 ◽  
Vol 546-549 ◽  
pp. 1931-1934
Author(s):  
Chun Li Wu ◽  
Hai Liang Yang
Keyword(s):  
Finite Element ◽  
Propagation Velocity ◽  
Operating Temperature ◽  
Superconducting Magnet ◽  
Experimental Result ◽  
The Finite Element Method ◽  
Analysis Model ◽  
Element Analysis ◽  
The Stability ◽  
Quench Propagation

Quench propagation velocity is an important parameter to the stability and protection issues of superconducting magnet. In this paper, the finite element method (FEM) numerical simulation of quench propagation velocity has been performed for using the powerful analysis software COSMOS by establishing a suitable thermal analysis model of Bi-2223/Ag superconducting multifilamentary tape. The effects of quench energy and operating temperature on the quench propagation velocity have been studied. The analysis shows that the simulation result basically coincides with the experimental result.

Stability Analyses of Western Slopes in Jointed Rock Masses for GuangYang Highway

2011 ◽  
Vol 368-373 ◽  
pp. 234-240
Author(s):  
Shu Li Wang ◽  
Man Gen Mu ◽  
Ran Wang ◽  
Wen Bo Cui
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Limit Equilibrium ◽  
Western Slope ◽  
Seismic Load ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Limit Equilibrium Methods ◽  
The Stability ◽  
Element Method

This paper presents the results of a study on a joint slope deformation affecting the western slope of the GuangYang highway (YangQuan, China). Fieldwork identified the ongoing deformational process and assisted in defining its mechanisms, evolution and controlling factors. Here we discuss how to use limit equilibrium methods to calculate the behavior of slopes and to use the finite element analysis to evaluate the stability, displacements of slopes and soil-slope stabilization interaction. The finite element method with shear strength reduction (SSR) technique is explained in Phase2D. This method is effective for the prediction of the stability of slope. Based on numerical comparisons between the limit equilibrium methods and finite element method, it is suggested that the finite element method with SSR technique is a reliable and maybe unique approach to evaluate the slope stability. The paper also took into account effectiveness of the large rain and seismic load. The results of the numerical analysis are consistent with the observed slope surface evidence.

The Simulation and Analysis of the New Type Large Vacuum Container Flange Welding Process

2014 ◽  
Vol 472 ◽  
pp. 671-676
Author(s):  
Bo Tao Liu ◽  
Yan Qi ◽  
Xiao Han ◽  
Shi Zeng Lv ◽  
Guo Feng Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Strength ◽  
Hollow Structure ◽  
Welding Process ◽  
The Finite Element Method ◽  
Material Consumption ◽  
Stiffness Property ◽  
New Type ◽  
The Stability

Flange is the key part of the large vacuum container and its stiffness property affects the sealing effect and the stability of the container. Large flange welding process will have a greater impact on its structural strength. In view of the traditional way of forming large vacuum container flange has problems that processing and manufacturing are difficult, more material consumption, and poor stiffness, a new type of flange structure was support. The new design has hollow structure and the welding process of cover flange was simulated through the finite element method. After that, the stress and the deformation were analyzed and then the proper welding scheme was optimized.

Optimization Research on Workpiece Clamping Deformation Using Genetic Algorithm and Finite Element Method

2011 ◽  
Vol 189-193 ◽  
pp. 2153-2160
Author(s):  
Yu Wen Sun ◽  
Chuan Tai Zhang ◽  
Qiang Guo
Keyword(s):  
Genetic Algorithm ◽  
Finite Element Method ◽  
Finite Element ◽  
Machining Accuracy ◽  
Clamping Force ◽  
The Finite Element Method ◽  
Linear Programming Method ◽  
Fixture Layout ◽  
The Stability ◽  
Element Method

Optimal fixture involves fixture layout and clamping force determination. It is critical to ensure the machining accuracy of workpiece. In this paper, the clamping process is analyzed with the consideration of cutting forces and frictions using the finite element method. Then the fixture layout and clamping force are optimized by minimizing the workpiece deformation via a Genetic Algorithm (GA). Subsequently, linear programming method is used to estimate the stability of workpiece. It is shown through an example that the proposed method is proved to be efficient. The optimization result is not only far superior to the experiential one, but also the total optimization time can be reduced significantly.

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