A theoretical proof of the invalidity of dynamic relaxation arc-length method for snap-back problems

2021 ◽  
Author(s):  
Pengfei Zhang ◽  
Chao Yang
Keyword(s):  
Arc Length ◽  
Dynamic Relaxation ◽  
Back Problems

Geometrically nonlinear analysis of shells by various dynamic relaxation methods

2017 ◽  
Vol 14 (5) ◽  
pp. 381-405 ◽  
Author(s):  
Mohammad Rezaiee-Pajand ◽  
Hossein Estiri
Keyword(s):  
Nonlinear Analysis ◽  
Thin Shells ◽  
Arc Length ◽  
Dynamic Relaxation ◽  
Content Type ◽  
Structural Types ◽  
Geometric Nonlinear ◽  
Dr Method ◽  
Geometric Nonlinear Analysis ◽  
Number Of Iterations

Purpose Numerical experiences reveal that the performances of the dynamic relaxation (DR) method are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. To achieve this task, 12 famous approaches are briefly introduced. The differences among these schemes are between the estimation of the time step, the mass and the damping matrices. In this study, several benchmark structures are analyzed by using these 12 techniques. Based on the number of iterations and the analysis duration, their performances are graded. Numerical findings reveal the high efficiency of the kinetic DR (kdDR) approach and Underwood’s strategy. Design/methodology/approach Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells have not been investigated. In this paper, 12 famous DR methods have been used for solving these structures. It should be noted that the difference between these approaches is in the estimation of the fictitious parameters. The aforementioned techniques are used to solve several numerical samples. Then, the performances of all schemes are graded based on the number of iterations and the analysis duration. Findings The final ranking of each strategy will be obtained after studying all numerical examples. It is worth emphasizing that the number of iterations and that of convergence points of the arc length algorithms are dependent on the value of the initial arc length. In other words, a slight change in the magnitude of the arc length may lead to the wrong responses. Contrary to this behavior, the analyzer’s role in the dynamic relaxation techniques is considerably less than the arc length method. In the DR strategies when the answer approaches the limit points, the iteration number increases automatically. As a result, this algorithm can be used to analyze the structures with complex equilibrium paths. Research limitations/implications Numerical experiences reveal that the DR method performances are related to the structural types. This paper is devoted to compare the DR schemes for geometric nonlinear analysis of shells. Practical implications Geometric nonlinear analysis of shells is a sophisticated procedure. Consequently, extensive research studies have been conducted to analyze the shells efficiently. The most important characteristic of these structures is their high resistance against pressure. This study demonstrates the performances of various DR methods in solving shell structures. Originality/value Up to now, the performances of various DR algorithms for geometric nonlinear analysis of thin shells are not investigated.

The visual perception of arc length on a real surface

1997 ◽  
Author(s):  
J. Farley Norman ◽  
Joseph S. Lappin ◽  
Hideko F. Norman
Keyword(s):  
Visual Perception ◽  
Real Surface ◽  
Arc Length

Dimensions of plane and solid angles and their units in the International System of Units (SI)

2020 ◽  
pp. 26-32
Author(s):  
M. I. Kalinin ◽  
L. K. Isaev ◽  
F. V. Bulygin
Keyword(s):  
Solid Angle ◽  
International System ◽  
International Committee ◽  
Plane Angle ◽  
Arc Length ◽  
Weights And Measures ◽  
International System Of Units ◽  
System Of Units ◽  
In Series ◽  
Solid Angles

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.

Choice of Noncircular Gears Hobbing Linkage Methods

2019 ◽  
Vol 13 (1) ◽  
pp. 69-74
Author(s):  
Wang Yazhou ◽  
Xiao Junfeng ◽  
Liu Yongping ◽  
An Jianmin
Keyword(s):  
Machine Tools ◽  
High Density ◽  
Arc Length ◽  
Linkage Methods ◽  
High Uniformity ◽  
Linkage Method ◽  
Noncircular Gears

Background: Various relevant patents and papers which have reported noncircular gears synthesize the advantages of circular gears and cam mechanisms, and are widely used in many types of mechanical instruments. Hobbing is a better method for fabricating noncircular gears. There are 4 linkagemethods to hob noncircular gears. However, which linkage method should be chosen practically has not yet been reported. Objective: The goal of this work is to choose the best linkage method for hobbing noncircular gears. Method: Firstly, the hobbing models of noncircular gears was deduced. Then, based on the model, hobbing linkage methods of noncircular gears were obtained. Thirdly, under different hobbing linkage methods, their aspects (developing regularity of hobbing cutter trace, arc length of program blocks and motion axes of machine tools) were compared. Results: Finally, with the best characteristics of a high density of shaping cutter trace, high uniformity of arc length of program blocks and ease of control, the equal arc-length of gear billet (EALGB) is obtained. It has been proven that EALGB is an excellent linkage method to hob noncircular gears. Conclusion: It has been proven that EALGB is an excellent linkage method to hob noncircular gears.

scholarly journals Affine Subspaces of Curvature Functions from Closed Planar Curves

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Leonardo Alese
Keyword(s):  
Arc Length ◽  
Planar Curves ◽  
Affine Subspaces ◽  
Planar Curve ◽  
Real Functions ◽  
Discrete Counterpart ◽  
Equivalent Conditions

AbstractGiven a pair of real functions (k, f), we study the conditions they must satisfy for $$k+\lambda f$$ k + λ f to be the curvature in the arc-length of a closed planar curve for all real $$\lambda $$ λ . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.

scholarly journals A Feedrate Planning Method for the NURBS Curve in CNC Machining Based on the Critical Constraint Curve

2021 ◽  
Vol 11 (11) ◽  
pp. 4959
Author(s):  
Peng Guo ◽  
Yijie Wu ◽  
Guang Yang ◽  
Zhebin Shen ◽  
Haorong Zhang ◽  
...  
Keyword(s):  
Planning Method ◽  
Cnc Machining ◽  
Arc Length ◽  
Kinematic Constraint ◽  
Nurbs Curve ◽  
Planning Strategy ◽  
Feedrate Planning ◽  
Curvature Constraint ◽  
Planning Methods ◽  
The Relationship

The curvature of the NURBS curve varies along its trajectory, therefore, the commonly used feedrate-planning method, which based on the acceleration/deceleration (Acc/Dec) model, is difficult to be directly applied in CNC machining of a NURBS curve. To address this problem, a feedrate-planning method based on the critical constraint curve of the feedrate (CCC) is proposed. Firstly, the problems of existing feedrate-planning methods and their causes are analyzed. Secondly, by considering both the curvature constraint and the kinematic constraint during the Acc/Dec process, the concept of CCC which represents the relationship between the critical feedrate-constraint value and the arc length is proposed. Then the CCC of a NURBS curve is constructed, and it has a concise expression conforming to the Acc/Dec model. Finally, a feedrate-planning method of a NURBS curve based on CCC and the Acc/Dec model is established. In the simulation, a comparison between the proposed method and the conventional feedrate-planning method is performed, and the results show that, the proposed method can reduce the Acc/Dec time by over 40%, while little computational burden being added. The machining experimental results validate the real-time performance and stability of the proposed method, and also the machining quality is verified. The proposed method offers an effective feedrate-planning strategy for a NURBS curve in CNC machining.

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