scholarly journals Conformable fractional hyper geometric equation

2018 ◽  
Keyword(s):  
Geometric Equation

A Method for Calculating Deformation of Long-Distance Pipeline Based on Strain

2011 ◽  
Vol 291-294 ◽  
pp. 3385-3390 ◽  
Author(s):  
Li Qi Yi ◽  
Ke Qin Ding ◽  
Cai Fu Qian
Keyword(s):  
Numerical Method ◽  
Large Deformation ◽  
Cross Section ◽  
Long Distance ◽  
Geometric Equation ◽  
The Relationship

In this paper, a method for calculating deformation of long-distance pipeline by using strain is presented. We analyze the pipe as a beam. According to geometric equation of beam’s large deformation, we establish the relationship between strain and displacement. With numerical method, beam’s deformation can be got by using different positions’ strain of a cross-section and a generatrix.

scholarly journals A Revisit of the Boundary Value Problem for Föppl–Hencky Membranes: Improvement of Geometric Equations

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 631 ◽  
Author(s):  
Yong-Sheng Lian ◽  
Jun-Yi Sun ◽  
Zhi-Hang Zhao ◽  
Xiao-Ting He ◽  
Zhou-Lian Zheng
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Boundary Value ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circular Membrane ◽  
Computational Accuracy ◽  
Power Series Method ◽  
Membrane Problem ◽  
Geometric Equation

In this paper, the well-known Föppl–Hencky membrane problem—that is, the problem of axisymmetric deformation of a transversely uniformly loaded and peripherally fixed circular membrane—was resolved, and a more refined closed-form solution of the problem was presented, where the so-called small rotation angle assumption of the membrane was given up. In particular, a more effective geometric equation was, for the first time, established to replace the classic one, and finally the resulting new boundary value problem due to the improvement of geometric equation was successfully solved by the power series method. The conducted numerical example indicates that the closed-form solution presented in this study has higher computational accuracy in comparison with the existing solutions of the well-known Föppl–Hencky membrane problem. In addition, some important issues were discussed, such as the difference between membrane problems and thin plate problems, reasonable approximation or assumption during establishing geometric equations, and the contribution of reducing approximations or relaxing assumptions to the improvement of the computational accuracy and applicability of a solution. Finally, some opinions on the follow-up work for the well-known Föppl–Hencky membrane were presented.

scholarly journals The Generalized Gielis Geometric Equation and Its Application

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 645 ◽  
Author(s):  
Peijian Shi ◽  
David A. Ratkowsky ◽  
Johan Gielis
Keyword(s):  
Power Law ◽  
Morphological Features ◽  
Original Version ◽  
Link Function ◽  
Plant Leaves ◽  
Special Cases ◽  
Geometric Equation ◽  
Special Case

Many natural shapes exhibit surprising symmetry and can be described by the Gielis equation, which has several classical geometric equations (for example, the circle, ellipse and superellipse) as special cases. However, the original Gielis equation cannot reflect some diverse shapes due to limitations of its power-law hypothesis. In the present study, we propose a generalized version by introducing a link function. Thus, the original Gielis equation can be deemed to be a special case of the generalized Gielis equation (GGE) with a power-law link function. The link function can be based on the morphological features of different objects so that the GGE is more flexible in fitting the data of the shape than its original version. The GGE is shown to be valid in depicting the shapes of some starfish and plant leaves.

scholarly journals Large Deflection Analysis of Axially Symmetric Deformation of Prestressed Circular Membranes under Uniform Lateral Loads

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1343
Author(s):  
Xue Li ◽  
Jun-Yi Sun ◽  
Zhi-Hang Zhao ◽  
Xiao-Ting He
Keyword(s):  
Power Series ◽  
Initial Stress ◽  
Axisymmetric Deformation ◽  
Radial Coordinate ◽  
Axially Symmetric ◽  
Computational Accuracy ◽  
Power Series Method ◽  
Deflection Analysis ◽  
Membrane Problem ◽  
Geometric Equation

In this study, the problem of axisymmetric deformation of peripherally fixed and uniformly laterally loaded circular membranes with arbitrary initial stress is solved analytically. This problem could be called the generalized Föppl–Hencky membrane problem as the case where the initial stress in the membrane is equal to zero is the well-known Föppl–Hencky membrane problem. The problem can be mathematically modeled only in terms of radial coordinate owing to its axial symmetry, and in the present work, it is reformulated by considering an arbitrary initial stress (tensile, compressive, or zero) and by simultaneously improving the out-of-plane equilibrium equation and geometric equation, while the formulation was previously considered to fail to improve the geometric equation. The power-series method is used to solve the reformulated boundary value problem, and a new and more refined analytic solution of the problem is presented. This solution is actually observed to be able to regress into the well-known Hencky solution of zero initial stress, allowing the considered initial stress to be zero. Moreover, the numerical example conducted shows that the obtained power-series solutions for stress and deflection converge very well, and have higher computational accuracy in comparison with the existing solutions.

scholarly journals On a geometric equation involving the Sobolev trace critical exponent

2013 ◽  
Vol 2013 (1) ◽  
pp. 405
Author(s):  
Mohamed Al-Ghamdi ◽  
Hichem Chtioui ◽  
Khadija Sharaf
Keyword(s):  
Critical Exponent ◽  
Geometric Equation

scholarly journals Over-constraints detection and resolution in geometric equation systems

2017 ◽  
Vol 90 ◽  
pp. 84-94 ◽  
Author(s):  
Hao Hu ◽  
Mathias Kleiner ◽  
Jean-Philippe Pernot
Keyword(s):  
Geometric Equation

The Study on Neutral Axis of Concrete Filled Steel Tube Component with Round Section

2011 ◽  
Vol 94-96 ◽  
pp. 1115-1119
Author(s):  
Xue Ying Yang ◽  
Yuan Mei Li ◽  
Wen Tao Dong ◽  
Bo Zhang
Keyword(s):  
Mechanical Properties ◽  
Material Properties ◽  
Equilibrium Equation ◽  
Steel Tube ◽  
Neutral Axis ◽  
Concrete Material ◽  
Concrete Filled Steel Tube ◽  
Tension And Compression ◽  
Geometric Equation ◽  
Round Section

The equation to determine the neutral axis of concrete filled steel tube(CFST) component with round section is presented in this paper. The geometric equation, physical equation and static equilibrium equation of CFST are analyzed to determine its section neutral axis. The compressed mechanical properties of CFST component are analyzed with the concrete material properties divided into tension and compression parts.Comparing the numerical results with the experimental results it can be verified that the equation to determine the neutral axis of CFST component with round section is useful to solve the problems that the tension and compression material properties of concrete are different.

scholarly journals A geometric equation with critical nonlinearity on the boundary

2005 ◽  
Vol 218 (1) ◽  
pp. 75-99 ◽  
Author(s):  
Veronica Felli ◽  
Mohameden Ould Ahmedou
Keyword(s):  
Critical Nonlinearity ◽  
Geometric Equation
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