A Simple and Effective Pipe Elbow Element—Linear Analysis

1980 ◽  
Vol 47 (1) ◽  
pp. 93-100 ◽  
Author(s):  
K. J. Bathe ◽  
C. A. Almeida
Keyword(s):  
Radial Displacement ◽  
Linear Analysis ◽  
Pipe Bend ◽  
Pipe Elbow ◽  
Von Karman ◽  
Displacement Based ◽  
Von Kármán ◽  
Displacement Patterns ◽  
Bend Element

The formulation of a new, simple, and effective displacement-based pipe bend element is presented. The displacement assumptions are axial, torsional, and bending displacements that vary cubically along the axis of the elbow with plane sections remaining plane, and a generalization of the von Karman pipe radial displacement patterns to include the ovalization effects. The amount of ovalization varies cubically along the elbow with full compatibility between elbows. The pipe bend element has been implemented, and the results of various sample analyses are presented, which illustrate the effectiveness of the element.

In-Plane Bending of a Short-Radius Curved Pipe Bend

1967 ◽  
Vol 89 (2) ◽  
pp. 271-277 ◽  
Author(s):  
N. Jones
Keyword(s):  
Power Series ◽  
Radial Displacement ◽  
Neutral Axis ◽  
Pipe Bend ◽  
Curved Pipe ◽  
Original Theory ◽  
Von Karman ◽  
Plane Bending ◽  
Von Kármán ◽  
Logical Extension

The analysis developed in this article is a logical extension, or generalization, of Von Karman’s original theory [1] on curved pipe bends. It can be shown, for long-radius pipe bends which have a negligible shift of the neutral axis, that the solution presented here reduces to that of Von Karman. It is evident from the results of this analysis that the stresses in and flexibility of curved pipe bends are virtually independent of γ(a/ρ) (even for γ approaching unity) and depend almost entirely on the simple Von Karman pipe factor λ(tρ/a2). Errors arising from premature truncation of the selected power series for the radial displacement are discussed, and a guide given to the number of terms necessary for a particular problem.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

scholarly journals A Review on Analytical Modeling for Collapse Mode Capacitive Micromachined Ultrasonic Transducer of the Collapse Voltage and the Static Membrane Deflections

Micromachines ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 714
Author(s):  
Jiujiang Wang ◽  
Xin Liu ◽  
Yuanyu Yu ◽  
Yao Li ◽  
Ching-Hsiang Cheng ◽  
...  
Keyword(s):  
Analytical Modeling ◽  
Ultrasonic Transducer ◽  
Governing Equations ◽  
Von Karman ◽  
Von Kármán Equations ◽  
Collapse Mode ◽  
Capacitive Micromachined Ultrasonic Transducer ◽  
Gap Height ◽  
Von Kármán ◽  
Analytical Expressions

Analytical modeling of capacitive micromachined ultrasonic transducer (CMUT) is one of the commonly used modeling methods and has the advantages of intuitive understanding of the physics of CMUTs and convergent when modeling of collapse mode CMUT. This review article summarizes analytical modeling of the collapse voltage and shows that the collapse voltage of a CMUT correlates with the effective gap height and the electrode area. There are analytical expressions for the collapse voltage. Modeling of the membrane deflections are characterized by governing equations from Timoshenko, von Kármán equations and the 2D plate equation, and solved by various methods such as Galerkin’s method and perturbation method. Analytical expressions from Timoshenko’s equation can be used for small deflections, while analytical expression from von Kármán equations can be used for both small and large deflections.

scholarly journals Blow-up results for a quasilinear von Karman equation of memory type

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Mi Jin Lee ◽  
Jum-Ran Kang
Keyword(s):  
Blow Up ◽  
Suitable Condition ◽  
Nondecreasing Function ◽  
Initial Energy ◽  
Nonincreasing Function ◽  
Positive Initial Energy ◽  
Von Karman ◽  
Von Karman Equation ◽  
Memory Type ◽  
Von Kármán

Abstract In this paper, we consider the blow-up result of solution for a quasilinear von Karman equation of memory type with nonpositive initial energy as well as positive initial energy. For nonincreasing function $g>0$ g > 0 and nondecreasing function f, we prove a finite time blow-up result under suitable condition on the initial data.

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