Closed form solution for displacements of thick cylinders with varying thickness subjected to non-uniform internal pressure

2003 ◽  
Vol 16 (6) ◽  
pp. 731-748 ◽  
Author(s):  
H.R. Eipakchi ◽  
G.H. Rahimi ◽  
S. Esmaeilzadeh Khadem
Keyword(s):  
Internal Pressure ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Varying Thickness

Creep Deflection of Thick-Walled Piping due to Combined Bending and Internal Pressure

1990 ◽  
Vol 112 (3) ◽  
pp. 251-255 ◽  
Author(s):  
I. Finnie ◽  
M. Shirmohamadi
Keyword(s):  
Internal Pressure ◽  
Closed Form ◽  
Satisfactory Agreement ◽  
Correction Factor ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Piping System

A closed-form solution is derived for the creep deflection in thick-walled piping subjected to combined internal pressure and bending moment. The solution is limited to the situation usually encountered in practice with sustained gravity loads and support forces in which the additional stresses due to bending are small compared to those due to internal pressure. For this case, it is shown that a simple correction factor may be applied to an elastic computation of pipe deflections to include the effect of creep. Predictions using this factor show satisfactory agreement with observations on a thick-walled piping system which had been in service for 20 years.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

A CLOSED-FORM PRICING FORMULA FOR EUROPEAN EXCHANGE OPTIONS WITH STOCHASTIC VOLATILITY

2021 ◽  
pp. 1-10
Author(s):  
Puneet Pasricha ◽  
Anubha Goel
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stochastic Volatility Model ◽  
Strike Price ◽  
Volatility Model ◽  
Exchange Options ◽  
Pricing Formula ◽  
Exchange Option

This article derives a closed-form pricing formula for the European exchange option in a stochastic volatility framework. Firstly, with the Feynman–Kac theorem's application, we obtain a relation between the price of the European exchange option and a European vanilla call option with unit strike price under a doubly stochastic volatility model. Then, we obtain the closed-form solution for the vanilla option using the characteristic function. A key distinguishing feature of the proposed simplified approach is that it does not require a change of numeraire in contrast with the usual methods to price exchange options. Finally, through numerical experiments, the accuracy of the newly derived formula is verified by comparing with the results obtained using Monte Carlo simulations.

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