Analysis of 3-Dimensional Creased Cracks

2019 ◽  
Vol 827 ◽  
pp. 416-421
Author(s):  
Yohei Sonobe ◽  
Takuichiro Ino ◽  
Atsuhiro Koyama ◽  
Akihide Saimoto
Keyword(s):  
Closed Form ◽  
Weighting Function ◽  
Crack Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
3 Dimensional ◽  
Stress Boundary Condition ◽  
Triangular Area ◽  
Stress Boundary ◽  
Isolated Point

A method of analysis for calculating a precise distribution of a stress intensity factor alonga front of 3D crack was improved by introducing a closed-form integral. In the present study, the crackface is discretized with number of triangular boundary elements on which the weighting function ofbody force doublet varies linearly with coordinate variables. A closed form solution of a resultant forceover an arbitrary planar-triangular area due to a presence of an isolated point force was derived andused to satisfy a stress boundary condition of a creased crack problem. In principle, arbitrary shaped3D cracks which may contain asperities and multiple creased lines in its face can be solved by presentapproach.

Some dual series equations with an application in the theory of elasticity

1982 ◽  
Vol 92 (3-4) ◽  
pp. 241-251 ◽  
Author(s):  
J. Tweed
Keyword(s):  
Closed Form ◽  
Trigonometric Series ◽  
Singular Integral ◽  
Crack Problem ◽  
Closed Form Solution ◽  
Singular Integral Equations ◽  
Theory Of Elasticity ◽  
Form Solution ◽  
Dual Series Equations ◽  
Carleman Type

SynopsisIn this paper the author investigates a system of simultaneous dual trigonometric series equations. A closed form solution is obtained by reducing the dual series to singular integral equations of Carleman type. The use of these equations is then illustrated by their application to a crack problem in the theory of elasticity.

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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