Configuring Marine Riser Tapered Stress Joints Used in Top-Supported Applications

2004 ◽  
Vol 126 (3) ◽  
pp. 201-207 ◽  
Author(s):  
Cormack C. Gordon ◽  
Don W. Dareing
Keyword(s):  
Differential Equation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Marine Riser ◽  
Cross Sectional ◽  
Marine Risers ◽  
Dynamic Analyses ◽  
Stress Levels ◽  
Method Of Solution ◽  
Type Differential Equation

The objective of this paper is to present a direct and useful method for establishing the configuration of tapered stress joints for marine risers so that stress levels are fairly balanced over the length of the stress joint and within acceptable stress levels. The method of solution approximates straight tapered stress joints with one, whose cross sectional moment of inertia varies parabolically along the stress joint. This approximation leads to the classic Euler type differential equation, which can be solved directly giving a closed form solution. The formulation of deflection and stresses should be of use to designers of marine tubulars. Even though the focus of the study is on a static analysis of top located stress joints, the method of solution can be adapted to mudline attachment locations as well as dynamic analyses.

scholarly journals Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 331 ◽  
Author(s):  
Huda Bakodah ◽  
Abdelhalim Ebaid
Keyword(s):  
Differential Equation ◽  
Closed Form ◽  
Closed Form Solution ◽  
Approximate Solutions ◽  
Form Solution ◽  
Proportional Delay ◽  
Delay Term ◽  
The Laplace Transform ◽  
Linear Differential ◽  
Delay Differential

The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was first applied to this equation, and then the decomposition method was implemented to establish a closed-form solution. The present closed-form solution is reported for the first time for the Ambartsumian equation. Numerically, the calculations have demonstrated a rapid rate of convergence of the obtained approximate solutions, which are displayed in several graphs. It has also been shown that only a few terms of the new approximate solution were sufficient to achieve extremely accurate numerical results. Furthermore, comparisons of the present results with the existing methods in the literature were introduced.

RATIONAL APPROXIMATION OF THE ROUGH HESTON SOLUTION

2019 ◽  
Vol 22 (03) ◽  
pp. 1950010 ◽  
Author(s):  
JIM GATHERAL ◽  
RADOŠ RADOIČIĆ
Keyword(s):  
Differential Equation ◽  
Rational Approximation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Heston Model ◽  
Scaling Limits ◽  
Riccati Differential Equation ◽  
Hawkes Processes ◽  
Heavy Tailed ◽  
Fractional Diffusions

Pricing in the rough Heston model of Jaisson & M. Rosenbaum [(2016) Rough fractional diffusions as scaling limits of nearly unstable heavy tailed Hawkes processes, The Annals of Applied Probability 26 (5), 2860–2882] requires the solution of a fractional Riccati differential equation, which is not known in explicit form. Though numerical schemes to approximate this solution do exist, they inevitably require significantly more time to compute than the closed-form solution in the classical Heston model. In this paper, we present a simple rational approximation to the solution of the rough Heston Riccati equation valid in a region of its domain relevant to option valuation. Pricing using this approximation is both fast and very accurate.

Pascal's recurrence relation and even-aged-forest stand dynamics

1992 ◽  
Vol 22 (12) ◽  
pp. 1996-1999
Author(s):  
Rolfe A. Leary ◽  
Hien Phan ◽  
Kevin Nimerfro
Keyword(s):  
Differential Equation ◽  
Relative Density ◽  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Integral Form ◽  
Forest Stand ◽  
Form Solution ◽  
Density Change ◽  
Stand Dynamics

A common method of modelling forest stand dynamics is to use permanent growth plot remeasurements to calibrate a whole-stand growth model expressed as an ordinary differential equation. To obtain an estimate of future conditions, either the differential equation is integrated numerically or, if analytic, the differential equation is solved in closed form. In the latter case, a future condition is obtained simply by evaluating the integral form for the age of interest, subject to appropriate initial conditions. An older method of modelling forest stand dynamics was to use a normal or near-normal yield table as a density standard and calibrate a relative density change equation from permanent plot remeasurements. An estimate of a future stand property could be obtained by iterating from a known initial relative density. In this paper we show that when the relative density change equation has a particular form, the historical method also has a closed form solution, given by a sequence of polynomials with coefficients from successive rows of Pascal's arithmetic triangle.

Nonlinear Vertical Vibration of Tension Leg Platforms with Homotopy Analysis Method

2015 ◽  
Vol 7 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Arash Reza ◽  
Hamid M. Sedighi
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Mass Coefficient ◽  
Added Mass Coefficient

AbstractOne of the useful methods for offshore oil exploration in the deep regions is the use of tension leg platforms (TLP). The effective mass fluctuating of the structure which due to its vibration can be noted as one of the important issues about these platforms. With this description, dynamic analysis of these structures will play a significant role in their design. Differential equations of motion of such systems are nonlinear and providing a useful method for its analysis is very important. Also, the amount of added mass coefficient has a direct effect on the level of nonlinearity of partial differential equation of these systems. In this study, Homotopy analysis method has been used for closed form solution of the governing differential equation. Linear springs have been used for modeling the stiffness of this system and the effects of torsion, bending and damping of water have been ignored. In the study of obtained results, the effect of added mass coefficient has been investigated. The results show that increasing of this coefficient decreases the bottom amplitude of fluctuations and the system frequency. The obtained results from this method are in good agreement with the published results on the valid articles.

Structural Performance of Buried Steel Pipelines Crossing Strike-Slip Faults

2014 ◽  
Author(s):  
Polynikis Vazouras ◽  
Panos Dakoulas ◽  
Spyros A. Karamanos
Keyword(s):  
Closed Form ◽  
Local Buckling ◽  
Closed Form Solution ◽  
Strike Slip ◽  
Form Solution ◽  
Strike Slip Fault ◽  
Performance Criteria ◽  
Cross Sectional ◽  
Soil System ◽  
Inelastic Material

The performance of pipelines subjected to permanent strike-slip fault movement is investigated by combining detailed numerical simulations and closed-form solutions. A closed-form solution for the force-displacement relationship of a buried pipeline subjected to tension is presented and used in the form of nonlinear springs at the two ends of the pipeline in a refined finite element model, allowing an efficient nonlinear analysis of the pipe-soil system at large strike-slip fault movements. The analysis accounts for large deformations, inelastic material behaviour of the pipeline and the surrounding soil, as well as contact and friction conditions on the soil-pipe interface. Appropriate performance criteria of the steel pipeline are adopted and monitored throughout the analysis. It is shown that the end conditions of the pipeline have a significant influence on pipeline performance. For a strike-slip fault normal to the pipeline axis, local buckling occurs at relatively small fault displacements. As the angle between the fault normal and the pipeline axis increases, local buckling can be avoided due to longitudinal stretching, but the pipeline may fail due to excessive axial tensile strains or cross sectional flattening.

scholarly journals Behaviour under Moving Distributed Masses of Simply Supported Orthotropic Rectangular Plate Resting on a Constant Elastic Bi-Parametric Foundation

2020 ◽  
pp. 64-92
Author(s):  
T. O. Awodola ◽  
S. Adeoye
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Fourth Order ◽  
Closed Form Solution ◽  
Form Solution ◽  
Order Partial Differential Equation ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Simply Supported ◽  
Orthotropic Rectangular Plate

This work investigates the behavior under Moving distributed masses of orthotropic rectangular plates resting on bi-parametric elastic foundation. The governing equation is a fourth order partial differential equation with variable and singular co-efficients. The solutions to the problem are obtained by transforming the fourth order partial differential equation for the problem to a set of coupled second order ordinary differential equations using the technique of Shadnam et al[1]. This is then simplified using modified asymptotic method of Struble. The closed form solution is analyzed, resonance conditions are obtained and the results are presented in plotted curves for both cases of moving distributed mass and moving distributed force.

Transient analytical solution of M/D/1/N queues

2002 ◽  
Vol 39 (04) ◽  
pp. 853-864
Author(s):  
Jean-Marie Garcia ◽  
Olivier Brun ◽  
David Gauchard
Keyword(s):  
Differential Equation ◽  
Probability Distribution ◽  
Analytical Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Dependent ◽  
Simple Analytical Expression ◽  
Analytical Expression ◽  
Boundary States ◽  
Dependent Probability

An analytical expression of the time-dependent probability distribution of M/D/1/N queues initialised in an arbitrary deterministic state is derived. We also obtain a simple analytical expression of the differential equation governing the transient average traffic which only involves probabilities of boundary states. As a by-product, a closed form solution of the departure rate from the system is also determined.

Sign in / Sign up

Export Citation Format

Share Document