The Analytical Solution of Single Pipe Piles under Axially and Laterally Free Loads

2011 ◽  
Vol 383-390 ◽  
pp. 1701-1707
Author(s):  
Zhe Wang ◽  
Si Fa Xu ◽  
Guo Cai Wang ◽  
Yong Zhang
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Lateral Deformation ◽  
Lateral Loads ◽  
Axial Loads ◽  
Influence Curves ◽  
The Earth ◽  
Inclined Loads ◽  
Single Pipe ◽  
Foundation Type

The analytical solution of a single pipe piles under axially and laterally loads is presented, when the laterally loads is optional free load. As piles foundations are becoming a preferred foundation type, piles usually work under simultaneous axial and lateral loads in engineering. To analyze the function of free loads to pipe piles under inclined loads conditions, in the basis of ‘m’ method, deformation differential equation of elastic piles under inclined loads is established first in the paper with analytical method. Differential equation has two parts in according to the piles in the earth or in the air, and lateral deformation, obliquity, moment; shearing force of the piles can be gotten respectively by soluting equations. In the end of the paper, influences of several parameters is analyzed of the top axial loads, the top lateral loads and the free loads, and their influence curves are given.

Helical Buckling of Pipes in Extended Reach and Horizontal Wells—Part 2: Frictional Drag Analysis

1993 ◽  
Vol 115 (3) ◽  
pp. 196-201 ◽  
Author(s):  
J. Wu ◽  
H. C. Juvkam-Wold
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Laboratory Experiments ◽  
Horizontal Wells ◽  
Force Balance ◽  
Axial Loads ◽  
Frictional Drag ◽  
Well Completion ◽  
Helical Buckling ◽  
Drag Analysis

This paper studies the frictional drag of helically buckled pipes (drillstring and tubing) in extended reach and horizontal wells to correctly predict the actual bit weight or packer load, in cases where helical buckling of pipes may have occurred. Helical buckling of pipes in such wells may occur, since large axial loads are often required. The differential equation of axial force balance with consideration of the axial friction for helically buckled pipes is resolved, and the solution shows that when the pipes are helically buckled, the frictional drag will become very large. The actual bit weight for drilling or packer load for well completion may therefore become much smaller than estimated under the unbuckled pipe conditions. The analytical solution is also shown to agree with the results from laboratory experiments, which simulate the real wellbore-pipe conditions. An example is provided to show the calculation procedure and the importance of the results.

scholarly journals Analytical solution to bending of stiffened and continuous antisymmetric laminates

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Liecheng Sun ◽  
Issam E. Harik
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Displacement Function ◽  
The Other ◽  
Order Partial Differential Equation ◽  
Eighth Order ◽  
Coupling Problem ◽  
Simply Supported ◽  
General Response

AbstractAnalytical Strip Method is presented for the analysis of the bending-extension coupling problem of stiffened and continuous antisymmetric thin laminates. A system of three equations of equilibrium, governing the general response of antisymmetric laminates, is reduced to a single eighth-order partial differential equation (PDE) in terms of a displacement function. The PDE is then solved in a single series form to determine the displacement response of antisymmetric cross-ply and angle-ply laminates. The solution is applicable to rectangular laminates with two opposite edges simply supported and the other edges being free, clamped, simply supported, isotropic beam supports, or point supports.

scholarly journals An Improved Analytical Solution for Process-Induced Residual Stresses and Deformations in Flat Composite Laminates Considering Thermo-Viscoelastic Effects

Materials ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 2506 ◽  
Author(s):  
Chao Liu ◽  
Yaoyao Shi
Keyword(s):  
Differential Equation ◽  
Finite Element ◽  
Analytical Solution ◽  
Residual Stresses ◽  
Composite Laminates ◽  
Composite Structures ◽  
Numerical Models ◽  
Element Analysis ◽  
Current Time ◽  
Viscoelastic Effects

Dimensional control can be a major concern in the processing of composite structures. Compared to numerical models based on finite element methods, the analytical method can provide a faster prediction of process-induced residual stresses and deformations with a certain level of accuracy. It can explain the underlying mechanisms. In this paper, an improved analytical solution is proposed to consider thermo-viscoelastic effects on residual stresses and deformations of flat composite laminates during curing. First, an incremental differential equation is derived to describe the viscoelastic behavior of composite materials during curing. Afterward, the analytical solution is developed to solve the differential equation by assuming the solution at the current time, which is a linear combination of the corresponding Laplace equation solutions of all time. Moreover, the analytical solution is extended to investigate cure behavior of multilayer composite laminates during manufacturing. Good agreement between the analytical solution results and the experimental and finite element analysis (FEA) results validates the accuracy and effectiveness of the proposed method. Furthermore, the mechanism generating residual stresses and deformations for unsymmetrical composite laminates is investigated based on the proposed analytical solution.

scholarly journals INTERACTION OF A LONG PILE OF FINITE STIFFNESS WITH SURROUNDING SOIL AND FOUNDATION CAP

Vestnik MGSU ◽  
2015 ◽  
pp. 72-83
Author(s):  
Armen Zavenovich Ter-Martirosyan ◽  
Zaven Grigor’evich Ter-Martirosyan ◽  
Tuan Viet Trinh
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Carrying Capacity ◽  
Strain State ◽  
Order Differential Equation ◽  
Deformation Modulus ◽  
First Case ◽  
Equivalent Modulus ◽  
Underlying Soil ◽  
Surrounding Soil

The article presents the formulation and analytical solution to a quantification of stress strain state of a two-layer soil cylinder enclosing a long pile, interacting with the cap. The solution of the problem is considered for two cases: with and without account for the settlement of the heel and the underlying soil. In the first case, the article is offering equations for determining the stresses of pile’s body and the surrounding soil according to their hardness and the ratio of radiuses of the pile and the surrounding soil cylinder, as well as formulating for determining equivalent deformation modulus of the system “cap-pile-surrounding soil” (the system). Assessing the carrying capacity of the soil under pile’s heel is of great necessity. In the second case, the article is solving a second-order differential equation. We gave the formulas for determining the stresses of the pile at its top and heel, as well as the variation of stresses along the pile’s body. The article is also formulating for determining the settlement of the foundation cap and equivalent deformation modulus of the system. It is shown that, pushing the pile into underlying layer results in the reducing of equivalent modulus of the system.

scholarly journals A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Alvaro H. Salas S ◽  
Jairo E. Castillo H ◽  
Darin J. Mosquera P
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Analytical Solution ◽  
Initial Conditions ◽  
Negative Ions ◽  
Nonlinear Problems ◽  
New Approach ◽  
Weierstrass Elliptic Function ◽  
Electronegative Plasma ◽  
The Given

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z ″ = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

SOLVING THE ASIAN OPTION PDE USING LIE SYMMETRY METHODS

2010 ◽  
Vol 13 (08) ◽  
pp. 1265-1277 ◽  
Author(s):  
NICOLETTE C. CAISTER ◽  
JOHN G. O'HARA ◽  
KESHLAN S. GOVINDER
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Solution ◽  
Stock Price ◽  
Ad Hoc ◽  
Lie Symmetry ◽  
Asian Option ◽  
Asian Options ◽  
Lie Point Symmetries ◽  
Reduced Order

Asian options incorporate the average stock price in the terminal payoff. Examination of the Asian option partial differential equation (PDE) has resulted in many equations of reduced order that in general can be mapped into each other, although this is not always shown. In the literature these reductions and mappings are typically acquired via inspection or ad hoc methods. In this paper, we evaluate the classical Lie point symmetries of the Asian option PDE. We subsequently use these symmetries with Lie's systematic and algorithmic methods to show that one can obtain the same aforementioned results. In fact we find a familiar analytical solution in terms of a Laplace transform. Thus, when coupled with their methodic virtues, the Lie techniques reduce the amount of intuition usually required when working with differential equations in finance.

AN ANALYTICAL SOLUTION OF THE COSMIC RAYS TRANSPORT EQUATION IN THE PRESENCE OF THE GEOMAGNETIC FIELD

2002 ◽  
Vol 17 (12n13) ◽  
pp. 1645-1653
Author(s):  
MARINA GIBILISCO
Keyword(s):  
Magnetic Field ◽  
Cosmic Rays ◽  
Analytical Solution ◽  
Transport Equation ◽  
Geomagnetic Field ◽  
The Earth ◽  
Factorization Technique ◽  
Diffusion Motion ◽  
Geomagnetic Fields ◽  
The Magnetic Field

In this work, I study the propagation of cosmic rays inside the magnetic field of the Earth, at distances d ≤ 500 Km from its surface; at these distances, the geomagnetic field deeply influences the diffusion motion of the particles. I compare the different effects of the interplanetary and of the geomagnetic fields, by also discussing their role inside the cosmic rays transport equation; finally, I present an analytical method to solve such an equation through a factorization technique.

scholarly journals Geometric shape features extraction using a steady state partial differential equation system

2019 ◽  
Vol 6 (4) ◽  
pp. 647-656 ◽  
Author(s):  
Takayuki Yamada
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Steady State ◽  
Analytical Solution ◽  
Geometric Shape ◽  
Geometrical Shape ◽  
Shape Features ◽  
Partial Differential ◽  
Topological Constraint ◽  
Numerical Examples

Abstract A unified method for extracting geometric shape features from binary image data using a steady-state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to extract the thickness, orientation, and skeleton simultaneously. The main advantage of the proposed method is that the orientation is defined without derivatives and thickness computation is not imposed a topological constraint on the target shape. A one-dimensional analytical solution is provided to validate the proposed method. In addition, two-dimensional numerical examples are presented to confirm the usefulness of the proposed method. Highlights A steady state partial differential equation for extraction of geometrical shape features is formulated. The functions for geometrical shape features are formulated by the solution of the proposed PDE. Analytical solution is provided in one-dimension. Numerical examples are provided in two-dimension.

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