Large Displacement Analysis of a Marine Riser

1985 ◽  
Vol 107 (1) ◽  
pp. 54-59 ◽  
Author(s):  
T. Huang ◽  
S. Chucheepsakul
Keyword(s):  
Strain Energy ◽  
Equilibrium Configuration ◽  
Numerical Procedure ◽  
Stationary Condition ◽  
Arc Length ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Marine Riser ◽  
Highly Nonlinear ◽  
Rectangular Coordinates

A method of static analysis for a marine riser experiencing large displacements is presented. The method is suitable for analyzing a riser having a known top tension and a possible slippage at the top slip joint. Utilizing the stationary condition of a functional coupled with an equilibrium equation, one can conveniently obtain the equilibrium configuration numerically. The configuration is expressed in terms of the rectangular coordinates. The functional representing the energy and work of the riser system is expressed in terms of the horizontal coordinate which is parameterized in terms of the vertical depth instead of arc length. For a two-dimensional problem, two multipliers must be included in the functional. One of the two represents the variable axial force along the length of the riser and the other corresponds to the strain energy per unit riser length due to bending. Utilizing the finite element method, a numerical procedure to obtain the configuration of static equilibrium is given. The resulting algebraic equations are highly nonlinear and the Newton-Raphson iterative procedure is used to solve the equations. An example is given.

Post-Buckling Analysis of a Uniform Self-Weight Beam with Application to Catenary Riser

2019 ◽  
Vol 19 (04) ◽  
pp. 1950047 ◽  
Author(s):  
Ong-Art Punjarat ◽  
Somchai Chucheepsakul
Keyword(s):  
Axial Force ◽  
Strain Energy ◽  
Equilibrium Configuration ◽  
Virtual Work ◽  
Beam Theory ◽  
Energy Functional ◽  
Arc Length ◽  
Bending Strain ◽  
Highly Nonlinear ◽  
Post Buckling

This paper focused on a simply supported beam under uniform self-weight, subjected to an axial force at the roller end. The principle of virtual work-energy was used to formulate the equation for the nonlinear deformation of the beam, which involves the bending strain energy, the virtual work due to self-weight, and the virtual work of the axial force applied at the free-sliding roller end. The work–energy functional was expressed in terms of the arc-length coordinate. The functional vanished, yielding the static equilibrium configuration of the beam — a highly nonlinear problem. Finite element and Newton–Raphson iterative methods were used to solve the problem. The beam theory was extended to large sag analysis of a catenary riser. With this, some interesting features of the various configurations of the catenary riser under various end forces were evaluated.

Analysis of Large-Sag Extensible Catenary with Free Horizontal Sliding at One End by Variational Approach

2017 ◽  
Vol 17 (07) ◽  
pp. 1750070 ◽  
Author(s):  
Thongchai Phanyasahachart ◽  
Chainarong Athisakul ◽  
Somchai Chucheepsakul
Keyword(s):  
Variational Approach ◽  
Equilibrium Configuration ◽  
Virtual Work ◽  
Stationary Condition ◽  
Arc Length ◽  
Axial Deformation ◽  
Vertical Coordinate ◽  
The One ◽  
Equilibrium Consideration ◽  
Work Done

A variational approach for the static equilibrium configuration analysis of a large-sag extensible catenary with free horizontal sliding at one end is developed, considering the virtual work done by the catenary self-weight and the horizontal tension at the free sliding end support. The virtual work of the cable system is expressed in terms of the vertical coordinate, which is a function of the unstrained arc length of the cable. The stationary condition is applied to the virtual work functional to obtain the equilibrium configuration of the catenary. The validity of the variational approach is ensured by Euler’s equation, which is identical to the one derived by the force equilibrium consideration of a catenary segment. The finite element method is used to evaluate the numerical results. A parametric study is performed to demonstrate the effect of axial deformation on the equilibrium configuration of a large-sag extensible free horizontal sliding catenary. The results indicate that as the axial deformation increases, the total arc-length and horizontal span length of the cable also increase. Particularly, the very large-sag catenary configurations are studied and exhibited in this study.

Stress Analysis of a Tire Under Vertical Load by a Finite Element Method

1977 ◽  
Vol 5 (2) ◽  
pp. 102-118 ◽  
Author(s):  
H. Kaga ◽  
K. Okamoto ◽  
Y. Tozawa
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Temperature Rise ◽  
Strain Energy ◽  
Internal Stresses ◽  
Vertical Load ◽  
The Finite Element Method ◽  
Internal Temperature ◽  
Element Method

Abstract An analysis by the finite element method and a related computer program is presented for an axisymmetric solid under asymmetric loads. Calculations are carried out on displacements and internal stresses and strains of a radial tire loaded on a road wheel of 600-mm diameter, a road wheel of 1707-mm diameter, and a flat plate. Agreement between calculated and experimental displacements and cord forces is quite satisfactory. The principal shear strain concentrates at the belt edge, and the strain energy increases with decreasing drum diameter. Tire temperature measurements show that the strain energy in the tire is closely related to the internal temperature rise.

scholarly journals Two matrix methods for solution of nonlinear and linear Lane-Emden type equations with mixed condition by operational matrix

2015 ◽  
Vol 4 (3) ◽  
pp. 420 ◽  
Author(s):  
Behrooz Basirat ◽  
Mohammad Amin Shahdadi
Keyword(s):  
Bernstein Polynomials ◽  
Operational Matrix ◽  
Numerical Procedure ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Mixed Condition ◽  
Matrix Methods ◽  
Numerical Examples ◽  
Linear Algebraic Equations ◽  
The Given

<p>The aim of this article is to present an efficient numerical procedure for solving Lane-Emden type equations. We present two practical matrix method for solving Lane-Emden type equations with mixed conditions by Bernstein polynomials operational matrices (BPOMs) on interval [<em>a; b</em>]. This methods transforms Lane-Emden type equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equations. We also give some numerical examples to demonstrate the efficiency and validity of the operational matrices for solving Lane-Emden type equations (LEEs).</p>

Influence of new surface micro-structures on the performance behaviours of fluid film tilting pad thrust bearings

2021 ◽  
pp. 095440622110309
Author(s):  
JC Atwal ◽  
RK Pandey
Keyword(s):  
Mass Conservation ◽  
Performance Parameters ◽  
Algebraic Equations ◽  
The Finite Element Method ◽  
Thrust Bearings ◽  
Lubrication Equation ◽  
Tilting Pad ◽  
Minimum Film Thickness ◽  
Newton Raphson ◽  
Micro Structures

Performance parameters such as power loss, minimum film thickness, and maximum oil temperature of the sector-shaped tilting pad thrust bearings employing the new micro-structural geometries on pad surfaces have been investigated. The lubrication equation incorporating the mass-conservation issue is discretized using the finite element method and the solution of resulting algebraic equations is obtained employing a Newton-Schur method. The pad equilibrium in the analysis is established using the Newton-Raphson and Braydon methods. The influence of attributes of micro-structures such as depth, circumferential and radial positioning extents have been explored on the performance behaviours. It is found that with the new micro-structured pad surfaces, the performance parameters significantly improved in comparison to conventional plain and conventional rectangular pocketed pads.

scholarly journals Assessment of Linearization Approaches for Multibody Dynamics Formulations

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Francisco González ◽  
Pierangelo Masarati ◽  
Javier Cuadrado ◽  
Miguel A. Naya
Keyword(s):  
Mechanical System ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Practical Applications ◽  
Linearization Methods ◽  
Highly Nonlinear ◽  
Wide Range ◽  
The Way

Formulating the dynamics equations of a mechanical system following a multibody dynamics approach often leads to a set of highly nonlinear differential-algebraic equations (DAEs). While this form of the equations of motion is suitable for a wide range of practical applications, in some cases it is necessary to have access to the linearized system dynamics. This is the case when stability and modal analyses are to be carried out; the definition of plant and system models for certain control algorithms and state estimators also requires a linear expression of the dynamics. A number of methods for the linearization of multibody dynamics can be found in the literature. They differ in both the approach that they follow to handle the equations of motion and the way in which they deliver their results, which in turn are determined by the selection of the generalized coordinates used to describe the mechanical system. This selection is closely related to the way in which the kinematic constraints of the system are treated. Three major approaches can be distinguished and used to categorize most of the linearization methods published so far. In this work, we demonstrate the properties of each approach in the linearization of systems in static equilibrium, illustrating them with the study of two representative examples.

A Two Step Damage Prognosis Method for Beam-Like Truss Structures

2014 ◽  
Vol 578-579 ◽  
pp. 1092-1095
Author(s):  
Hao Kai Jia ◽  
Ling Yu
Keyword(s):  
Finite Element Method ◽  
Strain Energy ◽  
Truss Structure ◽  
Truss Structures ◽  
Second Step ◽  
The Finite Element Method ◽  
Modal Strain Energy ◽  
Damage Prognosis ◽  
Modal Curvature ◽  
Simulation Results

In this study, a two step damage prognosis method is proposed for beam-like truss structures via combining modal curvature change (MCC) with modal strain energy change ratio (MSECR). Changes in the modal curvature and the elemental strain energy are selected as the indicator of damage prognosis. Different damage elements with different damage degrees are simulated. In the first step, the finite element method is used to model a beam-like truss structure and the displacement modes are got. The damage region is estimated by the MCC of top and bottom chords of a beam-like truss structure. In the second step, the elemental MSECR in the damage region is calculated and the maximum MSECR element is deemed as the damage element. The simulation results show that this method can accurately locate the damage in the beam-like truss structure.

scholarly journals An axisymmetric problem for a penny-shaped crack under the influence of the Steigmann–Ogden surface energy

2021 ◽  
Vol 477 (2248) ◽  
Author(s):  
Anna Y. Zemlyanova
Keyword(s):  
Surface Energy ◽  
Numerical Procedure ◽  
Material System ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Penny Shaped Crack ◽  
Normal Traction ◽  
Parametric Studies ◽  
Shaped Crack ◽  
Isotropic Elastic Medium

A problem for a nanosized penny-shaped fracture in an infinite homogeneous isotropic elastic medium is considered. The fracture is opened by applying an axisymmetric normal traction to its surface. The surface energy in the Steigmann–Ogden form is acting on the boundary of the fracture. The problem is solved by using the Boussinesq potentials represented by the Hankel transforms of certain unknown functions. With the help of these functions, the problem can be reduced to a system of two singular integro-differential equations. The numerical solution to this system can be obtained by expanding the unknown functions into the Fourier–Bessel series. Then the approximations of the unknown functions can be obtained by solving a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. Parametric studies of the dependence of the solutions on the mechanical and the geometric parameters of the system are undertaken. It is shown that the surface parameters have a significant influence on the behaviour of the material system. In particular, the presence of surface energy leads to the size-dependency of the solutions and smoother behaviour of the solutions near the tip of the crack.

scholarly journals Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Juliano dos Santos Becho ◽  
Marcelo Greco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rheological Model ◽  
Iterative Process ◽  
Numerical Procedure ◽  
Viscoelastic Behavior ◽  
Retardation Time ◽  
The Finite Element Method ◽  
Divergence Problem ◽  
Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

On the Axial-Flexural-Torsional Coupling of Underwater Slender Cylinders

2012 ◽  
Author(s):  
Waldir T. Pinto ◽  
Carlos A. Levi
Keyword(s):  
Large Strains ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Three Dimensional Model ◽  
Cylindrical Structures ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Torsional Coupling ◽  
Lift Forces ◽  
Drag And Lift

This paper presents a numerical model for the simulation of the axial-flexural-torsional coupling of undewater cylindrical structures. Cylindrical structures are largely utilized in the marine environment in a wide range of applications as in risers, marine cables, flexible pipes, mooring systems and so on. They may exhibit complex axial-flexural-torsional coupling, which makes the structural analysis highly nonlinear. In addition, the fluid-structure interaction may include flow induced vibrations, frequency lock-in and internal flow effects. The proposed three-dimensional model assumes that the structure aspect ratio is very high, its cross section is circular, the cable is elastic and may experience large displacements and large strains, as long as the elastic regime holds. The steady state load on the cylinder consists of the self-weight and buoyancy, drag and lift forces, in addition to a distributed residual twist along the cylinder. The drag and lift forces are evaluated by Morison type formulation. The governing differential equations are derived from first principles, assuming Newtonian mechanics. Then, they are solved numerically by a finite element formulation based on nonlinear space frame elements. The resulting set of algebraic equations is solved by a minimization technique that uses the Newton-Raphson algorithm. Results show the ability of the model to predict the static configuration of equilibrium of the cylinder and to capture the coupling between axial, flexural and torsional responses of the cylinder.

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