Numerical Solution Of The Axisymmetric Arc Governing Equations On Arbitrary Unstructured Meshes

2005 ◽  
Author(s):  
R.E. Blundell ◽  
M.T.C. Fang
Keyword(s):  
Numerical Solution ◽  
Unstructured Meshes ◽  
Governing Equations

The interaction of a fibre tangle with an airflow

1967 ◽  
Vol 27 (3) ◽  
pp. 561-580 ◽  
Author(s):  
Paul A. Taub
Keyword(s):  
Unsteady Flow ◽  
Numerical Solution ◽  
Analytical Model ◽  
Method Of Characteristics ◽  
Solution Procedure ◽  
Governing Equations ◽  
Stress Strain ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Flow Configurations

An analytical model of the interaction of a fibre tangle with an airflow is proposed. This model replaces the discrete fibres by a continuum medium with a non-linear stress-strain law. The governing equations have been examined for one-dimensional unsteady flow configurations and have been found to possess five characteristic directions.A numerical-solution procedure, based upon the method of characteristics, has been outlined and applied to the flow within a dilation chamber. A fibre sample is located at the centre of the chamber, which is alternately pressurized and depressurized.

Aeroelastic response of a swept wing with cubic structural non-linearities

2008 ◽  
Vol 222 (2) ◽  
pp. 229-248 ◽  
Author(s):  
M Razi ◽  
B Ghadiri
Keyword(s):  
Numerical Solution ◽  
Degrees Of Freedom ◽  
Linear Analysis ◽  
Swept Wing ◽  
Governing Equations ◽  
Aeroelastic Response ◽  
Runge Kutta Method ◽  
Non Linear ◽  
Flutter Boundary ◽  
The Time Domain

Linear and non-linear aeroelastic analyses of swept cantilever wings containing a cubic non-linearity in an incompressible flow are investigated. Expressions of aerodynamic forces and moments for an element of the swept wing are derived in the time domain using a relation between Theodorsen and Wagner's functions. Consequently, the governing aeroelastic equations of two degrees of freedom wings are derived for both swept backward and forward wings. Linear analysis is carried out via solving the governing equations with the standard fourth-order Runge—Kutta method. For the sake of verification of the derived formulas, the results of the numerical solution for a linear flutter boundary are compared with the experimental data in several cases. Considering softening and hardening cubic structural non-linearities, non-linear analysis of the swept wing is studied. For the wings containing hardening cubic non-linearities, the first- and third-order harmonic balance (HB) methods are employed to find the amplitude and frequency of limit cycle oscillations (LCOs). Comparison between results of the HB method and those of the numerical solution of the governing equations indicates a close agreement. Finally, few parameters on the linear and non-linear flutter boundaries and also the amplitude and frequency of the LCO are studied.

Numerical Solution of the Bio-Heat Transfer Equation with Uncertain Parameters Using the Sensitivity Analysis Methods

2017 ◽  
Vol 379 ◽  
pp. 39-47 ◽  
Author(s):  
Bohdan Mochnacki ◽  
Mariusz Ciesielski ◽  
Alicja Piasecka-Belkhayat
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Solution ◽  
Initial Conditions ◽  
Governing Equations ◽  
Interval Numbers ◽  
External Heat Source ◽  
Tissue Heating ◽  
Basic Model ◽  
Heterogeneous Tissue ◽  
The Mathematical Model

In the paper the numerical solution concerning the skin tissue heating in the case of uncertain thermophysical parameters is discussed. The solutions of this type of problems presented previously are based on the application of interval arithmetic. In particular, the parameters appearing in the governing equations and boundary-initial conditions are treated as the interval numbers. Here, the authors propose another approach using for this purpose the methods of sensitivity analysis. The mathematical model of the process concerns the heterogeneous tissue domain subjected to an external heat source. At the stage of numerical modeling both the basic model and the sensitivity ones are solved using the finite difference method. In the final part of the paper, a computational example is presented.

Large Deformation Analysis for a Cylindrical Hyperelastic Membrane of Rubber-Like Material under Internal Pressure

2001 ◽  
Vol 74 (1) ◽  
pp. 100-115 ◽  
Author(s):  
Xiaoping Guo
Keyword(s):  
Numerical Solution ◽  
Large Deformation ◽  
Initial Guess ◽  
Axisymmetric Deformation ◽  
Deformation Field ◽  
Deformation Analysis ◽  
Lagrangian Formalism ◽  
Equilibrium Path ◽  
Governing Equations ◽  
Deformation Instability

Abstract This work studies the large deformation of a cylindrical hyperelastic membrane circumferentially bonded and sealed at each end to a rigid tube. The membrane is subjected to the delivery of an inflating fluid through the tubular channel, causing it to undergo the large, quasi-static axisymmetric deformation. The membrane is made from a rubberlike material and assumed to be isotropic and incompressible. The Lagrangian formalism is employed to develop geometric relations of the deformation field and the system of governing equations in terms of principal stretches and Cauchy stresses. With the material's constitutive laws and proper boundary conditions, the incorporation of the geometric relations and governing equations is made to derive the numerical solution system of the deformation field in the form of two-point boundary-value problem as composed of four first-order ordinary differential equations. Special attention is given to relevant numerical formulation. The Newton-Raphson iterative algorithm, together with the fourth-order Runge—Kutta algorithm, is utilized. A geometric approximation on an inflated bulge is presented to give an initial guess to a deformed membrane profile. In an attempt to obtain convergent behavior of numerical solution along the equilibrium path of deformation, a displacement control strategy is suggested to mimic the quasi-static volume-controlled inflation process. Numerical results are presented. The occurrence of deformation instability is discussed. The effects of various strain energy density functions on inflation kinematics are analyzed.

Waves From Suddenly Punched Hole in Plate Subjected to Uniaxial Tension Field

1979 ◽  
Vol 46 (4) ◽  
pp. 873-877 ◽  
Author(s):  
J. B. Haddow ◽  
A. Mioduchowski
Keyword(s):  
Numerical Solution ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Finite Time ◽  
Gas Dynamics ◽  
Polar Coordinates ◽  
Governing Equations ◽  
Spatial Variables ◽  
Independent Variables ◽  
Stress Components

The plane-stress unloading waves emanating from a suddenly punched circular hole in a thin plate subjected to a uniform uniaxial tension field are considered. It is assumed that the plate is linearly elastic and that the plugging of the hole takes place over a finite time with the stress components at the circumference of the hole decreasing, linearly with time, to zero. A modification of the method of near characteristics, introduced by Sauer [1], for problems of gas dynamics with two or three spatial variables is used to obtain a numerical solution to the governing equations, which have three independent variables, time and two plane polar coordinates. The numerical results obtained approach those for the well-known statical solution, for a hole in a plate subjected to a tension field [2], as the time after the arrival of the wave front becomes large.

scholarly journals Approximation of H(div) with High-Order Optimal Finite Elements for Pyramids, Prisms and Hexahedra

2013 ◽  
Vol 14 (5) ◽  
pp. 1372-1414 ◽  
Author(s):  
Morgane Bergot ◽  
Marc Duruflé
Keyword(s):  
Finite Elements ◽  
Numerical Solution ◽  
Rate Of Convergence ◽  
Unstructured Meshes ◽  
High Order ◽  
Optimal Rate ◽  
Optimal Convergence ◽  
Optimal Rate Of Convergence ◽  
Hybrid Meshes ◽  
De Rham

AbstractClassical facet elements do not provide an optimal rate of convergence of the numerical solution toward the solution of the exact problem in H(div-norm for general unstructured meshes containing hexahedra and prisms. We propose two new families of high-order elements for hexahedra, triangular prisms and pyramids that recover the optimal convergence. These elements have compatible restrictions with each other, such that they can be used directly on general hybrid meshes. Moreover the H(div) proposed spaces are completing the De Rham diagram with optimal elements previously constructed for H1 and H(curl) approximation. The obtained pyramidal elements are compared theoretically and numerically with other elements of the literature. Eventually, numerical results demonstrate the efficiency of the finite elements constructed.

Inclusion and Misfit Effects in Hydrostatic Tension

1988 ◽  
Vol 55 (2) ◽  
pp. 355-360 ◽  
Author(s):  
Benjamin Wilner
Keyword(s):  
Numerical Solution ◽  
Spherical Particle ◽  
Elastic Constants ◽  
Normal Stresses ◽  
Governing Equations ◽  
Hydrostatic Tension ◽  
Elastic Plastic ◽  
Plastic Matrix ◽  
Matrix Subject

A study of the effect of an elastic spherical particle embedded in an infinite elastic-plastic matrix subject to hydrostatic tension is presented. Two types of particles will be considered: (1) a perfectly fitting inclusion, (2) a misfitting one. A numerical solution is developed to solve the governing equations. Various combinations of elastic constants and power hardening coefficients are studied for different load levels. The analysis is concentrated on the interfacial normal stresses and its dependence on the different parameters.

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