Numerical Simulation of Polymeric Gels

2015 ◽  
Author(s):  
Shawn A. Chester
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Steady State ◽  
Large Deformation ◽  
Governing Equations ◽  
Numerical Examples ◽  
Polymeric Gels ◽  
Finite Element Package ◽  
Fluid Diffusion ◽  
Transient And Steady State

Following [1], a theory for coupled fluid diffusion and large deformation is implemented as a user-element subroutine in the commercial finite element package ABAQUS. The governing equations are summarized along with details of the constitutive theory. A few numerical examples are provided to show the robustness of this methodology in both transient and steady state conditions.

New Mixed Finite Element Formulations for Transient and Steady State Creep Problems

1989 ◽  
Vol 42 (11S) ◽  
pp. S150-S156
Author(s):  
Abimael F. D. Loula ◽  
Joa˜o Nisan C. Guerreiro
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Steady State Creep ◽  
Element Approximation ◽  
New Approach ◽  
Finite Element Approximations ◽  
Transient Problems ◽  
Transient And Steady State

We apply the mixed Petrov–Galerkin formulation to construct finite element approximations for transient and steady-state creep problems. With the new approach we recover stability, convergence, and accuracy of some Galerkin unstable approximations. We also present the main results on the numerical analysis and error estimates of the proposed finite element approximation for the steady problem, and discuss the asymptotic behavior of the continuum and discrete transient problems.

Transient and steady state behaviour of elasto–aerodynamic air foil bearings, considering bump foil compliance and top foil inertia and flexibility: A numerical investigation

2017 ◽  
Vol 231 (10) ◽  
pp. 1235-1253 ◽  
Author(s):  
Bo B. Nielsen ◽  
Ilmar F. Santos
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Elastic Foundation ◽  
Parameter Study ◽  
Finite Element Models ◽  
Foil Bearings ◽  
Aerodynamic Pressure ◽  
Foil Bearing ◽  
Foundation Model ◽  
Transient And Steady State

This work gives a theoretical contribution to the problem of modelling air foil bearings considering large sagging effects in the calculation of the non-linear transient and steady state response of a rigid rotor. This paper consists of two parts: the development of a miltiphysics model of the air foil bearing, and a numerical parameter study of a rigid journal supported in an air foil bearing with a partially supported top foil. The mathematical model of the air foil bearing is centred around the finite element models of both the air film and the top foil structure. These finite element models utilise two types of eight-node isoparametric elements. The rotor is modelled as a rigid body without rotational inertia, i.e. as a journal. The bump foil is included via a bilinear version of the simple elastic foundation model. This paper introduces the bilinear simple elastic foundation model, which combined with the top foil structure model, enables a separation of the top foil and the bump foil. A phenomenon associated within areas of the top foil is where the aerodynamic pressure is sub-ambient. The parameter study investigates the performance of three air foil bearings with partially supported top foils and one air foil bearing with a fully supported top foil. The steady state responses of a journal supported by these air foil bearings are investigated for varied rotational speeds and journal unbalances as well as the top foil sagging in the unsupported area. The study reveals that sub-harmonic vibrations associated with a large journal unbalance can be eliminated by a proper design layout of the bump foil, i.e. placement of the unsupported area. The positive effect is attributed to ‘equivalent shallow pockets’ formed by the sagging top foil.

Transient and Steady-State Dynamic Finite Element Modeling of Belt-Drives

2002 ◽  
Vol 124 (4) ◽  
pp. 575-581 ◽  
Author(s):  
Michael J. Leamy ◽  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Angular Velocity ◽  
Frictional Contact ◽  
Finite Element Solution ◽  
Belt Drive ◽  
Element Solution ◽  
Dynamic Finite Element ◽  
Time Accuracy ◽  
Transient And Steady State

In this study, a dynamic finite element model is developed for pulley belt-drive systems and is employed to determine the transient and steady-state response of a prototypical belt-drive. The belt is modeled using standard truss elements, while the pulleys are modeled using rotating circular constraints, for which the driver pulley’s angular velocity is prescribed. Frictional contact between the pulleys and the belt is modeled using a penalty formulation with frictional contact governed by a Coulomb-like tri-linear friction law. One-way clutch elements are modeled using a proportional torque law supporting torque transmission in a single direction. The dynamic response of the drive is then studied by incorporating the model into an explicit finite element code, which can maintain time-accuracy for large rotations and for long simulation times. The finite element solution is validated through comparison to an exact analytical solution of a steadily-rotating, two-pulley drive. Several response quantities are compared, including the normal and tangential (friction) force distributions between the pulleys and the belt, the driven pulley angular velocity, and the belt span tensions. Excellent agreement is found. Transient response results for a second belt-drive example involving a one-way clutch are used to demonstrate the utility and flexibility of the finite element solution approach.

The Numerical Simulation for Vibroacoustic Phenomena of a Slender Elastic Shell

2012 ◽  
Vol 479-481 ◽  
pp. 1365-1370
Author(s):  
Zhi Xi Yang ◽  
Sheng Hua Qiu
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Thin Shell ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Elastic Shell ◽  
Numerical Examples ◽  
Longitudinal Acoustic ◽  
3 Dimensional ◽  
Variational Formulas

The vibroacoustic phenomena for the slender elastic thin shell filled with water by finite element method is introduced in this paper. The unsymmetric (u, p) variational formulas and finite element procedures are implemented for 3 dimensional structures of vibroacoustic environment based on the displacement field u and the fluid acoustic pressure field p. As illustrated by numerical examples, the longitudinal acoustic pressure eigenmodes will be occurred besides the transverse bendable eigenmodes of the slender shell, nonetheless the eigenvalues and the order of eigenmodes for the fluid acoustic pressure field can only be determined by the flexibility and geometry stiffness of the slender shell.

scholarly journals Modelling of Permeation Grouting Through Soils

2020 ◽  
Vol 10 (1) ◽  
pp. 11-16
Author(s):  
S. B. Coskun ◽  
T. Tokdemir
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Finite Element ◽  
Porous Medium ◽  
Capillary Pressure ◽  
Immiscible Fluids ◽  
Saturated Soils ◽  
Governing Equations ◽  
Permeation Grouting ◽  
Element Technique

AbstractIn this study, mathematical modeling of permeation grouting through fully saturated soil is proposed based on immiscible multiphase flow theory. Grout flow in the medium is modeled together with the existing water as the simultaneous flow of two immiscible fluids. In the model, the porous medium is assumed as isotropic and rigid, fluids are assumed as incompressible and capillary pressure is assumed as negligible. Governing equations are discretized using upstream weighted finite element technique and results show that, proposed models give good results and may be used in the numerical simulation of grouting through fully saturated soils.

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