scholarly journals Finite Element Analysis of Biot’s Consolidation with a Coupled Nonlinear Flow Model

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Yue-bao Deng ◽  
Gan-bin Liu ◽  
Rong-yue Zheng ◽  
Kang-he Xie
Keyword(s):  
Finite Element ◽  
Flow Model ◽  
Numerical Solutions ◽  
Continuity Condition ◽  
Nonlinear Flow ◽  
Weighted Residual Method ◽  
Element Analysis ◽  
Vertical Drains ◽  
Soil Skeleton ◽  
Force Equilibrium

A nonlinear flow relationship, which assumes that the fluid flow in the soil skeleton obeys the Hansbo non-Darcian flow and that the coefficient of permeability changes with void ratio, was incorporated into Biot’s general consolidation theory for a consolidation simulation of normally consolidated soft ground with or without vertical drains. The governing equations with the coupled nonlinear flow model were presented first for the force equilibrium condition and then for the continuity condition. Based on the weighted residual method, the finite element (FE) formulations were then derived, and an existing FE program was modified accordingly to take the nonlinear flow model into consideration. Comparative analyses using established theoretical solutions and numerical solutions were completed, and the results were satisfactory. On this basis, we investigated the effect of the coupled nonlinear flow on consolidation development.

scholarly journals Analytical and numerical solutions for a single vertical drain including the effects of vacuum preloading

2005 ◽  
Vol 42 (4) ◽  
pp. 994-1014 ◽  
Author(s):  
Buddhima Indraratna ◽  
Cholachat Rujikiatkamjorn ◽  
Iyathurai Sathananthan
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Numerical Solutions ◽  
Soft Clay ◽  
Vacuum Pressure ◽  
Excess Pore Pressure ◽  
Soil Consolidation ◽  
Vacuum Preloading ◽  
Element Analysis ◽  
Vertical Drains

A system of vertical drains combined with vacuum preloading is an effective method to accelerate soil consolidation by promoting radial flow. This study presents the analytical modeling of vertical drains incorporating vacuum preloading in both axisymmetric and plane strain conditions. The effectiveness of the applied vacuum pressure along the drain length is considered. The exact solutions applied on the basis of the unit cell theory are supported by finite element analysis using ABAQUS software. Subsequently, the details of an appropriate matching procedure by transforming permeability and vacuum pressure between axisymmetric and equivalent plane strain conditions are described through analytical and numerical schemes. The effects of the magnitude and distribution of vacuum pressure on soft clay consolidation are examined through average excess pore pressure, consolidation settlement, and time analyses. Lastly, the practical implications of this study are discussed.Key words: consolidation, finite element method, soft clay, vacuum preloading, vertical drains.

An Axisymmetric Single-Path Model for Gas Transport in the Conducting Airways

2005 ◽  
Vol 128 (1) ◽  
pp. 69-75 ◽  
Author(s):  
Srinath Madasu ◽  
Ali Borhan ◽  
James S. Ultman
Keyword(s):  
Finite Element ◽  
Numerical Solutions ◽  
Diffusion Processes ◽  
Path Model ◽  
Navier Stokes ◽  
Straight Tube ◽  
Element Analysis ◽  
Continuity Equations ◽  
Longitudinal Position ◽  
Single Path

In conventional one-dimensional single-path models, radially averaged concentration is calculated as a function of time and longitudinal position in the lungs, and coupled convection and diffusion are accounted for with a dispersion coefficient. The axisymmetric single-path model developed in this paper is a two-dimensional model that incorporates convective-diffusion processes in a more fundamental manner by simultaneously solving the Navier-Stokes and continuity equations with the convection-diffusion equation. A single airway path was represented by a series of straight tube segments interconnected by leaky transition regions that provide for flow loss at the airway bifurcations. As a sample application, the model equations were solved by a finite element method to predict the unsteady state dispersion of an inhaled pulse of inert gas along an airway path having dimensions consistent with Weibel’s symmetric airway geometry. Assuming steady, incompressible, and laminar flow, a finite element analysis was used to solve for the axisymmetric pressure, velocity and concentration fields. The dispersion calculated from these numerical solutions exhibited good qualitative agreement with the experimental values, but quantitatively was in error by 20%–30% due to the assumption of axial symmetry and the inability of the model to capture the complex recirculatory flows near bifurcations.

scholarly journals Dynamic Finite Element Analysis of Bending-Torsion Coupled Beams Subjected to Combined Axial Load and End Moment

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Mir Tahmaseb Kashani ◽  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Nonlinear Eigenvalue Problem ◽  
Analytical Data ◽  
Compressive Force ◽  
Weighted Residual Method ◽  
Element Analysis ◽  
Closed Form Solutions ◽  
Dynamic Finite Element ◽  
Coupled Beams

The dynamic analysis of prestressed, bending-torsion coupled beams is revisited. The axially loaded beam is assumed to be slender, isotropic, homogeneous, and linearly elastic, exhibiting coupled flexural-torsional displacement caused by the end moment. Based on the Euler-Bernoulli bending and St. Venant torsion beam theories, the vibration and stability of such beams are explored. Using the closed-form solutions of the uncoupled portions of the governing equations as the basis functions of approximation space, the dynamic, frequency-dependent, interpolation functions are developed, which are then used in conjunction with the weighted residual method to develop the Dynamic Finite Element (DFE) of the system. Having implemented the DFE in a MATLAB-based code, the resulting nonlinear eigenvalue problem is then solved to determine the coupled natural frequencies of illustrative beam examples, subjected to various boundary and load conditions. The proposed method is validated against limited available experimental and analytical data, those obtained from an in-house conventional Finite Element Method (FEM) code and FEM-based commercial software (ANSYS). In comparison with FEM, the DFE exhibits higher convergence rates and in the absence of end moment it produces exact results. Buckling analysis is also carried out to determine the critical end moment and compressive force for various load combinations.

Thermo-Mechanical Stress near Apex of a Bi-Material Wedge by a Novel Finite Element Analysis

2012 ◽  
Vol 525-526 ◽  
pp. 93-96
Author(s):  
Xue Cheng Ping ◽  
Lin Leng ◽  
Si Hai Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Elements ◽  
Mechanical Stress ◽  
Displacement Field ◽  
Thermal Loading ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Element Analysis

A super wedge tip element for application to a bi-material wedge is develop utilizing the thermo-mechanical stress and displacement field solutions in which the singular parts are numerical solutions. Singular stresses near apex of an arbitrary bi-material wedge under mechanical and thermal loading can be obtained from the coupling between the super wedge tip element and conventional finite elements. The validity of this novel finite element method is established through existing asymptotic solutions and conventional detailed finite element analysis.

THE SCALED BOUNDARY FINITE ELEMENT ANALYSIS OF SEEPAGE PROBLEMS IN MULTI-MATERIAL REGIONS

2012 ◽  
Vol 09 (01) ◽  
pp. 1240008 ◽  
Author(s):  
FENGZHI LI ◽  
QIANG TU
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Numerical Solutions ◽  
Data Preparation ◽  
Element Analysis ◽  
Satisfactory Accuracy ◽  
Analytical Results ◽  
Scaled Boundary Finite Element ◽  
Element Method

The scaled boundary finite element method (SBFEM) is used to solve the seepage problems with multi-material regions. Two models of dam base with waterproof screen and dam body with the regions of two materials are established. The numerical solutions are obtained and then compared with the analytical results or numerical solutions in the references. The conclusion shows that the SBFEM has more satisfactory accuracy and less data preparation amount.

scholarly journals A COMBINED STRAIN ELEMENT TO FUNCTIONALLY GRADED STRUCTURES IN THERMAL ENVIRONMENT

2020 ◽  
Vol 60 (6) ◽  
Author(s):  
Hoang Lan Ton-That
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Deformation Theory ◽  
Numerical Solutions ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Element Analysis ◽  
First Order ◽  
Graded Structures

Functionally graded materials are commonly used in a thermal environment to change the properties of constituent materials. They inherently withstand high temperature gradients due to a low thermal conductivity, core ductility, low thermal expansion coefficient, and many others. It is essential to thoroughly study mechanical responses of them and to develop new effective approaches for an accurate prediction of solutions. In this paper, a new four-node quadrilateral element based on a combined strain strategy and first-order shear deformation theory is presented to achieve the behaviour of functionally graded plate/shell structures in a thermal environment. The main notion of the combined strain strategy is based on the combination of the membrane strain and the shear strain related to tying points as well as bending strain with respect to a cell-based smoothed finite element method. Due to the finite element analysis, the first-order shear deformation theory (FSDT) is simple to implement and apply for structures, but the shear correction factors are used to achieve the accuracy of solutions. The author assumes that the temperature distribution is uniform throughout the structure. The rule of mixtures is also considered to describe the variation of material compositions across the thickness. Many desirable characteristics and the enforcement of this element are verified and proved through various numerical examples. Numerical solutions and a comparison with other available solutions suggest that the procedure based on this new combined strain element is accurate and efficient.

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