scholarly journals Horizontal Vibrations of Embedded Foundation in Multi-Layered Poroelastic Soils

2019 ◽  
Vol 5 (2) ◽  
pp. 179 ◽  
Author(s):  
Teerapong Senjuntichai
Keyword(s):  
Poroelastic Media ◽  
Soil Systems ◽  
Time Harmonic ◽  
Present Solution ◽  
Supporting Soil ◽  
Poroelastic Material ◽  
Discretization Technique ◽  
Matrix Scheme ◽  
Exact Stiffness Matrix ◽  
Interaction Problem

In this paper, the dynamic response of rigid foundations of arbitrary shape embedded in multi-layered poroelastic soils subjected to time-harmonic horizontal loading is presented. The soil-structure interaction problem is investigated by employing a discretization technique and flexibility equations based on the influence functions obtained from an exact stiffness matrix scheme. The present solution scheme is verified with relevant existing solutions of rigid foundations on homogeneous elastic and poroelastic media. A selected set of numerical results are illustrated to portray the influence of various parameters, namely, frequency of excitation, poroelastic material parameters, foundation shapes, embedded depth, and the supporting soil systems, on non-dimensional horizontal compliances of rigid foundations.

scholarly journals Unequal order T-spline meshes for fracture in poroelastic media

2021 ◽  
Vol 37 ◽  
pp. 669-679
Author(s):  
Tim Hageman ◽  
René de Borst
Keyword(s):  
Degrees Of Freedom ◽  
Fluid Transport ◽  
Crack Tip ◽  
Fracture Aperture ◽  
Closed Fracture ◽  
Order Continuity ◽  
Poroelastic Media ◽  
Minimum Number ◽  
Poroelastic Material ◽  
Spurious Oscillations

Abstract Spline-based meshes allow for a higher inter-element continuity. For coupled problems, e.g. poroelasticity, different meshes with different orders of interpolation are normally used for the various fields in order to avoid spurious oscillations. When including discontinuities in these meshes, there exist several options for the discretisation. Herein we will discuss two options which use T-splines, one aiming at a minimum number of degrees of freedom around the crack tip, the other trying to maximise this number. Both meshes retain a higher-order continuity along the fracture, but the mesh which maximises the number of degrees of freedom mesh introduces two additional degrees of freedom around the crack tip to allow for a sharper crack. The two discretisations are used to simulate a pressurised fracture inside a poroelastic material and the results are compared to results obtained using a Non-Uniform Rational B-Spline (NURBS) mesh. A comparison between the two discretisations shows the effect of including additional degrees of freedom close to the crack tip. However, both meshes yield similar results further away from the crack tip. It is shown that both T-spline meshes capture a fully closed discontinuity at the fracture tip, whereas the NURBS mesh retains a small opening due to the discontinuity which exists for the cracked as well as the intact elements. A fully closed fracture aperture results in T-splines with a lower discontinuity pressure compared to NURBS, making T-splines more suitable for simulations in which the fracture propagation is limited by the fluid transport within the fracture.

ANALYSIS AND FINITE ELEMENT METHODS FOR A FLUID-SOLID INTERACTION PROBLEM IN ONE DIMENSION

1996 ◽  
Vol 06 (08) ◽  
pp. 1119-1141 ◽  
Author(s):  
CH. MAKRIDAKIS ◽  
F. IHLENBURG ◽  
I. BABUŠKA
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Model Problem ◽  
Type System ◽  
Interaction Model ◽  
One Dimension ◽  
Regularity Properties ◽  
Time Harmonic ◽  
Fluid Solid Interaction ◽  
Interaction Problem

In this paper we study a time-harmonic fluid-solid interaction model problem in one dimension. This is a Helmholtz-type system equipped with boundary and transmission conditions. We show the existence of a unique solution to this problem and study its stability and regularity properties. We analyze the convergence of finite element methods with respect to appropriate energy norms. Computational results are also presented.

Dynamic Response of a Poroelastic Half-Space with Semi-Permeable Surface Subjected to Time-Harmonic Vertical Load

2012 ◽  
Vol 594-597 ◽  
pp. 2757-2762 ◽  
Author(s):  
Xi Luo ◽  
Xian Wei Zeng ◽  
Li Qun Tang
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Dynamic Response ◽  
Half Space ◽  
Governing Equation ◽  
Integral Transform ◽  
Numerical Results ◽  
Vertical Load ◽  
Poroelastic Media ◽  
Time Harmonic

Based on Biot’s elastodynamic theory for poroelastic media, the dynamic response of a poroelastic half-space due to a time-harmonic concentrated vertical load applied at the free surface is investigated. Different from previous treatments of the free surface as either fully permeable or fully impermeable, the free surface of a pororelastic half-space is treated in this study as a more realistic semi-permeable boundary condition, i.e. the permeability of the free surface is considered. The governing equation for axisymmetric motion of a poroelastic half-space is solved by applying the Hankel integral transform. Numerical results are presented to show the effects of semi-permeable boundary condition on the dynamic response of poroelastic half-space.

LOW-FREQUENCY APPROXIMATIONS FOR ACOUSTIC POROUS MATERIALS: LINEARISATION OF THE POROELASTIC EIGENVALUE PROBLEM

1997 ◽  
Vol 21 (4) ◽  
pp. 401-413 ◽  
Author(s):  
R. Panneton ◽  
N. Atalla
Keyword(s):  
Finite Element ◽  
Eigenvalue Problem ◽  
Porous Materials ◽  
Acoustic Waves ◽  
Low Frequency ◽  
Poroelastic Media ◽  
Linear Eigenvalue Problem ◽  
Non Linear ◽  
Frequency Independent ◽  
Poroelastic Material

Recently in acoustics, it was shown that a finite element discretisation of Biot’s dynamic equations — for poroelastic media — leads to a non-linear eigenvalue problem. This non-linearity comes from the complex dissipation mechanisms of the elastic and acoustic waves prevailing within the poroelastic material. These complex dissipation mechanisms are related to viscous and thermal effects. The main drawback of the non-linear eigenvalue problem is that it prevents the use of classical modal analysis techniques for efficient solution of the corresponding matrix system. Since the finite element method is mostly used at low-freuqencies, the objective of this paper is to derive low-frequency approximations on the viscous and thermal disssipation mechanisms that will be used to linearise the poroelastic eigenvalue problem. To achieve the linearisation, it will be shown that the first Lamé coefficient of the poroelastic medium can be considered frequency-independent for most acoustic porous materials.

Interactive Graphics for the Analysis of Tires

1985 ◽  
Vol 13 (3) ◽  
pp. 127-146 ◽  
Author(s):  
R. Prabhakaran
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Approximate Solutions ◽  
Interactive Graphics ◽  
Element Analysis ◽  
Analysis Process ◽  
Physical Problems ◽  
The Finite Element Analysis ◽  
Analysis Computer ◽  
Discretization Technique

Abstract The finite element method, which is a numerical discretization technique for obtaining approximate solutions to complex physical problems, is accepted in many industries as the primary tool for structural analysis. Computer graphics is an essential ingredient of the finite element analysis process. The use of interactive graphics techniques for analysis of tires is discussed in this presentation. The features and capabilities of the program used for pre- and post-processing for finite element analysis at GenCorp are included.

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