General quantitative analysis of stress partitioning and boundary conditions in undrained biphasic porous media via a purely macroscopic and purely variational approach

2015 ◽  
Vol 28 (1-2) ◽  
pp. 235-261 ◽  
Author(s):  
Roberto Serpieri ◽  
Francesco Travascio
Keyword(s):  
Porous Media ◽  
Quantitative Analysis ◽  
Boundary Conditions ◽  
Variational Approach ◽  
Stress Partitioning

Unsteady and porous media flow of reactive non-Newtonian fluids subjected to buoyancy and suction/injection

2015 ◽  
Vol 25 (7) ◽  
pp. 1682-1704 ◽  
Author(s):  
Tirivanhu Chinyoka ◽  
Daniel Oluwole Makinde
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Boundary Conditions ◽  
Flow Velocity ◽  
Flow System ◽  
Finite Difference Methods ◽  
Porous Media Flow ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Content Type

Purpose – The purpose of this paper is to examine the unsteady pressure-driven flow of a reactive third-grade non-Newtonian fluid in a channel filled with a porous medium. The flow is subjected to buoyancy, suction/injection asymmetrical and convective boundary conditions. Design/methodology/approach – The authors assume that exothermic chemical reactions take place within the flow system and that the asymmetric convective heat exchange with the ambient at the surfaces follow Newton’s law of cooling. The authors also assume unidirectional suction injection flow of uniform strength across the channel. The flow system is modeled via coupled non-linear partial differential equations derived from conservation laws of physics. The flow velocity and temperature are obtained by solving the governing equations numerically using semi-implicit finite difference methods. Findings – The authors present the results graphically and draw qualitative and quantitative observations and conclusions with respect to various parameters embedded in the problem. In particular the authors make observations regarding the effects of bouyancy, convective boundary conditions, suction/injection, non-Newtonian character and reaction strength on the flow velocity, temperature, wall shear stress and wall heat transfer. Originality/value – The combined fluid dynamical, porous media and heat transfer effects investigated in this paper have to the authors’ knowledge not been studied. Such fluid dynamical problems find important application in petroleum recovery.

A Variational Approach to Loaded Ply Structures

2003 ◽  
Vol 9 (1-2) ◽  
pp. 175-185 ◽  
Author(s):  
G. H.M. Van Der Heijden ◽  
J. M.T. Thompson ◽  
S. Neukirch
Keyword(s):  
Boundary Conditions ◽  
Energy Method ◽  
Variational Approach ◽  
Energy Analysis ◽  
Numerical Results ◽  
Equilibrium Equations

We show how an energy analysis can be used to derive the equilibrium equations and boundary conditions for an end-loaded variable ply much more efficiently than in previous works. Numerical results are then presented for a clamped balanced ply approaching lock-up. We also use the energy method to derive the equations for a more general ply made of imperfect anisotropic rods and we briefly consider their helical solutions.

scholarly journals Antiperiodic Solutions forp-Laplacian Systems via Variational Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lifang Niu ◽  
Kaimin Teng
Keyword(s):  
Boundary Conditions ◽  
Variational Methods ◽  
Variational Approach ◽  
Existence Of Solutions

We establish the existence of solutions forp-Laplacian systems with antiperiodic boundary conditions through using variational methods.

Comments on “Lamb's problem for fluid-saturated porous media”

1992 ◽  
Vol 82 (5) ◽  
pp. 2263-2273
Author(s):  
M. D. Sharma
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Elastic Solid ◽  
Porous Solid ◽  
Surface Boundary ◽  
Vertical Force ◽  
Saturated Porous Media ◽  
Concentrated Load ◽  
Lamb’S Problem

Abstract Philippacopoulos (1988) discusses axisymmetric wave propagation in a fluid-saturated porous solid half-space. The disturbance is considered to be produced by the concentrated load P0exp(iωt) acting vertically at the surface. Boundary conditions chosen imply that a vertical force acting on the surface of fluid-saturated porous solid exerts no pressure on the interstitial liquid. These boundary conditions do not seem appropriate. In the present study, the boundary conditions have been changed in order to satisfy the concept of porosity. These are also in accordance with those discussed by Deresiewicz and Skalak (1963) for the special case of interface between liquid and liquid-saturated porous media. Analytic expressions have been derived for the displacements at the surface. The limiting case of a dry elastic solid is also deduced. Effects of intergranular energy losses due to solid phase and of dissipation due to flow of pore fluid are exhibited on the displacements at the surface. Contrary to Philippacopoulos (1988), the displacements in saturated poroelastic solids are found to be larger than those in a dry elastic solid with same Lamb's moduli.

scholarly journals Free Vibration Analysis of Curved Laminated Composite Beams with Different Shapes, Lamination Schemes, and Boundary Conditions

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 1010 ◽  
Author(s):  
Bin Qin ◽  
Xing Zhao ◽  
Huifang Liu ◽  
Yongge Yu ◽  
Qingshan Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Variational Approach ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Beams ◽  
Arbitrary Boundary ◽  
Correlated Parameters ◽  
Laminated Composite Beams

A general formulation is considered for the free vibration of curved laminated composite beams (CLCBs) with alterable curvatures and diverse boundary restraints. In accordance with higher-order shear deformation theory (HSDT), an improved variational approach is introduced for the numerical modeling. Besides, the multi-segment partitioning strategy is exploited for the derivation of motion equations, where the CLCBs are separated into several segments. Penalty parameters are considered to handle the arbitrary boundary conditions. The admissible functions of each separated beam segment are expanded in terms of Jacobi polynomials. The solutions are achieved through the variational approach. The proposed methodology can deal with arbitrary boundary restraints in a unified way by conveniently changing correlated parameters without interfering with the solution procedure.

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