A Variational principle for three-dimensional steady flows of an ideal fluid

1965 ◽  
pp. 1-7
Author(s):  
Vladimir I. Arnold
Keyword(s):  
Variational Principle ◽  
Ideal Fluid ◽  
Three Dimensional ◽  
Steady Flows

STEADY FLOWS OF VISCOUS COMPRESSIBLE FLUIDS IN EXTERIOR DOMAINS UNDER SMALL PERTURBATIONS OF GREAT POTENTIAL FORCES

1993 ◽  
Vol 03 (06) ◽  
pp. 725-757 ◽  
Author(s):  
ANTONÍN NOVOTNÝ
Keyword(s):  
Existence And Uniqueness ◽  
Compressible Flows ◽  
Three Dimensional ◽  
Compressible Fluids ◽  
Steady Flows ◽  
Exterior Domains ◽  
Uniqueness Of Solutions ◽  
Small Perturbations ◽  
Zero Velocity ◽  
Potential Forces

We investigate the steady compressible flows in three-dimensional exterior domains, in R3 and [Formula: see text], under the action of small perturbations of large potential forces and zero velocity at infinity. We prove existence and uniqueness of solutions in L2-spaces, and study their regularity as well as the decay at infinity.

Modified Mixed Variational Principle and the State-Vector Equation for Elastic Bodies and Shells of Revolution

1992 ◽  
Vol 59 (3) ◽  
pp. 587-595 ◽  
Author(s):  
Charles R. Steele ◽  
Yoon Young Kim
Keyword(s):  
Variational Principle ◽  
Equations Of State ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Shells Of Revolution ◽  
Elastic Bodies ◽  
Mixed Variational Principle ◽  
Stress Components ◽  
Independent Variable ◽  
Nonsymmetric Deformation

A modified mixed variational principle is established for a class of problems with one spatial variable as the independent variable. The specific applications are on the three-dimensional deformation of elastic bodies and the nonsymmetric deformation of shells of revolution. The possibly novel feature is the elimination in the variational formulation of the stress components which cannot be prescribed on the boundaries. The result is a form exactly analogous to classical mechanics of a dynamic system, with the equations of state exactly in the form of the canonical equations of Hamilton. With the present approach, the correct scale factors of the field variables to make the system self-adjoint are readily identified, and anisotropic materials including composites can be handled effectively. The analysis for shells of revolution is given with and without the transverse shear deformation considered.

A Numerical Three-Dimensional Model for the Contact of Rough Surfaces by Variational Principle

1996 ◽  
Vol 118 (1) ◽  
pp. 33-42 ◽  
Author(s):  
Xuefeng Tian ◽  
Bharat Bhushan
Keyword(s):  
Variational Principle ◽  
Contact Problem ◽  
Rough Surfaces ◽  
Three Dimensional ◽  
Computation Time ◽  
Inversion Method ◽  
Three Dimensional Model ◽  
Perfectly Plastic ◽  
Contact Points ◽  
Uniqueness Of The Solution

A new numerical method for the analysis of elastic and elastic-plastic contacts of two rough surfaces has been developed. The method is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. The present variational approach guarantees the uniqueness of the solution of the contact problem and significantly reduces the computation time as compared with the conventional matrix inversion method, and thus, makes it feasible to solve 3-D contact problem with large number of contact points. The model is extended to elastic-perfectly plastic contacts. The model is used to predict contact statistics for computer generated surfaces.

Inflammatory Response of Endothelial Cells to Wall Shear Stress in Three Dimensional Stenotic Models

2009 ◽  
Author(s):  
Leonie Rouleau ◽  
Joanna Rossi ◽  
Jean-Claude Tardif ◽  
Rosaire Mongrain ◽  
Richard L. Leask
Keyword(s):  
Endothelial Cells ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Three Dimensional ◽  
Realistic Model ◽  
In Vitro Models ◽  
Steady Flows ◽  
Wall Shear

Endothelial cells (ECs) are believed to respond differentially to hemodynamic forces in the vascular tree. Once atherosclerotic plaque has formed in a vessel, the obstruction creates complex spatial gradients in wall shear stress (WSS). In vitro models have used mostly unrealistic and simplified geometries, which cannot reproduce accurately physiological conditions. The objective of this study was to expose ECs to the complex WSS pattern created by an asymmetric stenosis. Endothelial cells were grown and exposed for different times to physiological steady flows in straight dynamic controls and in idealized asymmetric stenosis models. Cell morphology was noticeably different in the regions with spatial WSS gradients, being more randomly oriented and of cobblestone shape. Inflammatory molecule expression was also altered by exposure to shear and endothelial nitric oxide synthase (eNOS) was upregulated by its presence. A regional response in terms of inflammation was observed through confocal microscopy. This work provides a more realistic model to study endothelial cell response to spatial and temporal WSS gradients that are present in vivo and is an important advancement towards a better understanding of the mechanisms involved in coronary artery disease.

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