Showing papers on "Shell balance published in 1997"

Interstitial fluid flow in tendons or ligaments: A porous medium finite element simulation

Abstract: The purpose of this study is to describe interstitial fluid flow in axisymmetric soft connective tissue (ligaments or tendons) when they are loaded in tension. Soft hydrated tissue was modelled as a porous medium (using Darcy's Law), and the finite element method was used to solve the resulting equations governing fluid flow. A commercially available computer program (FiDAP) was used to create an axisymmetric model of a biomechanically tested rat ligament. The unknown variables at element nodes were pressure and velocity of the interstitial fluid (Newtonian and incompressible). The effect of variations in fluid viscosity and permeability of the solid matrix was parametrically explored. A transient loading state mimicking a rat ligament mechanical experiment was used in all simulations. The magnitude and distribution of pressure, stream lines, shear (stress) rate, vorticity and velocity showed regular patterns consistent with extension flow. Parametric changes of permeability and viscosity strongly affected fluid flow behaviour. When the radial permeability was 1000 times less than the axial permeability, shear rate and vorticity increased (approximately 5-fold). These effects (especially shear stress and pressure) suggested a strong interaction with the solid matrix. Computed levels of fluid flow suggested a possible load transduction mechanism for cells in the tissue.

Theorie geometriquement exacte des coques en rotations finies et son implantation elements finis

Abstract: In this article, we review the significant progress on shell problem theoretical foundation and numerical implementation attained over a period of the last several years. First, a careful consideration of the three-dimensional finite rotations is given including the choice of optimal parameters, their admissible variations and the much revealing relationship between different parameters. A non-conventional derivation of the stress resultant shell theory is presented, which makes use of thevirtual work principle and local Cartesian frames. The presented derivation introduces no simplifying hypotheses regarding the shell balance equations, hence the resulting shell theory is referred to being the geometrically exact. The strain measures energy-conjugate to the chosen stress resultants are identified and the nature of the stress resultants with respect to the three-dimensional stress tensor is explained along with the resulting constitutive restrictions. Comments are made regarding a rather useful extension of the shell theory which accounts for the rotational degree of freedom about the director, the so-called drilling rotation. A linear shell theory is obtained as a very useful byproduct of the present work, by linearizing the present nonlinear shell theory about the reference configuration. It is shown that this non-conventional approach not only clarifies an often confusing derivation of the linear shell theory, but also leads to a novel linear shell theory capable of delivering significantly improved results and essentially exact solutions to the standard linear benchmark problems. Another important aspect of the nonlinear shell problem solution, the finite element approximation of the shell theory, is also discussed. The model problem of assumed shear strain interpolation is used to illustrate that numerical implementation which preserves the salient features of the theoretical formulation often brings an improved final result. For the selected rotation parameterization and the finite element interpolation, the issues of the consistent linearization of the nonlinear shell problem are addressed. In a number of numerical simulations, the latter is proved to play a crucial role not only in ensuring the robust performance of the Newton solution procedure, but also in linear and nonlinear buckling problems of shells. Several directions for future research are pointed out and some contemporary works of special interest are listed.