Three-Dimensional Axisymmetric Elastic Stresses in Intersections of Hollow Sphere and Cylinders (Torsion, Tension and Internal Pressure)

1989 ◽  
Vol 111 (3) ◽  
pp. 218-224
Author(s):  
M. Kishida ◽  
K. Sasaki ◽  
M. Kawano
Keyword(s):  
Internal Pressure ◽  
Hollow Sphere ◽  
Integral Method ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Diameter Ratio ◽  
Boundary Integral Method ◽  
Elastic Stresses ◽  
Photoelastic Experiment ◽  
The Mean

The three-dimensional axisymmetric elastic stresses in the intersections of hollow sphere and cylinders, subjected to torsion, tension and internal pressure, is analyzed easily and accurately by use of the indirect fictitious-boundary integral method. As a result, the influence of configuration parameters (e.g., the mean diameter ratio and the thickness ratio of hollow sphere and cylinder, and the roundness of a corner of intersection) on stress concentration is made clear. Furthermore, the other results, such as one obtained by photoelastic experiment, are evaluated by the present results.

scholarly journals A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

2017 ◽  
Vol 836 ◽  
pp. 952-997 ◽  
Author(s):  
Achim Guckenberger ◽  
Stephan Gekle
Keyword(s):  
Drug Delivery ◽  
Integral Equation ◽  
Boundary Integral Equation ◽  
Integral Method ◽  
Three Dimensional ◽  
Formal Proof ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Drug Uptake ◽  
Periodic Domains

A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date. In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

A Variational Boundary Integral Method for the Analysis of Three-Dimensional Cracks of Arbitrary Geometry in Anisotropic Elastic Solids

1999 ◽  
Vol 67 (2) ◽  
pp. 403-408 ◽  
Author(s):  
G. Xu
Keyword(s):  
Integral Method ◽  
Three Dimensional ◽  
Continuous Distribution ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Symmetric System ◽  
Dislocation Loops ◽  
Elastic Solids ◽  
Arbitrary Geometry ◽  
Anisotropic Elastic

A variational boundary integral method is developed for the analysis of three-dimensional cracks of arbitrary geometry in general anisotropic elastic solids. The crack is modeled as a continuous distribution of dislocation loops. The elastic energy of the solid is obtained from the known expression of the interaction energy of a pair of dislocation loops. The crack-opening displacements, which are related to the geometry of loops and their Burgers vectors, are then determined by minimizing the corresponding potential energy of the solid. In contrast to previous methods, this approach results in the symmetric system of equations with milder singularities of the type 1/R, which facilitate their numerical treatment. By employing six-noded triangular elements and displacing midside nodes to quarter-point positions, the opening profile near the front is endowed with the accurate asymptotic behavior. This enables the direct computation of stress intensity factors from the opening displacements. The performance of the method is assessed by the analysis of an elliptical crack in the transversely isotropic solid. It also illustrates that the conventional average schemes of elastic constants furnish quite inaccurate results when the material is significantly anisotropic. [S0021-8936(00)02702-1]

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