Efficient implementation of anisotropic three dimensional boundary-integral equation stress analysis

1978 ◽  
Vol 12 (9) ◽  
pp. 1383-1397 ◽  
Author(s):  
R. B. Wilson ◽  
T. A. Cruse
Keyword(s):  
Integral Equation ◽  
Stress Analysis ◽  
Boundary Integral Equation ◽  
Three Dimensional ◽  
Efficient Implementation ◽  
Boundary Integral ◽  
Dimensional Boundary

Some boundary integral equation solutions for three-dimensional stress concentration problems

1983 ◽  
Vol 18 (4) ◽  
pp. 207-215 ◽  
Author(s):  
M J Abdul-Mihsein ◽  
R T Fenner
Keyword(s):  
Integral Equation ◽  
Stress Concentration ◽  
Stress Analysis ◽  
Boundary Integral Equation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Circular Cylinders ◽  
Linear Elastic ◽  
Circular Holes ◽  
Stress Concentration Factors

The boundary integral equation (BIE) method for three-dimensional linear, elastic stress analysis is applied to some stress concentration problems associated with transverse circular holes in either hollow or solid circular cylinders subject to axial tension or torsion, also offset-oblique holes in cylinders subject to internal pressure. Satisfactory agreement is obtained with some previously published experimental results, although computed maximum stress concentration factors are generally higher than those obtained experimentally. The BIE method is shown to be a very useful tool for solving three-dimensional problems of engineering stress analysis.

Three-dimensional stress analysis by the boundary integral equation method

1978 ◽  
Vol 13 (4) ◽  
pp. 213-219 ◽  
Author(s):  
C L Tan ◽  
R T Fenner
Keyword(s):  
Integral Equation ◽  
Stress Analysis ◽  
Boundary Integral Equation ◽  
High Surface ◽  
Three Dimensional ◽  
Volume Ratio ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Clear Cut ◽  
Concentration Problem

The principles and development of the boundary integral equation (BIE) method for solving engineering problems are reviewed, with particular emphasis on applications in three-dimensional stress analysis. Its use in problems of this type is illustrated with the aid of three examples, one a classical stress concentration problem, the other two involving cracked components. Compared with a finite-element method, the BIE approach is shown to be capable of being both more accurate and more economical to use in terms of competing resources required and the cost of data preparation. These advantages may, however, be less clear-cut when predictions of stresses and displacements at a large number of points within a component are required, or when the component concerned has a relatively high surface-to-volume ratio.

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.

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