The Fatigue Life of Plan Coil Spring Forecasts Based on Potential Boundary Element

2012 ◽  
Vol 472-475 ◽  
pp. 2952-2957
Author(s):  
Jin Yue Tian ◽  
Fa Yong Nie ◽  
Li Dong Chen
Keyword(s):  
Integral Equation ◽  
Fatigue Life ◽  
Potential Problem ◽  
Three Dimensional ◽  
Coefficient Matrix ◽  
Boundary Integral ◽  
Coil Spring ◽  
Cauchy Integral ◽  
Cauchy Principal ◽  
Logarithmic Integral

The stress distribution of structure in plan coil spring usually is three dimensional. The singularities of Cauchy principal integral and logarithmic integral during calculating the elements of the coefficient matrix are studied respectively so that the singularity of Cauchy integral is eliminated in this paper, which is based on boundary integral equation in axisymmetric potential problem. Moreover, the order of singularity in logarithmic integral is reduced. Comparison between the results deduced here and the analytical solutions shows that the present derivation is correct and the algorithm is efficient as well.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document