Minimizing stress concentrations around an elliptical hole by concentrated forces acting on the uniaxially loaded plate

When concentrated forces are applied at any points of the outer region of an ellipse in an infinite plate, the complex potentials are determined using the conformal mapping method and Cauchy＇s integral formula. And then, based on the superposition principle, the analyt- ical solutions for stress around an elliptical hole in an infinite plate subjected to a uniform far-field stress and concentrated forces, are obtained. Tangential stress concentration will occur on the hole boundary when only far-field uniform loads are applied. When concen- trated forces are applied in the reversed directions of the uniform loads, tangential stress concentration on the hole boundary can be released significantly. In order to minimize the tangential stress concentration, we need to determine the optimum positions and values of the concentrated forces. Three different optimization methods are applied to achieve this aim. The results show that the tangential stress can be released significantly when the op- timized concentrated forces are applied.

Analyzing Multiple Phenotypes Based on Principal Component Analysis

Joint analysis of multiple phenotypes can have better interpretation of complex diseases and increase statistical power to detect more significant single nucleotide polymorphisms(SNPs)compare to traditional single phenotype analysis in genome-wide association analysis.Principle component analysis(PCA),as a popular dimension reduction method,has been broadly used in the analysis of multiple phenotypes.Since PCA transforms the original phenotypes into principal components(PCs),it is natural to think that by analyzing these PCs,we can combine information across phenotypes.Existing PCA-based methods can be divided into two categories,either selecting one particular PC manually or combining information from all PCs.In this paper,we propose an adaptive principle component test(APCT)which selects and combines the PCs adaptively by using Cauchy combination method.Our proposed method can be seen as a generalization of traditional PCA based method since it contains two existing methods as special situation.Extensive simulation shows that our method is robust and can generate powerful result in various situations.The real data analysis of stock mice data also demonstrate that our proposed APCT can identify significant SNPs that are missed by traditional methods.